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This seems to be an age old debate. Which is better? Xd6 vs 1d20? Probabilities  seem to dominate this discussion and it's fair enough. I'd say the biggest advantages are how the probabilities of both options affect the system math. But I wanted to look at it from an aesthetics perspective. I realise this is completely subjective and everyone will speak from their own personal biases and that's fine because I want to hear the reasons. I'm working on a ruleset and I am completely torn on the issue and don't know which way to side to land on.

So which do you find more aesthetically pleasing? Have all rolls be a 1 or more d6 or have multiple dice types with the primary dice being 1d20.

Advantages of Polyhedral Dice
* All D&D fans (and fans of d20 derivatives) are more likely to give your game a chance.
* You can get more granularity with weapon damage rolls as they'll always be some multiple of polyhedral dice. E.g. With polyhedral dice one attack can hit 3 targets for 1d6 each (average is 10.5) while another attack can hit a single target for 2d10 total (average is 11).

Disadvantages of Polyhedral Dice
* Those gamers who hate d20 and refuse to play any games with it won't play your game.
* With new gamers I have seen it time and time again. They take a good session or two to learn which roll uses which dice and if they only play once a month it can take up to 6 months for them to learn it.
* Dice are more expensive for new gamers (which is why attacks that require lots of dice almost always require d6).

Advantages of Using d6s
* Those gamers who hate d20 are more likely to give your game a chance.
* A certain percentage of D&D gamers will be willing to play your game.
* Everyone (including D&D gamers) has some d6s lying around. If they don't it is significantly cheaper to buy a box of them vs enough polyhedral dice that you can always roll them at one time.
* Newbies will always know which type of dice to roll.

Disadvantages of Using d6s
* Those D&D gamers who refuse to play anything that isn't d20 based won't play your game.
* You're limited to damage rolls being separated by intervals of 1d6. You can have a modifier to the damage roll, but is that aesthetically pleasing?

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So what do people think? Is it aesthetically pleasing?

Talking a little about the probabilities. I'll get to damage rolls in another post as I want to run some numbers first. But with skill checks this is where 3d6 may shine.

2d6 Skill Roll
Unskilled (DC 5): Skill Rank 0
Amateur (DC 10): Skill Rank 5
Professional (DC 15): 10
Expert (DC 20):15
Unparralleled (DC 25): 20
Epic (DC 30): 25

All checks have a 72.22% chance of succeeding.

3d6 Skill Roll
Unskilled (DC 5): Skill Rank -2
Amateur (DC 10): Skill Rank 3
Professional (DC 15): 8
Expert (DC 20):13
Unparralleled (DC 25): 18
Epic (DC 30): 23

All checks have an 80% chance of succeeding.

1d20 Skill Roll
Unskilled (DC 5): Skill Rank 0
Amateur (DC 10): Skill Rank 5
Professional (DC 15): 10
Expert (DC 20):15
Unparralleled (DC 25): 20
Epic (DC 30): 25

All checks have a 80% chance of succeeding.

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Why is the lowest DC at DC 5 and then all subsequent categories add +5 to the DC? Because as a GM it's easier for me to remember that the number is going to be around 15 vs 22 or 23. As people we tend to find it easier to jump ahead by lots of 5. I've seen this in D&D 4th edition, Pathfinder and D&D 5th edition. Multiples of 5 are always easier for DMs (IMO).

So in this scenario 2d6 and 1d20 have the same bonuses, although in 2d6 you're 7.78% less likely to succeed. In a d20 game -1 to a skill check isn't really seen as that big a deal and that's how I'm seeing the difference.

The 3d6 roll is the least aesthetically pleasing because it's not in multiples of 5.

The biggest problem I have with the 1d20 roll is that a DC 25, 55% of the time. An expert is meant to be good, but an unparralleled is meant to represent a Babe Routh or Don Bradman. They're a "once in a generation" type of person. They're not meant to be something an expert can do half the time. A way around this is to increase the Unparralleled DC to DC 30 and give an unparralleled person the ability to roll 2d20 and take the best result. According to google this takes the person with a +20 bonus to the check from succeeding 55% of the time to 80% of the time. Mathematically it achieves EXACTLY what I want and reduces the expert's chances to a mere 5% chance of success. However we've skipped DC 25 as being a category and introduced a new mechanic (roll 2d20 and take the best) that has to be given to the player somehow. That decreases the aesthetic beauty of the 1d20 roll.

If we look at 2d6 then they can only get a roll of DC 25 roughly 8% of the time. This means an expert can rarely match an unparalleled person, but really the expert is the pinnacle of mundane human achievement (Heroic tier in D&D 4th ed terminology) while it gives the unparralleled character a 72.22% chance of success without needing to introduce any special mechancis or increasing the DC by +10 instead of +5.

To be perfectly honest I'm inclined to abandon the d20 mechanic in favour of a 2d6 mechanic at this stage. However I'm hesitant simply because d20 is such a well known brand and unifying identity. All d20 games share a lot in common amongst their fans.

What do people think? Are there reasons for going with Xd6 over polyhedral dice that I haven't considered? Are there even more reasons to want to abandon polyhedral dice in favour of d6 that I haven't considered? Which do you find most aesthetically pleasing and why?

I prefer using multiple dice on a core mechanic over any single die but particularly d20. Rolling two or three d6 is much less swingy than a single d20. You tend to get more consistent results with multiple dice.

With 3-D printing becoming more popular, I don't see the cost of dice being much of a problem a few years from now.

In fact, with 3-D printing we may see an explosion in funky dice.
It's very hard now to market a game that uses d7's or d30's just because these dice require expensive online orders to obtain. Within ten years though, we might expect your typical new gamer to have the means to print them.

I think there's three things here: d20 resolution, step dice resolution, and multiple D6. D&D happens to be a hybrid d20/'polyhedra' (step die) system - it switches from one resolution system to the other for damage.
A real D20 system would be something like True20, and a real 'polyhedra' system would be something like Savage Worlds or Cortex.

Quote from: Bloody Stupid Johnson;833631I think there's three things here: d20 resolution, step dice resolution, and multiple D6. D&D happens to be a hybrid d20/'polyhedra' (step die) system - it switches from one resolution system to the other for damage.
A real D20 system would be something like True20, and a real 'polyhedra' system would be something like Savage Worlds or Cortex.

I used to have d14's and d16's (bought a pound of game-science dice).

I think the only thing between us and a d20 step-die resolution mechanic is the absence of d18's.

I prefer bell curves over straight linear distributions, but any XdY is fine by me.  It doesn't have to specifically be Xd6.  Even more than that, I like pool systems where each die is evaluated individually instead of adding them all up.  For purposes of this discussion, I can see how they might also qualify as "XdY", since they involve rolling multiple dice.

System math aside, it's also just plain fun to roll a huge handful of dice every now and then.

Quote from: JohnLynch;833511This seems to be an age old debate. Which is better? Xd6 vs 1d20?

You forgot another major option: d100. I preferences for RPGs from favorite to least favorite go: d100, d20, 2d6, 3d6, dice pools, weird dice (d14, etc.), unique dice (Warhammer Fantasy 3rd edition, etc.).

Quote from: RandallS;833679You forgot another major option: d100. I preferences for RPGs from favorite to least favorite go: d100, d20, 2d6, 3d6, dice pools, weird dice (d14, etc.), unique dice (Warhammer Fantasy 3rd edition, etc.).

I noted that too.

I'd go with d100, xd6 totaled with a wild die, 2d6, (first three are pretty much a time) then, d20, 2d10, 3d6, then pretty much anything else before we get to jenga towers and other weird shit.

The importance of bell curve distribution in die rolls is consistently overrated; what matters far more is the range and variance (in a statistical sense) of results for any given situation (skill level vs difficulty) and a sense of how that changes when the situation changes.

E.g. If all that matters is rolling 11+ it doesn't matter if you're rolling 3d6 or 1d20.

From a purely aesthetic perspective I've observed that non-gamers are fascinated when they see weird dice. So that's a mark in favor.

Against: few types of dice roll as nicely as d6's. They either roll too little (d4, d8) or they don't stop (d12, d20). D10's roll nicely, though.

Quote from: Cave Bear;833667I used to have d14's and d16's (bought a pound of game-science dice).

I think the only thing between us and a d20 step-die resolution mechanic is the absence of d18's.

DCC sort of went there. I can't remember if it actually uses d18s, but I think the 'dice chain' in it goes up to at least d24.

I like 2D6 and D20. I played lots of "handful of D10s" games, but for speed of resolution one or two dice is best.

Quote from: Arminius;833716The importance of bell curve distribution in die rolls is consistently overrated; what matters far more is the range and variance (in a statistical sense) of results for any given situation (skill level vs difficulty) and a sense of how that changes when the situation changes.

E.g. If all that matters is rolling 11+ it doesn't matter if you're rolling 3d6 or 1d20.

Agreed as far as that goes.  However, if you have a +2 modifier on that roll, then it becomes significant whether your distribution is flat or curved.  If you have two characters rolling, one with a base 11+ and the other with a base 6+ and they both have a +2 modifier on that roll, then flat vs. curved distribution is much more significant.

I like bell curves in my dice because they make modifiers more significant in the mid-range or when moving towards the mid-range and less significant as they move things out to the extremes.  You can't really do that with a flat distribution unless you want to break out calculators or lookup tables every time someone makes a roll.

Yup, when modifiers to target numbers come into play, a nonlinear distribution of the dice result can give you diminishing returns if that's what you want.

Quote from: nDervish;833787I like bell curves in my dice because they make modifiers more significant in the mid-range or when moving towards the mid-range and less significant as they move things out to the extremes.

It depends on how you look at it - but isn't it the other way round?

If you need 11+ on 3d6 then that's a 50% chance of failure. A bonus of +2 reduces that failure to only 26%, so you've halved the chance of failure.

On the other hand, if you need only 9+ on 3d6 then that's a 26% chance of failure, and a bonus of +2 reduces that chance of failure to 9%.

If you need 7+ on 3d6 then that's 9% chance failure, and +2 reduces that to 2%.

So in the first case you've halved the chance of failure, in the second case you've reduced it to by two thirds, and in the third case reduced it by almost four fifths.

Quote from: JoeNuttall;835463It depends on how you look at it - but isn't it the other way round?

Yes to the first. No to the second.

It depends on whether you are looking at the change in percentile points or as a ratio. Using your examples.

QuoteIf you need 11+ on 3d6 then that's a 50% chance of failure. A bonus of +2 reduces that failure to only 26%, so you've halved the chance of failure.
The ratio of the change is (50-26)/50 or a 48% decrease, but the change in absolute percentiles is a decrease of 50%-26%=24% points.

On the other hand, if you need only 9+ on 3d6 then that's a 26% chance of failure, and a bonus of +2 reduces that chance of failure to 9%.
The ratio of the change is (26-9)/26 or a 65% decrease, but the change in absolute percentiles is only 26%-9%=17% points.

If you need 7+ on 3d6 then that's 9% chance failure, and +2 reduces that to 2%
The ratio of the change is (9-2)/9 or a 78% decrease, but the change in absolute percentiles is now only 7% points.

So while the ratio of change is increasing the change in the number of percentage points is decreasing from 24 -> 17 -> 7.

Quote from: Bren;835466Yes to the first. No to the second.
It depends on whether you are looking at the change in percentile points or as a ratio.

Indeed it does, but I was referring to Dervish's assertion said that modifiers were

Quote from: nDervish;833787more significant in the mid-range

which they aren't. They are larger (percentage wise), but less significant.

Quote from: JoeNuttall;835515Indeed it does, but I was referring to Dervish's assertion said that modifiers were

which they aren't. They are larger (percentage wise), but less significant.

That depends on what definition of significant you use.

I think a lot of people would agree that saving $50,000 on buying a house is more significant than saving $2 on a latte even if the savings is 20% on the latte but only 10% on the house.

Quote from: Bren;835529I think a lot of people would agree that saving $50,000 on buying a house is more significant than saving $2 on a latte even if the savings is 20% on the latte but only 10% on the house.

I might agree to pay £50,000 more for a house, but I'll never agree to pay £50,000 more for a latte!

Quote from: JoeNuttall;835545I might agree to pay £50,000 more for a house, but I'll never agree to pay £50,000 more for a latte!

I should hope not. ;)

As a rule of thumb, I don't look for RPGs that attempt to reinvent the wheel. You don't need a clever mechanic. My top 3 favorite core mechanics are d100, d20, and d10, in that order.

The reasons I like them? Transparent probabilities. I would like to be easily compute those probabilities in my head. Because ultimately, linear or curve, makes no difference once you account for that one, intractable, ever-present variable that every RPG has (but analysts typically ignore)--the player.

For example, if you need to roll 12 or lower on 3d6, it's roughly the equal probability of having to roll a 15 or lower on d20. Say we're playing a 3d6 system but house-ruling in a d20 instead. All that means is if I, as a player, finds anything higher than a 25% whiff-factor unacceptable for my warrior character, I'm going to spend the extra points on my sword skill to get my score to 15. That's okay, though. Because my lower priority skills I'm fine succeeding only 25% of the time, which I can leave as low as 5 instead of having to buy them up to 8.

I understand some people like how modifiers tend to be big towards the middle, small on the extremes. But this assumes you're limited to just + or - modifiers to difficulty. It's not the only option. Requiring successive rolls are also possible.


And then there's also "degree of success." OD&D had "degree of success." They just called it the damage roll. Hits for 6 damage were more successful than hits for 3 damage. The degree of success has an unmistakable mechanical effect. It didn't apply to all things. Because degree of success doesn't matter in all things. Creatures with high hit points, it matters a lot how hard you hit them because it's going to take multiple hits for sure. If you're walking a tight rope over a chasm, ultimately what we're concerned about is whether you make it to the other side or plunge to your bloody death. What's a critical success going to mean? You were doing cartwheels?

The point of which to say is I try to avoid any mechanic that brings in too clever a "degree of success" system. We always have and always will be able to do that, when it's called for, by adding in a second die roll. Just like the damage die. I'm fine with critical hits that do something functionally different that the die roll can't do. Double damage? Sure. That means the attack may possible do damage above and beyond it's normal range. Bypassing armor in an armor absorb system? Awesome!

Especially for the "I love curve mechanic crowd," have you ever tried to graph the probability/effect distribution for degree of success roll on a given hit? The shape of that curve varies wildly depending on where on the core mechanic roll the target number for basic success was. Wouldn't it be better to just roll a fresh new die or dice so you can set the probability distribution of degrees of success exactly to match your aesthetic taste?


In essence, the beauty of successive dice rolls is that they can perform mathematical functions of multiplication and division without ever calling upon the math illiterates sitting around your table to have to make such calculations. Hands down, the most elegant solution, and as old as the hills. Let's see more tried and true. Wow me with its application.

Quote from: Lunamancer;867322In essence, the beauty of successive dice rolls is that they can perform mathematical functions of multiplication and division without ever calling upon the math illiterates sitting around your table to have to make such calculations. Hands down, the most elegant solution, and as old as the hills.

But slow as molasses in winter.

I find some players take seemingly forever to roll the dice (or die). Successive die rolling multiplies the time taken. So unless the successive die rolling is a known thing at the start, e.g. rolling both the to hit and the damage rolls in games like OD&D or Runequest, any successive die rolling just slows play down.

Quote from: Bren;867328But slow as molasses in winter.

I find some players take seemingly forever to roll the dice (or die). Successive die rolling multiplies the time taken. So unless the successive die rolling is a known thing at the start, e.g. rolling both the to hit and the damage rolls in games like OD&D or Runequest, any successive die rolling just slows play down.

Relative to what?

The slowest player at my table while playing D&D seriously can't add a strength modifier to the d20 hit roll without a calculator.

If we tailor made RPGs to suit slow players, they'd all suck, and those players would still hold up the game.

Quote from: Lunamancer;867357Relative to what?

Single die rolls.

If by "an age old debate" you mean "something that a very small number of people yap, run in circles, and piss themselves about and the vast majority of gamers think they're fucking idiots about," then yeah.

Quote from: JohnLynch;833511Disadvantages of Polyhedral Dice
* Those gamers who hate d20 and refuse to play any games with it won't play your game.

The technical term for such people is "fucknugget" and I don't want them within a hundred miles of my game anyway.

Which is okay, because in 42 years of this fucking stupid hobby the only place I've ever even HEARD of somebody refusing to play a game because of the god damned dice is in some obscure blocked drains of the Internet.

Quote from: Lunamancer;867322Especially for the "I love curve mechanic crowd," have you ever tried to graph the probability/effect distribution for degree of success roll on a given hit? The shape of that curve varies wildly depending on where on the core mechanic roll the target number for basic success was. Wouldn't it be better to just roll a fresh new die or dice so you can set the probability distribution of degrees of success exactly to match your aesthetic taste?

Nope, can't say I have.  I definitely could, but I see no reason to.  I don't care what those curves look like.  I have never felt a need to "set the probability distribution of degrees of success" (or even of simple success/failure).  As a GM, I don't approach the game from a standpoint of "Hmm...  The PC should have a 75% chance to succeed, so what do I need to set the Difficulty to in order to get a 75% success chance?"  My approach is "The Difficulty is X.  Period.  No matter who tries it or what their skill level is.  And the chance of success will be whatever it will be."

I don't want to set the probabilities.  That's what the rules are for.

Quote from: Bren;867424Single die rolls.

Well, if we're not adding modifiers to those single die rolls that require slow players to pull out calculators, then the equivalent to a system of successive die rolls would be also a single die roll, so the point is moot.

Oh wait. Forgot something. If you're using 3d6 as your core mechanic rather than a d20, slow players are going to have to have their calculators out anyway.

Quote from: nDervish;867468Nope, can't say I have.  I definitely could, but I see no reason to.  I don't care what those curves look like.

This was specifically directed at people who claim to prefer "curve" dice mechanics. If you don't care about probability distributions then it makes little difference.

Quote from: Lunamancer;867479Well, if we're not adding modifiers to those single die rolls that require slow players to pull out calculators, then the equivalent to a system of successive die rolls would be also a single die roll, so the point is moot.

Oh wait. Forgot something. If you're using 3d6 as your core mechanic rather than a d20, slow players are going to have to have their calculators out anyway.

:confused: Your experience is completely alien to me. I've never yet played a game that required calculators to resolve die rolls. I'm struggling to think what that would even look like and why anyone would ever choose to play that game.

Roll 3d6 get a 7 add +1 for DEX, +3 for Combat ability, -2 for Opponent's defense equals a 9. Where does a calculator even come into this?

Aside from rolling 2d6 instead of 3d6 this is exactly the sort of calculation that Honor+Intrigue uses. Most players can do the arithmetic easily. If they can't, I can. (Far faster than the average RPG player can shake, rattle, and  roll a die.) Rolling a series of dice to get a similar result would just waste my time.

Maybe you can provide an example of the problem and what you see as a solution.

Quote from: Bren;867493:confused:

Okay. No new information, just a quick recap.

I proposed successive dice rolls as an option that would allow a linear core mechanic to easily handle modifiers that are non-linear while avoiding math.

You said that would be "slow as molasses" because apparently some player can be slow about rolling dice. I asked slow relative to what, because the slow player in my group is so slow at math that he can't add a strength modifier to a d20 to hit roll without a calculator.

This isn't an alien RPG I'm talking about.

QuoteRoll 3d6 get a 7 add +1 for DEX, +3 for Combat ability, -2 for Opponent's defense equals a 9. Where does a calculator even come into this?

He would literally take out the calculator, add every number that rolled up on each die, add the +1 for dex using the calculator, then add 3 for the combat ability, then punch in -2 for the opponent's defense. And then we hope he didn't hit the wrong button by mistake. Sometimes it takes 2 or 3 tries.

QuoteMost players can do the arithmetic easily. If they can't, I can. (Far faster than the average RPG player can shake, rattle, and  roll a die.)

And all that is is an assertion. Doesn't make it right or true. Slow at math? Sllow at rolling dice? Makes little difference to me. RPG design "computation speed" arguments have always been entirely baseless. I'm fast at both. As a player, when I do shake the dice, I get to do more shaking than I even like just waiting for the GM to tell me to throw.

Quote from: Lunamancer;867509You said that would be "slow as molasses" because apparently some player can be slow about rolling dice.

In my experience most players are slow at rolling the dice. Slow as in "come on baby, daddy needs a new pair of shoes" shake, rattle, and rolling. And that is ignoring the die that rolls off the table requiring a reroll. If you've rarely gamed with players who do that, then your experience is really different than mine over the past 45+ years.

QuoteI asked slow relative to what, because the slow player in my group is so slow at math that he can't add a strength modifier to a d20 to hit roll without a calculator.

It's unfortunate that he is playing a game where he has to repeatedly add those modifiers. I'm so glad that there are so many other games to choose from that don't require players to do lots of arithmetic during play.

QuoteHe would literally take out the calculator, add every number that rolled up on each die, add the +1 for dex using the calculator, then add 3 for the combat ability, then punch in -2 for the opponent's defense. And then we hope he didn't hit the wrong button by mistake. Sometimes it takes 2 or 3 tries.

It's unfortunate that he is playing a game where he has to repeatedly perform such an onerous task.

QuoteAnd all that is is an assertion. Doesn't make it right or true.

No it doesn't. No more than your assertions are true or right. They are just assertions.

Quote from: Lunamancer;867322Wouldn't it be better to just roll a fresh new die or dice so you can set the probability distribution of degrees of success exactly to match your aesthetic taste?

You asked this question. I gave you my answer. Which was that, no it wouldn't be better.

If you didn't want to read answers that didn't agree with your assertion, then in Crom's name why did you ask the question in the first place?

Quote from: Bren;867542In my experience most players are slow at rolling the dice. Slow as in "come on baby, daddy needs a new pair of shoes" shake, rattle, and rolling.

A lot of people I've gamed with have done that. It just wasn't so exaggerated as to take more time than adding modifiers to the die result. I could point to D&D Live to show it's not just the circles I game in. Those guys consistently roll faster than they add.

QuoteIt's unfortunate that he is playing a game where he has to repeatedly add those modifiers.

He's having fun. We've got his two favorite games in the rotation.

QuoteNo it doesn't. No more than your assertions are true or right. They are just assertions.

I began stating my preference, answering the question posed by the subject of the thread. I went on to show how it can be used to capture the benefits of a different type of mechanic. I never made any assertions to the superiority in speed of one mechanic over another. I suppose I did assert, through implication, that addition/subtraction is quicker and easier than multiplication/division, and that many gamers like to avoid having to multiply or divide as part of a core mechanic. Nobody's disputed those points.

I also asserted that typically when analyzing a system, people ignore the ever-present variable of the player on account of its intractability and showed how player desires could counter the effects of changing probability distribution. This point COULD be highly disputed. But, so far, it hasn't been.

QuoteYou asked this question. I gave you my answer. Which was that, no it wouldn't be better.

As far as I can tell, you never answered THAT question. And again, it was only directed towards people who care about probability distributions. Not everyone does. I personally don't consider it that high on my list because, again, the intractable ever-present player makes it so real play doesn't match what the math says should happen. If it's not important, it's not important.

I stated the real reason for my preference--it has nothing to do with probability distributions. It has to do with transparency. Not everyone wants that or cares about it one way or another. I do. I find it very helpful.

Quote from: Lunamancer;867678I began stating my preference, answering the question posed by the subject of the thread. I went on to show how it can be used to capture the benefits of a different type of mechanic. I never made any assertions to the superiority in speed of one mechanic over another. I suppose I did assert, through implication, that addition/subtraction is quicker and easier than multiplication/division, and that many gamers like to avoid having to multiply or divide as part of a core mechanic. Nobody's disputed those points.

Your example of adding modifiers used addition, not multiplication. So you were implying it was faster than addition. You then introduced your experience with your innumerate friend as an example of how multiple die rolls was supposed to be easier i.e. faster than adding modifiers to a roll. I questioned your assertion based on my experience.

QuoteI also asserted that typically when analyzing a system, people ignore the ever-present variable of the player on account of its intractability and showed how player desires could counter the effects of changing probability distribution. This point COULD be highly disputed. But, so far, it hasn't been.

I didn't find this point interesting enough to remark on.

QuoteAs far as I can tell, you never answered THAT question.

Since "THAT" has no reference, I have no idea which question you are referring to. Is it some other question you asked? One of the half a dozen or so questions the OP asked. I have no clue.

Now YOU asked if it would be better to roll a fresh new dice. I answered that question. In the negative. I also explained why. You seem to want to refute my experience with players who are slow to roll the dice with your experience with your innumerate player.

I agree that he sounds like a problem in search of a solution. I've done a lot of gaming over the decades with a lot of different players. I've never gamed with anyone who is that incompetent at addition. I have gamed with people who were not very quick at addition or other arithmetic. If their ability to add modifiers (or calculate the odds for critical or special successes) became the critical path activity to moving a turn along I find I can add the numbers (or calculate the odds) for them which saves time. They just need to roll the dice and note what they rolled.

Is there some reason why this guy likes making everyone wait while he laboriously adds small numbers on his calculator? Is there some reason you all want him to do that? It seems to bug you, so I'm curious what advantage you find to the wait time plus the error correcting time.

As I said, I don't enjoy wait time. So for slow die rollers, I suppose I could roll the dice for them. But I've decided not to do that (except in very limited circumstances). Mostly because I find that a lot of players like rolling the dice themselves. Traditionally rolling dice is part of the game and the games it developed from so that probably shouldn't surprise anyone.

Why do players like rolling the dice themselves? [1]

For some rolling the dice mentally links their action to their character's action. A few feel they have some control over the dice or their PC's fate. For some rolling the dice is a kinesthetic experience they enjoy. And for others, they just like rolling the dice. I like rolling the dice myself, so I get that. So I don't roll the dice for the players even if it might be faster. (It probably won't be faster, but that is neither here nor there since lack of speed isn't why I make the decision to have them roll the dice.)

QuoteI stated the real reason for my preference--it has nothing to do with probability distributions. It has to do with transparency. Not everyone wants that or cares about it one way or another. I do. I find it very helpful.

Transparency is nice. Runequest/CoC/BRP systems are great for that. More transparent than D20 since you don't need to multiply by five to get the probability. However, rolling multiple dice turns simple probabilities into cumulative probabilities.

So calculating the probability that I hit, combined with the probability my target fails to actively defend, combined with the probability that my damage exceeds the armor absorption of the target to find out the probability that I do any damage to the target that round requires multiple multiplications to compute.[2] How does this result in actual, rather than theoretical, transparency of the probability?

Answer: Frequently it doesn't.

Each of those single die rolls is a simple, linear probability so each step is easy to compute so this gives the illusion that the relevant cumulative probability is transparent when, in practice, it usually isn't at all transparent to most players because they can't or don't compute the cumulative probability from each of the conditional linear probabilities. Which means the outcome is similar in lack of transparency to using a nonlinear randomization method like rolling 2d6, 3d6, 2d10, or whatever nonlinear method chosen.

[1] A few players are afraid the GM will cheat. A few players want the chance to do their own cheating. I'm ignoring those reasons in making my decision that the players typically roll the dice themselves.

[2] And it requires at least one more step to calculate the probability that the blow has any immediate effect on the target this round (like death, incapacitation, or a penalty). And a similar series of conditional probabilities is required to determine the probability that the player's PC does not get hit for an immediate effect this round. The end result is rarely transparent.

Quote from: Lunamancer;867322Especially for the "I love curve mechanic crowd," have you ever tried to graph the probability/effect distribution for degree of success roll on a given hit?

I have.  In my system (roll 2d10, every 0 is replaced by another set of 2d10) it's a nice smooth curve. For anything with a <50% chance of success, +3 means you double your chances of success, -3 means you halve it. So +1 and -1 always have the same effect.

Quote from: Lunamancer;867322The shape of that curve varies wildly depending on where on the core mechanic roll the target number for basic success was.

It doesn't ;)

Quote from: Lunamancer;867322Wouldn't it be better to just roll a fresh new die or dice so you can set the probability distribution of degrees of success exactly to match your aesthetic taste?

The issue isn't so much degrees of success, but what effect a bonus gives you, and this cannot be replaced with a second roll. A bonus on to hit cannot be replaced with a bonus on damage.

Quote from: JoeNuttall;867706A bonus on to hit cannot be replaced with a bonus on damage.

It can if armor works as damage absorption. It depends on the reason for the bonus. I like that as GM I would have the option of applying it to one roll, the other, or both.

In the Lejendary Adventure system, Soldiers and Knights are differentiated in their combat abilities by the soldier having higher hit probabilities, knights deal more damage. The odds of a soldier scoring a hit that causes some damage is much higher than the knight for unarmored or lightly-armored opponents. For medium to heavy opponents, the knight has the advantage.

So, no, the two aren't interchangeable in the strictest sense. And they aren't intended to be. Adding/subtracting from the first roll is meant to provide adjustments that ARE linear. The purpose of the successive die roll is to create an adjustment that is non-linear. There is no good reason why all modifiers should be of one type and never the other.

Quote from: Bren;867687Your example of adding modifiers used addition, not multiplication. So you were implying it was faster than addition.

No. It was proposed as a way to avoid having to do multiplication or division in a linear core mechanic system and yet still have access to non-linear modifiers to task resolution.

I'm using a linear system. I don't want to ask players to do multiplication and division. So this is a faster solution.

QuoteYou then introduced your experience with your innumerate friend as an example of how multiple die rolls was supposed to be easier

No. I used that as an example of why your assertion was false. I did not assert multiple die rolls were quicker than adding. To the contrary, my consistent position has been that mileage varies, so I treat them as equally time consuming since neither is inherently slower than the other. I even made it very clear that I have zero intention of catering to the very worst characteristics of gamers. The fact that you game with some exceptionally slow rollers is simply not impressive.

QuoteSince "THAT" has no reference

"That" refers to the question I posed that you claimed to be answering but never even really addressed or answered it at all. You paraphrase it again here:

QuoteNow YOU asked if it would be better to roll a fresh new dice.

That question dealt specifically with probability distributions of degrees of success. Your only responses have been about math speed vs rolling speed. You haven't responded at all about probability distributions.

QuoteTransparency is nice. Runequest/CoC/BRP systems are great for that. More transparent than D20 since you don't need to multiply by five to get the probability. However, rolling multiple dice turns simple probabilities into cumulative probabilities.

Multiple rolls aren't always necessary. In most instances, they're not. I've tried in the past to draw analogies to thinks like Huffman code, where higher frequency characters are coded in fewer bits than would otherwise be required, while lower frequency characters are coded with more bits than would otherwise be required.

Indeed, the majority of characters will require MORE bits than would be required for each character in a system that codes them equally. But it still is more efficient overall because the majority of characters are used with relatively low frequency. So their existence doesn't undermine the benefits of the system.

If I'm playing Lejendary Adventure, there are a number of ways for characters to "defend" themselves. If someone's firing missiles at you, just moving erratically will give them a negative hit modifier. If you have defensive skills, they usually translate to damage reduction. The idea being even if you can't avoid damage completely, you can mitigate it some.

There is a Luck ability. Most characters don't have it. If you do, you can use it once in a round to call for a second die roll to "lucky dodge" an attack. There are also a couple of other tactical options. They take up your actions for the round, so they're not used very often. And there are speed requirements as well, so they're not always options at all.

Almost all weapons do 1d20 damage, but each weapon has a different "minimum" damage range. If I'm using a longsword (minimum damage 4) and have a +3 damage bonus due to strength, then the minimum damage I would cause is 7. Most stock enemies (orcs or bandits) have armor protection between 4 and 6. So, again, in a lot of cases, the probability on the hit roll is enough to tell you the chance to hit.

However, if the bandit picks up a shield, now we have a non-linear modifier (but probably not so for a knight). Do we lose transparency? Yes and no. Yes, because if you're looking at the probability of ultimately causing harm, we have to multiply two probabilities. No, because even if you "hit" but just don't cause enough damage, you're still damaging the shield. The more you hit the shield, the sooner it becomes useless and you get to go back to removing that non-linear modifier against you.

If the bandit also quick enough to have options like diving to avoid attack or parrying, those things take up his action for the round. He won't use them if you didn't hit in the first place. So that roll still matters. So while, again, it introduces a non-linear adjustment, once again that first transparent roll matters. The same if he had the Luck ability and went to use it. He only gets one per round. Especially if you're skilled enough to make multiple attacks, getting that lucky dodge out of the way with the first attack makes a big difference for that second attack, which reverts to that totally transparent state.

The latter cases in general are more typical of how successive rolls work, where there is generally time for decision-making in between, so what's transparent is still significant. The bandit with shield example is really the best case against transparency, because there is no decision in between the hit roll and damage roll. And I'm willing to live with that.

Quote from: Lunamancer;867760I'm using a linear system. I don't want to ask players to do multiplication and division. So this is a faster solution.

Perhaps. It’s unclear what multiplication and division you are replacing. You introduced slow addition, so I responded to that.

QuoteNo. I used that as an example of why your assertion was false.

Your innumerate player is an extreme outlier. He doesn’t disprove that multiple die rolls are generally a more time consuming process than simple addition and subtraction. Especially given that the addition and subtraction can be done by someone who is faster at computation whereas multiple die roll generally is not done (or cannot be done) by the fastest die roller at the table.

QuoteI did not assert multiple die rolls were quicker than adding. To the contrary, my consistent position has been that mileage varies, so I treat them as equally time consuming since neither is inherently slower than the other.

Asserting that they are equally time consuming is itself an assertion. Arguing that you should switch to multiple die rolls because it is easier than adding modifiers is arguing that it is in fact faster. If they were equally easy you would be indifferent between them for reasons of ease and you don’t appear to be indifferent.

QuoteI even made it very clear that I have zero intention of catering to the very worst characteristics of gamers.

Given that the “worst characteristics of gamers” is vague to the point of meaninglessness I’m not sure what to make of this. I asked why you or the innumerate player insist on him going through the laborious task of adding modifiers. You didn’t answer that. If it isn’t catering to a flaw of the gamer why do it and what is it?

QuoteThe fact that you game with some exceptionally slow rollers is simply not impressive.

They aren’t exceptionally slow. In my five decades of gaming experience most players I’ve observed go through a fairly slow process when rolling the dice in comparison to quickly picking up the right die, immediately rolling the die or dice and reading off the result. The time it takes for someone who is reasonably adept at arithmetic to solve 7+1+3-2 = 9 is at least as fast as the time it takes many if not most players to to actually roll.  [1]

It is true that some players go through a lengthy die rolling process, just like some players go through incredible contortions performing elementary calculations. I’m not talking about those extremely slow rolling players, though they certainly add to the negative aspects of adding additional die rolls to the process. I do observe that your method helps alleviate the delay cause by your innumerate player, but does nothing for the delay caused by exceptionally slow die rollers whereas what I proposed easily handles both extremes.

QuoteThat question dealt specifically with probability distributions of degrees of success. Your only responses have been about math speed vs rolling speed. You haven't responded at all about probability distributions.

Perhaps I don’t understand what two alternatives you are asking me to choose between or respond to.

I apologize if I did not make it clear, but aesthetically I am indifferent between linear and nonlinear die rolling methods.[2] I thought that would be clear from the fact that I mentioned systems that use both linear and nonlinear systems. So let me be clear. I am indifferent between linear and nonlinear systems as a matter of aesthetics. To pick one over the other I need some objective or subjective benefit to the system.

What I prefer is a mixture of speed of resolution, transparency regarding the PC’s abilities, and whatever effect I am looking for from that particular system (which will vary). I especially dislike wait time during play. It bores me.

Systems that allow the GM to perform calculation steps for players who are slow calculators and to check arithmetic for innumerate players decrease wait time in play. Systems that require each player to perform their own calculations increase wait time as well as the error rate.

Systems that require multiple die rolls in sequence (as opposed to rolling a handful of dice or to rolling both the attack dice and the damage dice at the same time) increase wait time in play.

So if I am going to increase wait time, I want a benefit. In your post, no actual (as opposed to vaguely theoretical) benefit has been suggested in comparison to existing methods in use. So given the uncertainty of any possible benefit, I choose the certainty of less wait time.

I thought I said that already, but it seems I didn't communicate clearly. Do you understand my answer to your question now?

QuoteHowever, if the bandit picks up a shield, now we have a non-linear modifier (but probably not so for a knight). Do we lose transparency? Yes and no. Yes, because if you're looking at the probability of ultimately causing harm, we have to multiply two probabilities.

I referred to this as immediate impact, i.e. something that happens this roll to end the combat or change the odds of success in the next roll as opposed to something that erodes some quantity without materially changing the odds of achieving an immediate impact.  

QuoteNo, because even if you "hit" but just don't cause enough damage, you're still damaging the shield. The more you hit the shield, the sooner it becomes useless and you get to go back to removing that non-linear modifier against you.

If the bandit also quick enough to have options like diving to avoid attack or parrying, those things take up his action for the round. He won't use them if you didn't hit in the first place. So that roll still matters. So while, again, it introduces a non-linear adjustment, once again that first transparent roll matters. The same if he had the Luck ability and went to use it. He only gets one per round. Especially if you're skilled enough to make multiple attacks, getting that lucky dodge out of the way with the first attack makes a big difference for that second attack, which reverts to that totally transparent state.

You seem to be conflating the roll mattering with the roll being transparent. The problem you point out with lack of transparency in nonlinear rolls has nothing to do with nonlinear rolls not mattering. They matter at least as much as linear rolls.

The problem with nonlinear rolls is the difficulty in intuiting or quickly calculating the probabilities for victory, survival, and any lesser conditional effects. But if you look at how multiple linear rolls affect the calculation or intuition of the actual probabilities of victory, survival, and any lesser conditional effects, the lack of transparency between the two methods is very similar if not identical. So I don’t see any reason to strongly prefer one over the other in matters of actual transparency.

[1] It is also slower than some multiplication and division, e.g. when playing Runequest 2, I either already have memorized or can easily calculate that an 80% chance to succeed has a 4% for a critical (.05*.8), 16% chance for a special or critical (.2*.8), and a 2% chance for a fumble in Runequest 2 by the time most players have rolled the dice, read the number, and announced it.

[2] Among the games that I’ve played and run somewhat extensively are the following.

• OD&D and AD&D that predominantly use linear rolls either as single die rolls (like a saving throw) or multiple die rolls like attack and damage.  
• Runequest 2 and 3, Call of Cthulhu, Pendragon and other games in that family that predominantly use linear rolls again either as single rolls (the resistance table or unopposed skill rolls) or multiple die rolls (attack vs. defense rolls, damage rolls vs. static armor values [or even armor rolls as in Stormbringer and Hawkmoon). Runequest even includes some nonlinear rolls, usually for some damage or effect.
• WEG’s D6 which almost exclusively uses nonlinear die rolls consisting of multiple D6s. This total is compared either vs. a target difficulty or vs. an opposed roll (which consists of multiple D6s). Damage is computed using the same methodology.
• Honor+Intrigue which uses a roll of 2d6+modifiers vs. a target difficulty (usually a 9) or vs. an opposing roll of 2d6+modifiers. H+I also uses a bonus/penalty of rolling additional dice tossing out the lowest die roll (for a bonus) or highest die roll (for penalty). Damage rolls a second roll and are usually a single die, though a few weapons use multiple dice.

Quote from: Lunamancer;867749It can if armor works as damage absorption.

I wouldn't think much of a system that had no bonuses on to hit, only bonuses on damage.

Quote from: Lunamancer;867749Adding/subtracting from the first roll is meant to provide adjustments that ARE linear.

You were saying people should drop curved mechanics in favour of your system, and I was suggesting that the power of a curved mechanic is in how it handles modifiers to the roll, and that this cannot be replicated with your proposal - your response appear to be that it is "meant" not to do this.

To address the other point of your original post - I don't want the proportion of "complete successes" to be a fixed proportion of "successes". If someone nearly always succeeds at a task then I want them to almost always have a complete success, whereas if they hardly ever succeed at a task I want them to only very rarely have one of their successes be a complete success.

Honestly, what's aesthetically unpleasing to me most is arbitrary difficulty numbers, and stat ratings that don't have clearly defined real-world equivilants This doesnt mean each point of strength needs to equal a specific weight in lbs, "weight classes" are much more appealing, but when a character has STR 12, I want to have some general idea of what the hell that means, preferably with some common denominator examples.

2d6. Nothing further to be said :)

Quote from: Bren;867770Perhaps. It's unclear what multiplication and division you are replacing.

The multiplication or division that would otherwise be required for non-linear modifiers to a linear die mechanic.

QuoteYour innumerate player is an extreme outlier.

It's true. I've never met anyone slower. But it's not like there aren't plenty of people who are almost as bad.

QuoteHe doesn't disprove that multiple die rolls are generally a more time consuming process than simple addition and subtraction.

It provides a counter example to the universality of what you were proposing. I also disagree with your "general" case, but "general" is too vague to prove or disprove anything. You can go and watch the D&D Live videos on YouTube. Sometimes those guys give the dice extra shakes before rolling. Sometimes they take a little extra time adding the numbers. Most of the time they roll quickly and add quickly, but the time it takes to add is consistently longer than the time it takes to roll.

QuoteEspecially given that the addition and subtraction can be done by someone who is faster at computation whereas multiple die roll generally is not done (or cannot be done) by the fastest die roller at the table.

Depends what kind of "multiple die roll" you're talking about. I pointed out a couple different cases. Hit & Damage rolls, which are automatic, or Hit with the other person deciding whether to dodge or parry, which require additional choice. If it's automatic, there's no reason both dice can't be rolled simultaneously. If it requires choice, I would say 1) it's the choice that is likely to be the most time-consuming part and 2) because it involves a choice, that time is not a downtime in the game, choice IS the game.

QuoteAsserting that they are equally time consuming is itself an assertion.

You are asserting that I asserted, but I did not. I never asserted that they are equal. I said I treat them as equal because I understand that mileage varies. I feel something somewhere got your panties in a bunch and you're now trying to twist everything to justify it.

QuoteArguing that you should switch to multiple die rolls because it is easier than adding modifiers is arguing that it is in fact faster. If they were equally easy you would be indifferent between them for reasons of ease and you don't appear to be indifferent.

I did not argue anyone should switch to multiple dice rolls. I stated (and this is for the third time, so you might want to take notes this time) my aesthetic preference is for a linear mechanic, d100, d20, d10, in that order. The main reason is transparency. This has nothing to do with speed. In fact, in response to your post I said that I felt measuring "processor speeds" of game mechanics is largely baseless. I merely pointed out successive dice rolls provide an alternative to multiplication and division.

QuoteGiven that the "worst characteristics of gamers" is vague to the point of meaninglessness I'm not sure what to make of this.

It's simple. I don't plan for the lowest common denominator. I'm not going to dumb down math for calculator boy. I'm not going to try to do a billion things in one die roll just because some nerds think they're Vegas high rollers. I also won't remove randomness from character generation just because some people think it's unfair. Nor do I ignore class/race restrictions or what have you just because a player cries, "Muh creativity!"

QuoteThey aren't exceptionally slow. In my five decades of gaming experience most players I've observed go through a fairly slow process when rolling the dice in comparison to quickly picking up the right die, immediately rolling the die or dice and reading off the result.

I understand that most gamers have their dice-rolling rituals, and since I'm usually GM I don't have time for such nonsense. I've seen slow rolls as part of those rituals. I've seen fast rolls as well, as if the die isn't rolled then and there, you'll miss the good number. I have one guy who even makes sure, in between rolling dice, all of his dice rest with the number he wants to roll face up reasoning that it will cause the molecules in the dice to slowly rest towards the bottom over time, weighting them to roll better results.

In general, though? No, I don't see dice rolling taking longer than adding up all the modifiers. And again, I point to D&D live as an experience outside of myself and my table to show, hey, it isn't so crazy after all for me to expect people to roll faster than what you're describing.

QuoteSystems that require multiple die rolls in sequence (as opposed to rolling a handful of dice or to rolling both the attack dice and the damage dice at the same time) increase wait time in play.

Tautological dichotomy. Either a choice is required between dice rolls or it isn't. If it is, the time in between isn't "wait time in play." It *is* play. And if no choice is required in between, the dice can be rolled simultaneously*. So, zero wait time either way. (*Unless, of course, the type of die of the second is dependent upon the outcome of the first. I'm not sure I'd enjoy such a thing as a core mechanic.)

Some players, probably most, choose to roll the two separately. Another dice rolling ritual. Even as GM I choose to roll them separately because for me it's faster to do all 10 orcs hit rolls in one shot, then all of the damage rolls of those that hit simultaneously in a second throw. I'm averaging much better than two-at-once that way.

QuoteI referred to this as immediate impact, i.e. something that happens this roll to end the combat or change the odds of success in the next roll as opposed to something that erodes some quantity without materially changing the odds of achieving an immediate impact.  

It's the literally the same thing as hit points. (In LA, both the shield and the character have a Health stat that damage is assigned to.) I deal 20 damage to the guy with 100 hit points. It didn't end the battle. Didn't change the probabilities of subsequent rolls. All it did is erode some quantity without any immediate impact.

QuoteYou seem to be conflating the roll mattering with the roll being transparent.

I don't see how the word conflating has anything to do with anything I said. In a sense, I was doing just the opposite. I was distinguishing differences. I just as easily say you seem to be conflating the transparency of the totality of steps it takes to reach the goal with the transparency of each individual step. But if we're going to just talk past each other, there's no point in this continuing.

Quote from: Lunamancer;867934I feel something somewhere got your panties in a bunch and you're now trying to twist everything to justify it.

It's interesting you say that as that is exactly how your posts have struck me from your first response. You asked for opinions about rolling multiple dice instead of single die. I provided my opinion that adding a die roll adds wait time to the game. That seems to me to be an obvious and non controversial statement. Rather than saying, yes but despite that I still prefer to roll linear dice in sequence because it provides such and such an advantage that I value more than any added wait time, you objected to the idea that it adds wait time.

Now if you had intended to ask my opinion only about how well such substitution would work for you at your table with your players (who I don't know) running your system (that I am unfamiliar with) then I did not understand that as the question you were actually trying to ask. So sorry. The answer to that question is, "How the fuck should I know?" or "Why are you asking me, it's your table?" or "You really haven't provided enough information to tailor an answer to the specific and  idiosyncratic needs of your particular table."

In objecting to the idea that sequential die rolling adds wait time, even in comparison to simple arithmetic calculations, you introduced your anti-Rain-Man innumerate player. This was to try to disprove what seems to me a very uncontroversial observation (that rolling dice in sequence takes more time than rolling a single die or set of dice) by focusing on my other observation that players generally don't just quickly pick up the die or dice, roll them, and read off the result. Many players go through the various rituals or physical ticks or just flat out don't know which die to pick up for the next sequential roll without asking. So the delay from die rolling is often not insignificant. And while the delay for calculation is also often not insignificant, I pointed out that if one has an innumerate player, or just a player who is markedly below the group average for arithmetic calculation, one can mitigate the delay caused by that player by having someone who is above average in calculation speed and accuracy perform the calculation. This is a method I have successfully used for over 40 years with multiple systems using  both linear and non linear resolution methods. It works for me. It also works for any group willing to use it, provided there are some people at the table with the time and ability to perform the calculation for the slower calculators.

I also pointed out why a similar mitigation for die roll delays of having a faster die roll do the die rolling for the players with lengthy rituals or physical die rolling ticks generally won't work. I won't repeat the reasons I mentioned as to why players prefer rolling the dice themselves and what it adds to the game experience. The reasons  are here (http://www.therpgsite.com/showpost.php?p=867687&postcount=33) if anyone is interested.

Obviously if there is some reason why the innumerate player has to perform his own calculations, my mitigation won't work. Off the top of my head, I can't recall a system that requires the player to perform all their own calculations, but there might be one out there or this might just be a preference of the player or the table which makes the added cost in wait time a function of their choice for how they want to play the game.

For some reason, you seem focused on trying to disprove my impression that die rolling takes unnecessary time as compared to simple calculation. You have several times referred to D&D Live videos. First, I am comfortable that my impressions of the time spent rolling die and calculating modifiers is reasonably accurate. I have over 44 years of experience with hundreds of players. In that time I have routinely and repeatedly done the calculation faster than the time taken by the vast majority of players rolling their dice. I have no reason to think that players from different cities, states, and countries and separated by decades of time or particularly unusual in their behavior. Second, my  speed is due in part to my being above average in arithmetic calculation speed and accuracy but also in part to my years of experience GMing the systems that I run. How much time some people I am never likely to play with spend rolling dice or calculating modifiers in a system that I don't play isn't all that pertinent to what will work for me in systems I do run with players I actually play with.

You are correct that choice of action is generally more time consuming than die rolling or modifier calculation. Like anything there are extremes in all those areas: the player who dithers and can't decide on an action, asks advice of the other players, asks for clarifying information from the GM, before finally, hesitantly deciding to act vs. the guy who unthinkingly yells, "I hit it with my axe!" in the blink of an eye; the player whose die rolling ritual involves practice rolls, exiling of bad dice, training the dice by lining up the number desired, wild rolls bouncing under the sofa that have to be retrieved, or dithering over which is the right type of die or number of dice to roll for this action vs. the person who quickly and quietly picks up the right die or dice, rolls it or them, and calls off the number, and we also have the anti-Rain-Man player needs a calculator to add 7+3+1-2 and who rather than getting 9 the first time ends up with 13 and has to repeat the whole laborious process of calculator addition vs. the person who can quickly and correctly add those numbers in their head and has memorized their frequently used modifier totals to further speed up their calculation. But in general, my 44+ years experience is that making up one's mind is far slower for most people than is rolling the dice or adding modifiers. However, even though the decision time is likely to be greater the wait time for die rolling is not nonexistent. Nor is the wait time for a second modifier calculation. And sequential rolling adds both of those wait times.

You mentioned a couple of times that sometimes dice can be rolled simultaneously to avoid sequential rolling. I pointed that out in my first response. I probably used the example of rolling both attack and damage dice at the same time. So there is no new ground here.

I alluded to the difference between ablating hit points (whether of a person or object) which results in no material or profound status change such as something that ends the combat (like death or incapacitation) or that provides a significant change in advantage to one side or the other (like penalties of wounds). So no new ground there either.

Quote from: Lunamancer;867934I stated (and this is for the third time, so you might want to take notes this time) my aesthetic preference is for a linear mechanic, d100, d20, d10, in that order. The main reason is transparency.

Yes I got that the first time. So use a transparent linear mechanic. I don't care. As I said, I am indifferent between whether the dice rolled are linear or semi-bell shaped and transparency is a good thing (fog of war, OOC knowledge, and such excepted).

I also pointed out that the more linear dice steps there are in sequence, the less transparent the actual result is because most people don't or can't quickly compute the relevant cumulative probabilities. I used the example of a system (like Runequest or Call of Cthulhu) where the chance of damaging a character in 6 point armor with a weapon doing 1d8+1 damage (simplified to ignore critical, special, and fumbles, hit locations, and breakage of parrying items) is
   (Attack%) x (1-Parry%) x (3/8)   

Note that 3/8 is the chance to roll damage that exceeds the 6 points of armor.

This is a straightforward, simple cumulative probability, but one that in my experience is beyond the ability or interest of most players to actually compute during play. And this simplified example ignores the significant additional calculation complication provided by particularly good or bad rolls, hit locations, hit points per location, hit points per parrying item, and item breakage. Yet those ignored factors are important, often crucial, to get actual transparency by understanding who really has the advantage in combat,

So in effect, sequential linear die rolling yields a similar lack of transparency of the exact odds as does nonlinear die rolling. Personally I am less concerned with some objective and mostly theoretical transparency. I am more concerned with the actual and subjective transparency for the players at the table. What the player actually understands during play is the only relevant measure of transparency. Not some cumulative or conditional probability that could, but almost never is, actually calculated in play.

QuoteIt's simple. I don't plan for the lowest common denominator. I'm not going to dumb down math for calculator boy. I'm not going to try to do a billion things in one die roll just because some nerds think they're Vegas high rollers. I also won't remove randomness from character generation just because some people think it's unfair. Nor do I ignore class/race restrictions or what have you just because a player cries, "Muh creativity!"

There are a number of entirely unrelated things here that you seem quite passionate about. But frankly I don't understand how you think these things are remotely relevant to this thread or to anything I wrote. I suspect you don't have much idea what I actually think about any of the things you mentioned since I have said nothing about wanting to "dumb down math", wanting to "do a billion things in one roll", "Vegas", "nerds", "high rollers", removing "randomness from character generation", or ignoring "race/class restrictions." I don't even play a game that has classes.  At this point I am starting to agree with Gronan's previous post (http://www.therpgsite.com/showpost.php?p=867428&postcount=24).


* Even our blind player liked rolling her own dice. She just relied on someone else, usually a neighboring player, to read off the die roll. She did calculate her own modifiers though.

Quote from: Bren;867956You asked for opinions about rolling multiple dice instead of single die.

I never really did. I asked one specific question that dealt specifically with probability distributions for degrees of success. So far, nobody's admitted they even care about that, so I haven't asked for the opinion of anyone posting so far. Now I understand there was some initial confusion over this, and I also know this has been cleared up already, so I have no idea why you're STILL talking about it.

QuoteAnd while the delay for calculation is also often not insignificant, I pointed out that if one has an innumerate player, or just a player who is markedly below the group average for arithmetic calculation, one can mitigate the delay caused by that player by having someone who is above average in calculation speed and accuracy perform the calculation.

As you later point out, sometimes this can be impractical. Sometimes I do the math for him myself, if I already know his relevant numbers after third or so round of combat. Often times, though, communicating the relevant numbers plus calculation time for someone faster would take even more time.

Another solution is I could say, "Dude. You've been playing RPGs for years. You obviously enjoy them. How about doing everyone a favor and learn to do fucking math? You'll get plenty of practice when we play."

Of course, you could also say, "Dude. I came here to play a game, not to watch your sweaty arm writhe around just because you believe it somehow effects the outcome of the roll. Even if it actually worked that would just make you a cheater instead of an idiot."

"Roll the dice faster" is a far more doable command than "do math faster." You know. I figured that bit of knowledge would be helpful to you since you're on the lookout to fix shit.

QuoteFor some reason, you seem focused on trying to disprove my impression that die rolling takes unnecessary time as compared to simple calculation. You have several times referred to D&D Live videos.

I haven't tried to disprove anything other than the time it takes to do math vs rolling dice is not universal or "uncontroversial."

Quotewild rolls bouncing under the sofa that have to be retrieved,

I have a solution for that one. Any dice that hit the floor become property of the house. If any player protests, remind them that the rabbit (or whatever household pet) may have pissed in the spot where the die landed.

QuoteYou mentioned a couple of times that sometimes dice can be rolled simultaneously to avoid sequential rolling. I pointed that out in my first response. I probably used the example of rolling both attack and damage dice at the same time. So there is no new ground here.

You say "sometimes." When wouldn't that be possible? The answer was the new ground I covered. Two reasons. Either because of the interposition of choice--which is not "wait" time since choosing is playing--or because the die type of the latter roll depends on the result of the former. I'm not 100% sure that I've never seen such a thing. But I don't recall any core mechanic that behaves that way.

QuoteI alluded to the difference between ablating hit points (whether of a person or object) which results in no material or profound status change such as something that ends the combat (like death or incapacitation) or that provides a significant change in advantage to one side or the other (like penalties of wounds). So no new ground there either.

I'm not 100% sure what you're saying here, so I'll just say what I think. You're free to agree or disagree. Damage matters to a shield just as it matters to hit points. Even if there are no wound penalties in the system. Because it affects further decision-making. If I'm walking around with 10 hit points and orcs be doing d8's, I know I can definitely survive one hit from an orc. If an orc then hits even just for 2 damage, that certainty goes out the window.

The same is true if I have 30 hit points. I know I can survive 3 hits from orcs. This may be just as potent information if the orcish front line consists of three attackers. I know if I come in striking range, I can survive one round of attacks. 6 hit points later, I lose that certainty.

The same is true if I have 30 hit points and a shield that has 20 hit points and can absorb up to 4 hit points per attack, up to 2 attacks per round. I know the shield will survive at least 2 rounds under the worst conditions. And I also know it will take at least 3 rounds to slay all three orcs. So how much damage the shield takes in the meantime could be make-or-break for the encounter.

QuoteI used the example of a system (like Runequest or Call of Cthulhu) where the chance of damaging a character in 6 point armor with a weapon doing 1d8+1 damage (simplified to ignore critical, special, and fumbles, hit locations, and breakage of parrying items) is
   (Attack%) x (1-Parry%) x (3/8)   

I understand the math involved. I just don't find it particularly relevant. There are generalized characterizations of every dice mechanic. They're not always accurate. If minimum damage, for example, is usually higher than armor ratings, then you don't get the multiplier effect for the base case. However, add in some modifiers (like +4 to armor for picking up a shield) and you suddenly achieve it.

As to defense rolls such as parrying, parrying in LA is not an automatic defensive action. It's a choice. So if I want to know my character's odds of hitting Parry Master McGee, it depends whether or not he's going to attempt to parry. I have no way of knowing that until I hit, so the only thing there is to calculate is my own skill roll.

And by the way, even this example is a little bogus because my desire for transparency of probability is NOT to help players calculate odds. It's so that when I'm using my judgment as GM to assign sit mods, I know what the probabilities will be as a reality check to make sure that my call is at least reasonable in my own opinion. When I'm assigning sit mods, it's not like I'm locking your hit bonus and the other guy's parry penalty (or vice versa) in tandem. I might give you a +20% bonus, and then, and I know in a very transparent way what sort of probability for success I'm assigning you. Now after that IF the other guy chooses to parry, maybe the situation calls for him to get a -10% penalty. Or maybe a -30%. Or maybe no penalty at all. Whatever I assign him, I'll also know in a very transparent way what his probability of parrying is going to be.

When it's all done with, in hindsight we can calculate what the odds were of you actually causing damage to him. And we can also calculate what it would have been had there been no modifiers and see what difference it made. And we can then also calculate the hit probability with and without those same modifiers for some hypothetical guy with a different skill level. And see what difference it made in that case. And we can compare the differences of the two cases to show, "Hey, these modifiers weren't linear." But in the moment? I have all the transparency of a linear mechanic to make my judgment calls.

QuoteThere are a number of entirely unrelated things here that you seem quite passionate about.

Not really.

QuoteBut frankly I don't understand how you think these things are remotely relevant to this thread or to anything I wrote.

I'm finding it ever more difficult to assume the position that your lack of understanding is honest. It was clearly clarifying my answer to your question and then illustrating some examples of how I mean it in practical terms.

You want bigger picture, circling back to the topic of the thread? Fine.

What I was getting at above when I said that I understand the math, it's just not accurate is that, yes, generically, there are ways you can model an exchange that might take place in a game. Or characterize the advantages and disadvantages of the different types of dice mechanics available.

What I am getting at is that even those vague generalities are just that, generalities. The "average" case is meaningless. Because it's not like I'm looking at a d20 and thinking of all the awesome things that I can do with it, and then all the terrible things I can do with it, then create a game around it that's a fair sample of both the good and the bad.

No. I'm going to do what any reasonable person would try to do. I'm going to create a game around the awesome things I can do with it. So it would be inaccurate to characterize the game according to the generalities one can make about the d20.

That's what's going on here. I prefer linear mechanics. I realize there are some things about them that some would consider downsides, especially relative to curve mechanics. To some degree I even agree the downsides do not exactly appeal to me. So what do I do? Do I just just accept I have to take the good with the bad? No. I find a way to get the features of curve mechanics that I want.

So, I mention successive rolls as a solution to that. Generically, do successive rolls have the problems you cite? Absolutely. So, same situation. Do I just accept that, or do I find a way to work around it?

You know the numbers. You know if my average guy does a minimum of 7 damage on a hit and the average armor absorption is 6, then there is no probability multiplier. The precise probability is easily knowable without calculation. And I can add or subtract modifiers from the hit roll. The modifiers will only be linear, but I'll still have transparency.

Now maybe instead the defender is an armored knight, with 12 points of armor. This radically changes the situation. Cuts the chance of causing hit point harm down by about half. Of course, a 1st level D&D character versus a negative AC doesn't exactly face linear probability modifiers. Repeating 20's. Probability is bounded by 0% and 100%. Linear probabilities--or any kind of curve, really, that is not asymptotic, will eventually buck those bounds and so some special handler will be needed. We all know that and accept it. We don't go around saying the THAC0 system is an example of a non-linear die mechanic.

Well, the analog in LA to the low skilled character against a "negative AC" is the potential that armor can negate all the damage from the attack. This is on the extreme end of the spectrum. If you want to say THAT particular case is not transparent, then fine. But it wouldn't be honest to then declare the entire system not transparent.

Hey welcome to the board Lunamancer.
(Sorry that the welcome thus far as been such as it is.)

Anyway, if I'm following the relevant sections of the conversation here it would be:

Quote from: nDervish;833787I like bell curves in my dice because they make modifiers more significant in the mid-range or when moving towards the mid-range and less significant as they move things out to the extremes.  You can't really do that with a flat distribution unless you want to break out calculators or lookup tables every time someone makes a roll.

Quote from: Lunamancer;867322I understand some people like how modifiers tend to be big towards the middle, small on the extremes. But this assumes you're limited to just + or - modifiers to difficulty. It's not the only option. Requiring successive rolls are also possible.

However, I don't think successive rolls usually have an effect on probability that's essentially similar to what bell-curves do, in any case.
I may be misunderstanding what you're proposing - I'm not familiar with Lejendary Adventures at all - but generally, successive rolls would be implemented as either:
- a reroll of the normal 'success chance' die or
- a separate roll for effect (equivalent to damage or whatever).

In the first case, you're not applying a multiplication of the base chance (e.g. a -3 penalty always inflicting a halving of success chance, say), rather you're squaring the base chance (n% becomes n-squared percent i.e. 50% drops to 25%, 70% to 49%, 90% to 81%).
I suppose, theoretically, you could instead have someone who succeeds flip a coin and then fail anyway on a head, or if its d100 have all odds then also fail, but it seems difficult to justify such a roll as anything other than arbitrary.

I'm not following why 'degree of success' has been brought up. I'm guessing you're assuming the bell-curve people are wanting a particular DoS (increasing margin of success) to be cumulatively rarer and that's why they want a bell-curve roll? I'm not of their kind ;), but I think its as likely they just want penalties for unusual difficulties to have a multiplicative effect on the actual success chance as to have +3 margin of success be twice as common as +0 successes.

Well, I often get the feeling that people are caught up on the idea of the "bell curve" more than the reality of the bell curve. Let's say we're doing a 2d10 roll-under system (for ease of calculation). And then look at what, say, the effects of a +5 modifier are:

Skill 2, jumps from 1% to 21%
Skill 5, jumps from 10% to 45%
Skill 8, jumps from 28% to 72%
Skill 11, jumps from 55% to 95%
Skill 14, jumps from 79% to 99%

I'm not 100% sure if people realize this is what the effect looks like, and if it's actually what they desire. Sure, skill 14 jumps only 20% while skill 11 jumps 40%, and skill 8 jumps 44%. Diminishing returns, right? Only lowly skill 2 also jumps only 20%. I'm not saying this is wrong. I'm asking if this is really what people think they're getting when they opt for the bell curve.

For me, the purpose of non-linear probability modifiers is so that I can adjust the situation in a way that may make an easy task have a decent chance of success for a low-skill character while not guaranteeing success for a high-skill character. (Or make things a heck of a lot more challenging for high skill characters while still allowing low-skill ones meaningful participation.)

For example, suppose I have an easy task, and there are three levels of player skill. Johnny B Bad with a base score of 20%, Joe Average with a 40% skill, and Dick Marvel with 80% skill.

Now say I calibrate it according to Joe Average, and I feel a 30% modifier makes it just right. Well, that gives Johnny B Bad a 50% chance of success, Joe Average 70%, and Dick Marvel goes off the charts with 110% (which the system probably truncates to 95% if I'm using a d20 mechanic).

But if instead of a "flat" 30% modifier, I introduce a successive die roll that cuts probability of failure in half, then Dick Marvel tops out at only 90%. This feels more right to me. I mean, yeah, it's an easy task. But it's not a sure thing. 10% is a good margin for failure. Joe Average ends up at the same 70%, and Johnny B Bad actually has a 60% chance. Again, this feels right. It is an easy task. Even someone unskilled should have better than a 50/50 shot.

I obviously can't speak for all lovers of the bell curve. Or even any of them. I can say the latter fits what I look for in non-linear probability adjustments more so than the real, honest-to-goodness bell curve does.

By the way, my three amigos under the 2d10 Bell Curve system would have Johnny B Bad with skill 7, Joe Average with skill 9.5, and Dick Marvel with skill 14. (Yes, I realize a fraction of a point wouldn't happen in actual play, but these mechanics never do translate precisely to one another.)

Calibrating for Joe Average would mean the Easy modifier would be +3.5. So odds of success for Johnny B Bad go from 21% to 50%, for Joe Average from 40% to 72%, and for Dick Marvel from 79% to 95/96%. I only calculated these as an afterthought, but it's eerily similar to just a straight d20 mechanic. Again, I ask, is this really the result people who opt for a bell curve mechanic are expecting?

Quote from: Lunamancer;868027You say "sometimes." When wouldn't that be possible?

Obviously when the result depends on the result of the first roll. I didn't mention that because it is or should be obvious. Without much thought, two examples of this come to mind.

• The dice rolled for damage in a number of games depends on the degree of success of the attack roll. In some games (RQ/CoC/BRP, H+I) it depends on a comparison of the degree of success of attack vs. defense.
• In games that use a roll and add mechanics like the wild die in WEG D6 the need for a second, third, or N+1 rolls depends on the result of the wild die in the Nth roll.

QuoteI'm not 100% sure what you're saying here, so I'll just say what I think. You're free to agree or disagree. Damage matters to a shield just as it matters to hit points. Even if there are no wound penalties in the system. Because it affects further decision-making. If I'm walking around with 10 hit points and orcs be doing d8's, I know I can definitely survive one hit from an orc. If an orc then hits even just for 2 damage, that certainty goes out the window.

Whether or not one can definitely survive is system dependent. I don't play systems where definite survival due to having enough hit points to shrug off a blow is likely. In most it isn't even possible for survival to be definite as opposed to being highly probable. That may affect how I look at what is relevant in calculating survival odds.

QuoteI understand the math involved. I just don't find it particularly relevant. There are generalized characterizations of every dice mechanic. They're not always accurate.

Within the limits of the simplification the math is fully generalized and accurate for the system I mentioned (RQ). The formula certainly allows for the case when the defenders armor is below the minimum damage roll. In that case that term in the equation becomes 100%. Perhaps you don't find cumulative probabilities relevant because you say you are solely and narrowly focused on the GM determining modifiers. I am not so narrowly focused. And neither are players. Note that a more complicated formula could be crafted for the unsimplified cases, but it would be significantly more complicated and since you don't seem familiar with RQ it wouldn't be especially informative.

QuoteAs to defense rolls such as parrying, parrying in LA is not an automatic defensive action. It's a choice. So if I want to know my character's odds of hitting Parry Master McGee, it depends whether or not he's going to attempt to parry. I have no way of knowing that until I hit, so the only thing there is to calculate is my own skill roll.

Parrying is not an automatic action in any system I have played. But assuming an opponent isn't going to parry by just ignoring the probability that your blow is parried gives a false idea of the likely outcome. For example, it treats the opponent with a 10% chance to parry the same as an opponent with a 90% chance to parry. Now I assume that attacking is also not an automatic action in your system of choice. (It isn't in any system I am familiar with.) In which case ignoring the parry chance is similar to treating two attackers with a 10% chance to hit and a 90% chance to hit as each automatically hitting since the defender doesn't know if they will or will not attack him.

QuoteAnd by the way, even this example is a little bogus because my desire for transparency of probability is NOT to help players calculate odds.

I didn't know that. Transparency is a term I see used in discussing the visibility of what is going on to two sides in a transaction or activity, e.g. transparency in how governmental decisions are made (https://www.transparency.org/). Here you are using transparency to describe your ability as the GM to understand what affect a modifier has on the probability of an outcome. There is no other side. That's probably not the word I would have used for that situation, but now I understand what you mean.

In any case, I do care about the transparency of probability for the player since that informs decision making in the game. The point I made was that sequential linear probabilities obscure the probability of the outcomes that are truly critical to player and GM decisions, i.e. Which side is likely to succeed? and Who is likely to survive and who is not? Perhaps you discount this because you are focused on GM assignation of modifiers in what seems to be a D&D derived class/level game where mere ablation of hits points without any definitive result that ends or significantly changes the combat, (e.g. a kill, incapacitation, disabling, penalty, or breakage result) is what occurs in the majority of successful attacks and but you seem to discount the value or importance in decision making of actually being able to assess what will end the combat and how likely that event is.

Personally, I am less concerned about the sort of transparency you describe for me as a GM. I already have a pretty well developed intuition about simple probabilities both linear and nonlinear based on a lot of experience and a bit of study. When picking up a new system, gaining an intuitive understanding of the odds is one of my major areas of attention. As a GM and I run practice simulations to learn the system and to hone my familiarity, especially when the system mechanic is not linear and obvious e.g. a simple d100 or d20 roll.  So for a game like Honor+Intrigue which uses a 2d6 roll I have a good intuition about the effect of a modifier of +N or –N to the chance of getting a success. I don't need to see or compute the exact probability to assign reasonable modifiers during play. In hindsight I can calculate the odds to see exactly what impact a modifier made. But it just isn't particularly relevant in the moment to assigning the modifier.

QuoteNot really.

No really. You mentioned a number of things you don't like

Quote from: Bren;867956wanting to "dumb down math", wanting to "do a billion things in one roll", "Vegas", "nerds", "high rollers", removing "randomness from character generation", or ignoring "race/class restrictions."

These dislikes do not seem related to linear mechanics or to issues of transparency. Some of the things you say you like (or at least you dislike their converse) aren't even better supported by linear mechanics.

• Not wanting to dumb down the math doesn't lead to a preference for linear mechanics. The advantage of linear mechanics is that they simplify the math compared to nonlinear mechanics. So anyone who prefers simpler math should want to use linear mechanics since they come closest to "dumb down math." The simplest random mechanic is the simple linear mechanic known as a coin flip.
• If you prefer random character generation, OD&D/AD&D is the classic random character generation RPG and it uses nonlinear mechanics (3d6) for the majority of the character generation.  
• And "race/class" restrictions is completely orthogonal to linear mechanics.

So not related in any way that I saw.

Quote from: Lunamancer;868027I never really did. I asked one specific question that dealt specifically with probability distributions for degrees of success. So far, nobody's admitted they even care about that, so I haven't asked for the opinion of anyone posting so far.

Well now there appears to be someone who cares (http://www.therpgsite.com/showpost.php?p=868028&postcount=44).

Quote from: Lunamancer;868034I'm not 100% sure if people realize this is what the effect looks like, and if it's actually what they desire.

Yes I realize the effect. Yes the effect is what I want or I wouldn't use that mechanic or that modifier.

QuoteAgain, I ask, is this really the result people who opt for a bell curve mechanic are expecting?

Again I answer, yes and yes.

It seems like what people say they want, approximately? Gathering from JoeNuttall and nDervishes' description of what they liked about bell-curves.
(I think JoeNuttall said he had a set his system to a fixed -3 =50%, after letting 10s on the 2d10 explode, ...though I don't think most Nd6 systems go through especially rigorous analysis).

Quote from: Lunamancer;868034But if instead of a "flat" 30% modifier, I introduce a successive die roll that cuts probability of failure in half, then Dick Marvel tops out at only 90%.

How would you do that specifically, though?
For instance, if you reduce Dick (80% base) failure chance by giving him a re-roll, with success generated by either roll, then his success chance would actually be 96% (20% chance of failure on either roll = 1 in 25 chance of failure overall).

Quote from: Bren;868037Well now there appears to be someone who cares (http://www.therpgsite.com/showpost.php?p=868028&postcount=44).

About the probability distribution, at any rate. I think most of the bell-curve people even, probably want a distribution change relating to success-chance, rather than degree-of-success.

Quote from: Lunamancer;868034Well, I often get the feeling that people are caught up on the idea of the "bell curve" more than the reality of the bell curve.

You've not commented on the bell curve in my post, which this doesn't apply to. There's a link in my sig "Open Dice" to the system which talks about the issue in your post, and how I solved it.

One side-effect of the exponential drop-off I mention in other blog posts is the consequence of having a roll to hit followed by a roll for damage. Bren talked about how probability wise this means that to calculate your chances you have to multiply the probabilities for each roll. But with logarithms multiplication becomes addition.

That is, since +3 in either roll has the effect of doubling the chance of success, it (mostly) doesn't matter where you have your bonuses (except for flavour and tenstion in the game). That means you can see how good you by just adding your bonuses, and no-one has to understand probabilities.

So the end result is actually more transparent than with two linear rolls.

Quote from: Bloody Stupid Johnson;868051How would you do that specifically, though?

Roll twice. Take best roll of two. Dick has .2 x .2 = .04 chance of failure. Joe has a .6 x .6 = .36 chance of failure. Johnny has a .8 x .8 = .64 chance of failure. So for success, Dick = 96%, Joe=64%, Johnny=36%.

But as you point out, the numbers he gave don’t match what is calculated by taking the best of two rolls or by using a rule like you have to fail two rolls to actually fail. So either he’s using a different method or his math is wrong.

Quote from: JoeNuttall;868058But with logarithms multiplication becomes addition.

That's the nice thing about logarithms alright. It's almost like they were created* just so people didn't have to do difficult multiplication by hand.


* If you thought I should have used a different verb than "created" like say, "discovered" then as far as the ontology of math you are Platonist.

Quote from: JoeNuttall;868058You've not commented on the bell curve in my post, which this doesn't apply to. There's a link in my sig "Open Dice" to the system which talks about the issue in your post, and how I solved it.

It's hard to make heads or tails of it without seeing the exact probabilities. I mean what I get based on the graph and estimating probabilities is that the cumulative probability still has an inflection in the curve. So that means both extreme high and extreme lows of the scale would have modifiers change probability of "success" by only a small percentage relative to points closer to the peak of the bell (or inflection point in the graph that link shows).

So if you have the exact probabilities, would you mind looking at what TN is associated with a 40% chance of success, how much of a bonus would that character need to have a 30% chance. Then apply that same bonus to someone whose base TN is such that the person has a 20% chance of success. What is that person's modified probability? And then repeat for someone whose base skill is such that normal chance for success is 80%. What is that final probability?

QuoteThat is, since +3 in either roll has the effect of doubling the chance of success, it (mostly) doesn't matter where you have your bonuses (except for flavour and tenstion in the game). That means you can see how good you by just adding your bonuses, and no-one has to understand probabilities.

So here I'm not following at all. I see in the link a 3 point adjustment is supposed to double/half probability of success. I can see how that might work for higher base TNs. It definitely does not work on the lower TN end of the scale.

I know for certain the only way to get a "2" is rolling 1 on each die right out of the gates. Which means if your TN is 3, you have a 99% chance of success. If you apply a -3 modifier to the dice, the odds of success (I'm guestimating) goes to the very high 80's. That is neither dropping the probability of success by half, nor doubling the probability of failure.

In essence, while you may have solved the problem for one end of the curve, the curve is still has the characteristic I pointed out about a regular bell-curve. Modifiers have the biggest percent-wise impact on the mid-range (or peak range or inflection range, whatever you want to call it) and relatively lower impact on BOTH high ends and low ends of the skill range.

Again, I say it isn't bad or wrong. I'm just not sure that's how all gamers who choose bell curve intend things to work.

Quote from: Bloody Stupid Johnson;868051How would you do that specifically, though?
For instance, if you reduce Dick (80% base) failure chance by giving him a re-roll, with success generated by either roll, then his success chance would actually be 96% (20% chance of failure on either roll = 1 in 25 chance of failure overall).

You generally don't make the exact same skill check twice. If I want to cut in half probability of failure, I flip a coin.

The concept actually arises completely organically in certain situations. Suppose a character is playing a game of chance where you place a wager and have a 1 in 3 chance of winning (you have to pick one of three boxes where one of them, determined at random, has the prize). But I have a character with Luck ability at 25%.

Do I make the character roll luck to win? Failure means loss? That would be silly. Your reward for having Luck is getting only a 25% chance to win rather than 33%.

Instead I could say if you pass your luck check, then by luck you choose the right box. But if you fail your luck check, you are left with the same chance anyone else would have. What this is doing is diminishing your chance of failure (from the perspective of a luck skill check) to two-thirds that of normal.

So if you have zero luck ability, your odds of getting the right box is 33%. The logical amount any person should have. A boost of 33% relative to 0% skill.

If you have 25%, your odds of getting the right box is 50%. A boost of 25% relative to skill 25%.

If you have 70% Luck, your odds of getting the right box go up to 80%. A boost of just 10% relative to skill.

Another situation where this comes up organically is I had borrowed the "firing into melee" rule from AD&D 1st Ed, where (adjusted for size) each person has an equal of being hit. I modified this for the Lejendary Adventure system, which has an Archery ability to say random selection only occurs when the ability check fails. You might still get your exact target by random selection, though. (I also added Archery as a proficiency to my AD&D games, it has this same effect.)

So if there are 4 potential targets, Johnny B Bad's probability of getting the right one (with his 20% skill) is 40%. For Joe Average (with his 40% skill) is 55%. Dick Marvel (with his 80% skill) is boosted to 85% of hitting the right target. Again, we see the percentage effects of positive adjustments have diminishing returns the higher in skill you are. This is consistent whether you're on the low, average, or high end of the scale.


I should also point out, because I feel this starting to get lost the deeper these discussions go on, that I still like linear modifiers. For some situations, maybe even a lot of them, I find them more appropriate.

Quote from: Lunamancer;868104Another situation where this comes up organically is I had borrowed the "firing into melee" rule from AD&D 1st Ed, where (adjusted for size) each person has an equal of being hit. I modified this for the Lejendary Adventure system, which has an Archery ability to say random selection only occurs when the ability check fails. You might still get your exact target by random selection, though. (I also added Archery as a proficiency to my AD&D games, it has this same effect.)

So if there are 4 potential targets, Johnny B Bad's probability of getting the right one (with his 20% skill) is 40%. For Joe Average (with his 40% skill) is 55%. Dick Marvel (with his 80% skill) is boosted to 85% of hitting the right target. Again, we see the percentage effects of positive adjustments have diminishing returns the higher in skill you are. This is consistent whether you're on the low, average, or high end of the scale.

It looks like you are saying that if Johnny is shooting at one single opponent with no one else in the way he has a 20% chance to hit the person he is aiming at. But if there are three other people around his chance of hitting the person he is aiming at is effectively 40%. Is that correct?

Quote from: Lunamancer;868097It's hard to make heads or tails of it without seeing the exact probabilities.

100%   99.00%   97.00%   94%   90%   85%   78%   71%   62%   53%   44%   35%   28%   22%   16%   12%   9%   6%   5%   4%   3.30%   2.60%   2.00%   1.50%   1.20%   0.90%   0.70%   0.60%   0.50%   0.40%

Quote from: Lunamancer;868097I mean what I get based on the graph and estimating probabilities is that the cumulative probability still has an inflection in the curve. So that means both extreme high and extreme lows of the scale would have modifiers change probability of "success" by only a small percentage relative to points closer to the peak of the bell (or inflection point in the graph that link shows).

You're missing what I said in my first post:

Quote from: JoeNuttall;867706For anything with a <50% chance of success, +3 means you double your chances of success, -3 means you halve it. So +1 and -1 always have the same effect.

It's not logarithmic for things you have a greater than 50% chance of success at. That's by design.

Quote from: Lunamancer;868097So if you have the exact probabilities, would you mind looking at what TN is associated with a 40% chance of success, how much of a bonus would that character need to have a 30% chance. Then apply that same bonus to someone whose base TN is such that the person has a 20% chance of success. What is that person's modified probability? And then repeat for someone whose base skill is such that normal chance for success is 80%. What is that final probability?

13+ is 35% chance of success, 14+ is 28% chance of success, so +1 makes you only 80% as likely to succeed.
16+ is 16% chance of success, 17+ is 12% chance of success, so +1 makes you 75% as likely to succeed.
As you can see from the graph the precise value of +1 varies slightly, but it's always around 80%.

As I said before, the system doesn't behave like that if your success rate is 80% as that's above 50%. The value of a +1 drops gradually to almost nothing.

Quote from: Lunamancer;868097In essence, while you may have solved the problem for one end of the curve, the curve is still has the characteristic I pointed out about a regular bell-curve. Modifiers have the biggest percent-wise impact on the mid-range (or peak range or inflection range, whatever you want to call it) and relatively lower impact on BOTH high ends and low ends of the skill range.

No, it doesn't happen at one end and at the other end it is there by design. I don't talk about why in that blog post as I thought that would overcomplicate the issue.

I originally had a pure logarithmic system but I didn't like that +1 changed you abruptly from 100% success to 80% success. I thought about that for a long time before deciding that wasn't what was wanted, so I replaced that with a 2-ended open system which was logarithmic for success in one direction and failure in the other. That was definitely a move in the right direction, but in practice no-one cared about the subtle difference between 98% success and 99% success, so I went for this third system as it was simpler.
 

Quote from: Lunamancer;868097Again, I say it isn't bad or wrong. I'm just not sure that's how all gamers who choose bell curve intend things to work.

What I've found out is that whether players like a mechanic or not is a combination of several things, and when writing a game you have to be prepared to chuck the coolest idea you ever had because it just didn't survive a playtest.

@Lunamancer: Thanks for clarifying.
Its working in those situations. I have my doubts that it can be applied across a range of situations though, without the extra die roll seeming fairly tacked-on in many of them.
I get that on the linear vs. nonlinear adjustments, with your method -assuming its justifiable - of course you can apply either form of modifier, whereas for the multiple-dice-roll its more difficult to go the other way and apply a 'linear' modification - short of having specific rolls that revert to d20 rather than 2d10, or the equivalent. And transparency is clearly better for linear rolls as well.

Quote from: Bren;868109It looks like you are saying that if Johnny is shooting at one single opponent with no one else in the way he has a 20% chance to hit the person he is aiming at. But if there are three other people around his chance of hitting the person he is aiming at is effectively 40%. Is that correct?

I'm assuming the roll to hit the correct person in melee would have to be on top of the normal to-hit roll? Or, at least there'd need to be some sort of to-hit penalty for firing into melee as well.

Quote from: Bloody Stupid Johnson;868125I'm assuming the roll to hit the correct person in melee would have to be on top of the normal to-hit roll? Or, at least there'd need to be some sort of to-hit penalty for firing into melee as well.

One would hope.

Based solely on tactile aesthetics, I have always preferred the feel of a pair of dice (of any sides) in my hand to that of a single die.  This probably explains my fondness for 2d6 systems.

Quote from: Bloody Stupid Johnson;868125@Lunamancer: Thanks for clarifying.
Its working in those situations. I have my doubts that it can be applied across a range of situations though, without the extra die roll seeming fairly tacked-on in many of them.

One thing about having a wealth of options for modifying probabilities for a given situation is it makes you think about WHY you're assigning a modifier. And I think if you stop and think about it, there are plenty of applications.

20 years ago when we were playing CyberPunk, we were afraid of driving. Every time we decided to get into a car, the GM made us make driving checks. On the one hand, it's reasonable. Accidents happen every day in even mundane travel. There should be some probability of that in the game.

On the other hand, it was absurd. He wasn't the greatest GM. Even if you maxed out your driving skill, you still had a 1 in 10 chance of failing the check. Race car drivers don't crash THAT frequently.

A more reasonable approach would be to have "wandering monster" checks while you're on the road. These could be things like traffic jams, rude drivers, etc. There's a small chance of especially dangerous road conditions that would actually require a check. This would be another organic example of factoring in a second probability check to reduce the rate of failure.

You are in essence reducing the opportunity for failure. And that is the case in the magic box game or firing into melee. There's a natural chance of just getting the right one by dumb luck, even before it becomes a question of skill.

Consider an attack where there is an active attempt at a parry. Only do something radical. View it from the perspective of the defender. If the attacker has a 50/50 hit probability, the probability that the attacker misses diminishes the opportunity to fail at your defense roll.

This sort of thing is virtually everywhere.

QuoteI get that on the linear vs. nonlinear adjustments, with your method -assuming its justifiable - of course you can apply either form of modifier, whereas for the multiple-dice-roll its more difficult to go the other way and apply a 'linear' modification - short of having specific rolls that revert to d20 rather than 2d10, or the equivalent. And transparency is clearly better for linear rolls as well.

Another way to get "curve" results out of a d20 mechanic is to instead roll 3d20 and take the middle result.

QuoteI'm assuming the roll to hit the correct person in melee would have to be on top of the normal to-hit roll? Or, at least there'd need to be some sort of to-hit penalty for firing into melee as well.

Yes. In AD&D, due to the chaos of melee, firing into melee calls for the target to be chosen randomly. That would mean the apt comparison is 40% likelihood of the intended target being the one selected in a group of 4, vs 100% likelihood in a group of 1. The hit roll still has to be high enough to hit the AC for whoever the target is. The idea of bringing in a proficiency is so instead of getting even odds, you skew them in your favor.

Quote from: Lunamancer;868176Yes. In AD&D, due to the chaos of melee, firing into melee calls for the target to be chosen randomly. That would mean the apt comparison is 40% likelihood of the intended target being the one selected in a group of 4, vs 100% likelihood in a group of 1. The hit roll still has to be high enough to hit the AC for whoever the target is. The idea of bringing in a proficiency is so instead of getting even odds, you skew them in your favor.

Assuming the targets are equally likely, the random probability of the intended target being chosen in a group of 4 is 25% not 40%.

Quote from: Bren;868192Assuming the targets are equally likely, the random probability of the intended target being chosen in a group of 4 is 25% not 40%.

Not for the character with 20% Archery ability.

Quote from: Lunamancer;868197Not for the character with 20% Archery ability.

Then you don't understand what the words "firing into melee calls for the target to be chosen randomly" means. Choosing the target randomly with, as I said, each target being equally likely means there is only a 25% chance to hit the target. Because you are randomly determining who gets hit, assuming anyone gets hit.

If what you meant to say was the following.

   There is a 20% chance for the crappy archer to hit his target and if he misses his intended target, then he hits some target anyway, rolling randomly among the possible targets to find out which target he hit. In that case even when he misses he still has a 25% chance to hit the intended target through dumb luck.*

Then you should have actually said that instead of ""firing into melee calls for the target to be chosen randomly".


* And piss-poor rules design.

Quote from: Bren;868202Then you don't understand what the words "firing into melee calls for the target to be chosen randomly" means.

I said what I meant and I meant what I said. I'm sorry if you have trouble following a conversation. That's really not my problem.

Quote from: JoeNuttall;868114100%   99.00%   97.00%   94%   90%   85%   78%   71%   62%   53%   44%   35%   28%   22%   16%   12%   9%   6%   5%   4%   3.30%   2.60%   2.00%   1.50%   1.20%   0.90%   0.70%   0.60%   0.50%   0.40%

Using these figures, for the sake of comparison, I ran through the example of Johnny B Bad, Joe Average, and Dick Marvel. Calibrated for Joe Average (so we're talking about that awkward +3.5 modifier for the sake of comparison), under this system Johnny B Bad would go from 22% to 49%, Joe Average from 40% to 71%, and Dick Marvel from 78% to 95/96%.

Not all that different from 2d10, which is unsurprising since yours is basically a 2d10 system with added features.

I do have to circle back, though, to the idea that once you truncated the probabilities for a totally linear system to fit a d20 system, the probabilities end up nearly identical.

Now an important difference speaks directly to what appears to have been one of your major design goals. To leave nothing impossible, instead of an arbitrary truncation, your tail end tapers off into finely patterned probabilities.

I'm just trying to communicate that the real difference between bell-curve and linear systems is NOT really substantial in the big picture. It matters for those extreme ends. Personally, I don't understand the obsession with extremes because I would imagine most of the game takes place closer to the middle. To me, it seems that's where a system or core mechanic truly needs to shine.

QuoteYou're missing what I said in my first post:

I thought I'd seen something like that earlier up-line. No worries. I knew you'd correct me.

QuoteWhat I've found out is that whether players like a mechanic or not is a combination of several things, and when writing a game you have to be prepared to chuck the coolest idea you ever had because it just didn't survive a playtest.

So this is me with my cynical hat on. The reason why I just prefer a linear mechanic over something like yours is probably the same reason why a lot of gamers prefer yours over something linear. It's pure mathurbation. Not function. The AD&D 1st Ed attack matrix produces a close approximate of what you've got, but it's got to do this thing with 6 repeating 20's to do it. As a mathematical function, it's less clean.*

A key difference and tradeoff is that under a d20 system, the hypothetical modifier is +6, vs +3.5 in your system (or a regular 2d10 system for that matter) shows that for the common range of play, your system tends to be more grainy, your mechanic having been specialized to a high degree of resolution on extremely improbable events.

This is to be expected because adding another die doesn't change the standard deviation by much. So a 2d10 system has a graininess more similar to a 1d10 system than a 1d20 system. Again, I understand that you did successfully achieve your design goal. But my preference, being d100 then d20 then d10 is in that order of preference mainly due to graininess.


* As a side note, I created a math shortcut so I wouldn't have to look up hit tables, where I calculate purely from THAC0. To do this, I simply treat a natural 20 as if it were really a 25. That simulates the 6 repeating 20's. Once I did that, though, I pondered further tinkering. Instead of natural 20 always getting a 5 point boost, why not a d10 variable? So it's a limited-depth diminished exploding d20 mechanic that gives extreme low probabilities more of a tapering off effect.

Nothing that you posted makes any sense, showing a deeply flawed understanding on every level followed up by

Quote from: Lunamancer;868213So this is me with my cynical hat on. The reason why I just prefer a linear mechanic over something like yours is probably the same reason why a lot of gamers prefer yours over something linear. It's pure mathurbation.

No that's you with your rude and foolish and blinkered hat on.

Quote from: Lunamancer;868205I said what I meant and I meant what I said. I'm sorry if you have trouble following a conversation. That's really not my problem.

What you said was self-contradictory.

Whether you intended to contradict yourself for some unknown reason or whether you just don't understand what you've said doesn't matter as in either case, there isn't any productive conversation to be had with you.

Quote from: Lunamancer;868034Well, I often get the feeling that people are caught up on the idea of the "bell curve" more than the reality of the bell curve. Let's say we're doing a 2d10 roll-under system (for ease of calculation). And then look at what, say, the effects of a +5 modifier are:

Skill 2, jumps from 1% to 21%
Skill 5, jumps from 10% to 45%
Skill 8, jumps from 28% to 72%
Skill 11, jumps from 55% to 95%
Skill 14, jumps from 79% to 99%

I'm not 100% sure if people realize this is what the effect looks like, and if it's actually what they desire. Sure, skill 14 jumps only 20% while skill 11 jumps 40%, and skill 8 jumps 44%. Diminishing returns, right? Only lowly skill 2 also jumps only 20%. I'm not saying this is wrong. I'm asking if this is really what people think they're getting when they opt for the bell curve.

As I said in an earlier post in the thread, I don't care what the actual percentages are, but, yes, in general terms, that is indeed what I'm looking for and what I expect to get.

Also, when I do think about the actual numbers, I tend to think about relative rather than absolute change - skill 2 becomes 21 times as likely, skill 5 is 4.5 times as likely, skill 8 is about 2.6 times as likely, skill 11 is 1.73 times as likely, and skill 14 is 1.25 times as likely.

Quote from: Lunamancer;868034For me, the purpose of non-linear probability modifiers is so that I can adjust the situation in a way that may make an easy task have a decent chance of success for a low-skill character while not guaranteeing success for a high-skill character. (Or make things a heck of a lot more challenging for high skill characters while still allowing low-skill ones meaningful participation.)

For me, the idea of a task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "outlier" and "contrived example".  If a rookie archer has a 50/50 chance to hit a target from a given distance, then a marksman is going to hit (and probably bullseye) that target every single time under the same conditions, barring some extreme circumstance (i.e., rolling a "fumble").  Or, going the other direction, an operation which would be tricky for a skilled surgeon is going to be botched every single time if someone with only basic first aid training attempts it, barring a miracle (i.e., rolling an "automatic success").

Quote from: JoeNuttall;868218Nothing that you posted makes any sense, showing a deeply flawed understanding on every level followed up by

No that's you with your rude and foolish and blinkered hat on.

I don't expect everyone to be a genius, so if you didn't grasp something that's one thing. But given your attitude, it seems like you didn't even try. Dishonesty is less forgivable.

But because I am not the rude one here, I will give you the benefit of the doubt and attempt to recap what I wrote into something more visual. "Your way" is based on the probabilities you posted for me for your mechanic. "My way" is the AD&D 1st Ed combat matrix with the little houserule I proposed to vary up the 6 repeating 20's.

Quote from: nDervish;868253As I said in an earlier post in the thread, I don't care what the actual percentages are, but, yes, in general terms, that is indeed what I'm looking for and what I expect to get.

Your design goal is your design goal, and that's unassailable. But ignoring the actual percentages? The players will care about them. Not the exact percentages, but it's not like seeing the number "15" on the character sheet for a skill will carry equal meaning regardless of whether they're playing GURPS or CoC. Players are sensitive to "whiff factor", especially when it comes to characters' primary skill. Your opinion, as a designer or GM, doesn't change their opinions. You have to address the actual percentages at some point.

QuoteFor me, the idea of a task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "outlier" and "contrived example".

Given that I've listed several organic examples (and I could have gone on forever listing more) the "contrived" argument doesn't even seem worth addressing unless you want to reference a specific example. So let's skip over to the "outlier" argument then.

I pointed out that bell-curve systems have smaller intervals on the extreme ends, larger intervals in the middle.

80% of all rolls on 2d10 will fall in between 6 and 16, or 11 possible results. Beyond which we begin to enter the realm of outliers. 80% of all rolls on 1d20 will fall in between 3 and 18, or 16 possible results. It seems the linear mechanic in this case yields over 40% more points of distinction than the curve one.

The reverse is also true. The 2d10 mechanic has 4 points of distinction to cover the highest 10% (17, 18, 19, and 20) and 4 points of distinction to cover the lowest 10% (2, 3, 4, and 5) whereas the d20 mechanic only has 2 distinctions for each (1-2 and 19-20).

My position is that I DO think outliers are important. That's why I mentioned in my first post on this thread some ways to mimic some of the benefits of  curve mechanics when using a linear one. So to come back and say, "Well, that's only outliers"? Well, duh! That's the whole point.

Quote from: Lunamancer;868304Your design goal is your design goal, and that's unassailable. But ignoring the actual percentages? The players will care about them. Not the exact percentages,  but it's not like seeing the number "15" on the character sheet for a skill will carry equal meaning regardless of whether they're playing GURPS or CoC.

When I say "actual percentages", I mean "exact numeric representations of the probability".  If I need to roll a certain number, then yes, I care about whether it's "likely" or "unlikely", but not about whether or not it's a 74.456468465% chance vs. 72.5686863%.

In GURPS, I know that needing to roll a 15 or better is very likely to succeed without having to also know that it's a... umm... (consults anydice.com)... 95.37% chance.  Not being able to express the chances as a percentage does not in any way hinder my ability to have a general sense of whether it's likely or not.

Quote from: Lunamancer;868304Given that I've listed several organic examples (and I could have gone on forever listing more) the "contrived" argument doesn't even seem worth addressing unless you want to reference a specific example.

I just did a quick scan over your contributions to this thread.  I found two specific examples, both of which are distinguished by being essentially luck-based, namely playing a game of chance and determining who gets hit by a shot fired into melee.  Given that "several" usually means more than two, I assume there must be others that I missed.  Please point me in their general direction.

As to the two examples I did find, I was talking about how likely a low-skilled character is to succeed vs. the chance of a high-skilled character to do so.  Since skill has little-to-no effect on a luck-based outcome, I don't consider luck-based situations to be germane.

Quote from: Lunamancer;868304My position is that I DO think outliers are important. That's why I mentioned in my first post on this thread some ways to mimic some of the benefits of  curve mechanics when using a linear one. So to come back and say, "Well, that's only outliers"? Well, duh! That's the whole point.

Oh, come on...  I said that I considered a set of situations (not outcomes or probabilities) to fall between "outlier" and "contrived example".  In what way is it unclear that I meant "outlier" in the sense of "something that lies outside the main body or group that it is a part of, as a cow far from the rest of the herd, or a distant island belonging to a cluster of islands" (the very first definition given for "outlier" on dictionary.com), not in the statistical sense?

So, here, let me rephrase for you:

For me, the idea of a skill-based task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "extremely unusual situation which is unlikely to come up often, if at all, either in-game or in real life" and "contrived example".

Quote from: Lunamancer;868287I am not the rude one here

Err.. excuse me - you just said this about my method:

Quote from: Lunamancer;868213It's pure mathurbation.

Are you really surprised that this ended the conversation abruptly?

Seems like we've hit the point of diminishing returns on this thread. Oh well.
 
Thus far I think the highlight for me was probably discussion on implementing Luck rolls, inasmuch as the idea of needing a secondary unmodified random roll as well to keep odds consistent).
(Though it would depend on the relative scaling of the Luck attribute as well; if a normal person has an 0% Luck you can freely call for a Luck roll as an extra; whereas if it has a non-zero default for theoretically-typical luck then an additional check gives too high a chance of the right box. In that case it'd be a matter of just modifying the Luck roll by enough to raise a default % up to the expected odds. Either way works in context.)

I have a vague sense of something else in here, but nothing's quite crystallized as yet.

Quote from: JoeNuttall;868312Err.. excuse me - you just said this about my method:

Are you really surprised that this ended the conversation abruptly?

No. I said that's a potential reason why some would like it. The context of the post as a whole made that abundantly clear. Normally, I would be understanding and see how you got the wrong thing out of it, but since you were dishonest in your last post and have refused to be a gentleman (or add anything on topic) in the face of my giving you the benefit of the doubt, I have no problem with the conversation ending right here. I'm just not going to let you putting words in my mouth or claiming I'm the rude one in this go unchallenged.

Quote from: nDervish;868311When I say "actual percentages", I mean "exact numeric representations of the probability".

Right. I wouldn't expect a player to know just through experience the difference between, say, 20% and 25%. One of the figures I track in the real world related to job performance, over a long period of time, has very consistently averaged 33%. But there are certainly data clusters where it looks more like 25% or even 20%. And others where it looks like 40 or 50%. That's why I use my lab rats, Johnny, Joe, and Dick, which have substantial skill differences between them, and I want to see how the probability shapes when a substantial skill modifier is applied. This is not for testing the minutia.

QuoteI just did a quick scan over your contributions to this thread.  I found two specific examples, both of which are distinguished by being essentially luck-based, namely playing a game of chance and determining who gets hit by a shot fired into melee.  Given that "several" usually means more than two, I assume there must be others that I missed.  Please point me in their general direction.

Bloody Stupid Johnson made the same point. I respond in Post #59 and name two more examples. Probably more importantly, I describe what's happening conceptually as cases where something about the situation itself denies the opportunity for failure. (The flip side is that in some cases something about the situation itself denies the opportunity for success.)

To give yet another example, I observed in a factory setting, first-year rookie machine operators would do just as well senior level operators. As long as the machines were running smoothly and there were no changeovers. Because in such situations, their skills as machine operators are not being tested at all. In fact, sometimes, due to peripheral skills, the newbs could even out-perform the veterans. However, introduce a change over or machine malfunction, the rookies get buried.

Of course, to properly manage the maintenance department, they keep records on frequency and severity of malfunctions. So there is a knowable, probabilistic framework in which the frequency and degree to which an operators skill will be tested.

QuoteFor me, the idea of a skill-based task being easy for an unskilled character while not guaranteeing success for a high-skill character sits somewhere in the space between "extremely unusual situation which is unlikely to come up often, if at all, either in-game or in real life" and "contrived example".

To continue with my factory example, I would agree (or rather not disagree) with you here in terms of the degree a machine problem the operator faces. If a rookie can most likely handle it, then a senior operator can definitely handle it. No argument there. However, if the factory foreman is called away for a couple of hours, what are the odds he's going to come back to a mess? Well, that would depend on whether or not there is a machine malfunction at all, and if so, only then do we need to ask how bad and how skilled is the operator handling it.

Quote from: Lunamancer;868375No. I said that's a potential reason why some would like it. The context of the post as a whole made that abundantly clear. Normally, I would be understanding and see how you got the wrong thing out of it, but since you were dishonest in your last post and have refused to be a gentleman (or add anything on topic) in the face of my giving you the benefit of the doubt, I have no problem with the conversation ending right here. I'm just not going to let you putting words in my mouth or claiming I'm the rude one in this go unchallenged.

You were insulting people who liked my method, not the method itself? This means you weren't being rude?

Quote from: Lunamancer;868287I don't expect everyone to be a genius, so if you didn't grasp something that's one thing. But given your attitude, it seems like you didn't even try. Dishonesty is less forgivable.

I think we both understand where my "attitutude" came from.

You said that your system (using a second roll) could give a fixed proportion (for example 50%) of successes being a complete success, and this didn't work in any system with a probability curve.

I said it that would work using my system for probabilities less than 50%.

Quote from: Lunamancer;868213Using these figures, for the sake of comparison, I ran through the example of Johnny B Bad, Joe Average, and Dick Marvel. Calibrated for Joe Average (so we're talking about that awkward +3.5 modifier for the sake of comparison), under this system Johnny B Bad would go from 22% to 49%, Joe Average from 40% to 71%, and Dick Marvel from 78% to 95/96%.

In the three examples you give from my numbers, one of them (Dick) has more than 50% chance of success so can be ignored. You also used the modifiers to make Joe Average to go over 50%. Also we're not considering the number of percentage points it moves, we're talking about the proportion it changes by.

To apply this to the original concept - what proportion of Joe or Jonny's successes are complete successes - you have to apply the modifier in the reverse direction to the one you applied it in.

For Joe Average with 40% chance of success, beating the target by +3.5 would give 16% chance of complete success. Johnny with a 22% chance of success would have 8% chance of complete success.

That means for successes by Joe Average, 16/40=39% are complete successes. For Johnny 36% are.

Quote from: Lunamancer;868213Not all that different from 2d10, which is unsurprising since yours is basically a 2d10 system with added features.

For target values less than 17 they are very close. Beyond that the graphs of cumulative probabilities look fairly close, but are actually proportionally quite different. For example getting 18+ is 9% in my system, but only 6% with 2d10. That looks close in the graph but is only two-thirds as likely.

This means the effect of +3 difficulty in both systems has quite a different effect.

12+ in my system is 44%, whereas with 2d10 it is 45%. Needing to beat it by 3 makes those percentages 22% and 21% respectively. So in both cases the chance of complete success given success would be half.

For 17+ in my system it is 12%, and with 2d10 it is 10%. Still not much difference – but the chance of beating it by 3 are 5% and 1% respectively.

Hence the chance of complete success given success stays as roughly half in my system, but becomes only 1 in 10 with 2d10.

That is, the proportional effect that a bonus gives you for middle probabilities in a 2d10 system is preserved in my system all the way to the high end.
 

Quote from: Lunamancer;868213I do have to circle back, though, to the idea that once you truncated the probabilities for a totally linear system to fit a d20 system, the probabilities end up nearly identical.

So 12+ is 45%, 15+ is 30%, so of successes at 12+, 67% of them would be complete successes.
Whereas 17+ is 20%, 20+ is 5%, so of successes at 17+, 25% of them would be complete successes.

So, in the respect that we were discussing, the systems are quite different.

Quote from: Lunamancer;868213Now an important difference speaks directly to what appears to have been one of your major design goals. To leave nothing impossible, instead of an arbitrary truncation, your tail end tapers off into finely patterned probabilities.

For the discussion at hand, the open-ended nature of my system is only relevant in so much as a logarithmic system *has* to be open-ended.

Quote from: Lunamancer;868213I'm just trying to communicate that the real difference between bell-curve and linear systems is NOT really substantial in the big picture. It matters for those extreme ends.

Except that all the examples I gave presenting differences were *not* at the "extreme" ends.

Quote from: Lunamancer;868213The AD&D 1st Ed attack matrix produces a close approximate of what you've got, but it's got to do this thing with 6 repeating 20's to do it. As a mathematical function, it's less clean.*
* As a side note, I created a math shortcut so I wouldn't have to look up hit tables, where I calculate purely from THAC0. To do this, I simply treat a natural 20 as if it were really a 25. That simulates the 6 repeating 20's. Once I did that, though, I pondered further tinkering. Instead of natural 20 always getting a 5 point boost, why not a d10 variable? So it's a limited-depth diminished exploding d20 mechanic that gives extreme low probabilities more of a tapering off effect.

The system you present is well known, it's the standard open ended system, as popularised by Rolemaster (1980) – but they used percentiles.

The numbers for the two cases (12+ and 17+) are identical to the plain d20 system.

Quote from: Lunamancer;868376Bloody Stupid Johnson made the same point. I respond in Post #59 and name two more examples.
...
To give yet another example, I observed in a factory setting, first-year rookie machine operators would do just as well senior level operators.

The point I was trying to make which started this side-thread was that, in a skill-based situation where a rookie has a good chance of success, I would expect an expert to be practically guaranteed to succeed.  The examples from #59 (driving, making an active parry) and the factory example all fit this expectation:

- In a situation where a rookie driver has a good chance to not crash, an expert driver will almost certainly not crash.

- If a rookie has a good chance to parry a certain blow, an expert swordsman is practically guaranteed to be able to parry that same blow.

- If a first-year machine operator can successfully operate a given machine, then it's nigh-unthinkable that someone who's been running the same kind of machine for years will screw it up.

Quote from: Lunamancer;868376However, if the factory foreman is called away for a couple of hours, what are the odds he's going to come back to a mess? Well, that would depend on whether or not there is a machine malfunction at all, and if so, only then do we need to ask how bad and how skilled is the operator handling it.

Yes, agreed.  But, from the operator's point of view, whether there's a malfunction and how bad the malfunction might be is essentially luck-based.  If there's no malfunction, then there's no need to make a skill roll at all.

What I'm disputing the (organic) existence of is situations where a skill roll would be made in which "Joe Average ends up at the same 70%, and Johnny B Bad actually has a 60% chance.", but "Dick Marvel tops out at only 90%", as you proposed in post #45 of this thread.  If they're machine operators and a malfunction occurs which Johnny B Bad has a 60% chance of handling, then Dick Marvel is no marvel if he has a 10% chance of failing to deal with it.

But, really, I think we're talking about different things here.  You seem to be focused on the operator's chance to get through his shift without problems (regardless of whether that's the result of him handling a malfunction or of there being no malfunction at all), while I'm talking only about his ability to handle a malfunction if and when one occurs.  The case where everything goes smoothly because there wasn't a malfunction at all is relevant to the case you appear to be making, while it's completely outside of mine, since I wouldn't make a skill roll in that case, thus rendering any modifiers which might be applied to the roll irrelevant.

Quote from: nDervish;868421The case where everything goes smoothly because there wasn't a malfunction at all is relevant to the case you appear to be making, while it's completely outside of mine, since I wouldn't make a skill roll in that case, thus rendering any modifiers which might be applied to the roll irrelevant.

I bet you don't make the PCs roll for success when walking a straight line down a flat, evenly surfaced road either.

OK I'm confused.:confused:

Quote from: nDervish;868421The point I was trying to make which started this side-thread was that, in a skill-based situation where a rookie has a good chance of success, I would expect an expert to be practically guaranteed to succeed.  The examples from #59 (driving, making an active parry) and the factory example all fit this expectation:

What you said earlier (before the necro) was:

Quote from: nDervish;833787Agreed as far as that goes.  However, if you have a +2 modifier on that roll, then it becomes significant whether your distribution is flat or curved.  If you have two characters rolling, one with a base 11+ and the other with a base 6+ and they both have a +2 modifier on that roll, then flat vs. curved distribution is much more significant.

I like bell curves in my dice because they make modifiers more significant in the mid-range or when moving towards the mid-range and less significant as they move things out to the extremes.  You can't really do that with a flat distribution unless you want to break out calculators or lookup tables every time someone makes a roll.

I thought at the time I'd understood that - notwithstanding nitpicking at the time over what "significant" meant - but as far as I can tell, these two statements are opposed.
Lunamancer's system with the extra rolls is, as far as I can tell, duplicating what the non-linear system does, which is what I thought you'd wanted. If you want a difficult task to just kill newbies, I would've thought a linear roll should be just fine.

And this is confusing as well.

Quote from: JoeNuttall;868416You said that your system (using a second roll) could give a fixed proportion (for example 50%) of successes being a complete success, and this didn't work in any system with a probability curve.

I said it that would work using my system for probabilities less than 50%.

Again, unless I missed something, I thought that the point of the second roll is to duplicate the non-linear effect with a linear roll. I don't know why you would you want to apply a second roll when you're already rolling 2d10?

Quote from: Bloody Stupid Johnson;868469Again, unless I missed something, I thought that the point of the second roll is to duplicate the non-linear effect with a linear roll. I don't know why you would you want to apply a second roll when you're already rolling 2d10?

You're correct, you wouldn't.
The point of Lunamancer's second roll was to generate fixed probabilities for levels of success, which Lunamancer said wasn't possible by using curved probabilities.

There are a lot of points out there I'd like to address, so quoting individuals is too cumbersome at this point. I'll just throw it out there and take from it what you will. Some of these paragraphs build on the previous, but each should be taken as its own separate idea:

• Regarding the purpose of the second die, there is no singular purpose. I use it for whatever I need. Used for a damage roll, sure, it's a de facto "degree of success."
• I'm not in favor of having degree of success automatically attached to a mechanic because it's not always meaningful in every situation. I only want it when I need it.
• Even something as easily understandable and quantifiable as damage can hit a point of meaninglessness. If you're playing AD&D and you attack a 4 hp Kobold with a longsword, there are only 5 possible outcomes: you miss (0 damage), you hit for 1 damage, you hit for 2 damage, you hit for 3 damage, you kill the kobold. Even though the damage die could come up with different numbers--4, 5, 6, 7, or 8, they are really all the same result.
• A mathy way of saying that is to differentiate between a probability distribution represented by x versus the effect, f(x). Very rarely do I ever see anyone talk about f(x). Kiss your tidy and neat curves goodbye if you do.
• As to the question I posed in my first post about probability distribution of the degree of success, the reason I posed that it may be problematic is because while I know they look more or less consistent "after" the 50% mark (when probability for basic success is less than 50%), the probability distribution of degree of success takes on all different shapes when chance to hit is above 50%. Proposing a mechanic that admittedly only functions consistently after the 50% mark is verifying my concern.
• I don't assume that a task that gives Johnny circa a 50/50 chance at success means that Dick should be nigh-guaranteed of success. First, I simply don't believe that's how the world works. But that is irrelevant. We're talking about a game. Expectations and perceptions matter more. And they vary from person to person.
• Saying that curved mechanics make modifiers in the mid range more significant is the flip side of the same coin that says the mid range has fewer points of differentiation and is therefore more grainy and less precise. 2d10, for example, has only 9 points of differentiation within one standard deviation whereas d20 has 14 points of differentiation.
• I can have my cake and eat it too if I use a linear mechanic to gain superior points of differentiation and just use larger modifiers and not even break a sweat. The "official" modifiers in the Lejendary Adventure game tend to be 1.5-2 times the magnitude as identical modifiers in AD&D. The real work becomes how to compress the extremes. But probability is always bound by 0% and 100%. So was going to compress the extremes anyway.
• Pareto's Law: 20% of your efforts yield 80% of your results, 80% of your efforts yield only 20% of your results. A linear mechanic works perfectly fine 80%+ of all times the dice mechanic is ever used. It requires little to no mental effort to create a mechanic and implement it. I prefer to focus my efforts on what yields results.
• If an RPG is built entirely around a linear mechanic, say a d20, and you prefer a bell curve, it's an easy fix. Roll 3d20 and take the middle.
• All else held equal--using pre-gens to factor out player preference in character builds--a character built under a d20 system will have a certain array of probabilities of success at tasks of various difficulties. By implementing the above idea to convert it to a bell curve system, the effect on those probabilities will be to push everything away from the 50% mark and towards the probability bounds of 0% and 100%.
• Why it is desirable to increase the number of flavors of Dick's and Johnny's and decrease the number of flavors of Joe's is beyond me. Different strokes for different folks, I guess.
• Eliminating the simplifying assumption and bringing back in player choice, this leaves little reason to have average stats at all. The return on adding a point of mid-range skill is far greater than the return of adding a point to lower or higher end skills. I would expect them all to be pushed into the lower end of the upper range.
• As for incentives of skills on the lower end, I can't say much about that without knowing what the rest of the system is like. Many systems make low skill levels very cheap to buy up. And there'd also be a question on how easy it is to ensure you get positive modifiers during play.

A little bit of necromancy, maybe even on myself, but a topic close to my gaming heart.

Doing his since 1977, and fiddling with it since 1978.  I like simple mechanic flow, and ones you can read from the dice without referencing a table.

I started with the 1D20, played Traveler and TFT as well, so your 2D6, 3D6 approach for a good 20 years, tried D100 for about 4 years, and for the last 10 years or so 2D10.  They all have their sweet spots, and fail in different ways.  I do prefer the multiple die because of the bell curve-like statistics.  2D10 had the best dynamic range of the bunch.  Also like that doubles is a easy way to give you a critical probability that varies with ability.

Yet I have been converted to another way in the last few years..

All the above are basically binary systems and suffer from lack of degree of success, which until I played a d6 system (Atomic Highway) I didn't think was a big deal.

And oddly, the d6 system captures the best of the old wargamey feel I loved so much, before this whole RPG thing was birthed.

So to me the d6 approach is the most esthetically pleasing.  Although the d8 and d4 I thought were always the coolest dice.