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*., 16% chance for a special or critical (.2*., 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 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.


* 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?