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.