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Author Topic: Probability Theory and You  (Read 6112 times)

mightybrain

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« Reply #75 on: May 13, 2020, 05:57:06 pm »
Quote from: Libramarian;1129857
Edit: I see where you made the mistake - the 30 x Strength rule applies to lifting things off the ground using your entire body, i.e. a deadlift, not a bench press. Men typically can deadlift twice as much as they bench press. Bjornsson recently deadlifted 1104lb.

If that were the metric, he would have a 37 strength in D&D terms.

mightybrain

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« Reply #76 on: May 13, 2020, 06:21:37 pm »
Quote from: Libramarian;1129857
I'm not sure on what world the average man can bench press 345lb, but it's not Earth! A typical man can't bench press 185lb without strength training.

D&D world is not like your local gym. For us, an average male weighs about 195 lbs and, untrained, lifts around 130 lbs according to this. In 5e D&D world that would give them an equivalent strength between 4 and 5.

Conversely, the average 5e D&D human with no athletics training (not that 5e grants any strength bonus for that anyway) has a strength between 11 and 12 and can lift around 345 lbs.

5e does a good job matching strength to expectations at the top end, but not so much in the middle or bottom. Which is why, I suggest, we don't have a good intuition for matching strength statistics to the world. We need to re-calibrate our understanding of what below average strength means in D&D world. Usually it means a lot stronger than you're imagining.
« Last Edit: May 13, 2020, 06:29:24 pm by mightybrain »

jhkim

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« Reply #77 on: May 13, 2020, 07:43:54 pm »
I think the debate is getting caught up some in specifics of arm-wrestling and/or kobolds, when it's really a broad thing about what die rolls are like.

First of all, this isn't some airy theoretical issue. There exist systems other than D&D that people play which have different probability distributions. Low-variance systems aren't common, but they also aren't unknown. I'd rate Unisystem as medium-variance, for example, and CORPS and Amber Diceless as low-variance.

So if you haven't played those - what's a low-variance system like? It means that expert PCs can really shine in their fields - often with guaranteed success. Conversely, though, if a PC doesn't have appropriate ability, then they more often have a guaranteed failure. It's a matter of personal taste whether one likes this, but it's neither impossible nor bizarre how they work. Now, those systems have other foibles and issues, so I don't purely pick those. But if we're talking about coming up with a new mechanic for a new system, I think it's worth considering what degree of variance you want.

Quote from: jhkim
I would ask you to think for a bit and picture this in your head. One of the strongest men in the world - an Olympic weight-lifter or the equivalent - has to arm-wrestle a little runt with below-average strength. He loses the first match, and he says "Can we do 2 out of 3? That would be more fair." He then goes on to win.
Quote from: GeekyBugle;1129778
In your example it takes a very special kind of GM to call for a roll.

If the disparity is that high the winner is adjudicated without the need of a roll since it falls under the stuff so easy to do you don't ask for a roll, Like walking.
The variance in the mechanics used affects *all* rolls. I'm picking an extreme example for illustration, but the mechanics just as strongly affect how a skill 4 vs skill 5 contest works.

Higher variance in the die roll leads to more upsets with the lower-stat figure outperforming the higher-stat figure. Lower variance in the die roll means that there's less variation relative to skill.


Quote from: Jaeger;1129879
RPG systems are horrible 'reality' emulators.

Trying to do make an RPG model "how x is done in real life" is the worst design paradigm you can have for making an RPG system.

RPG's are Genre Emulators.

How I want my RPG system to model the Genre of play I want to see at the table, is the better design paradigm.
Different people want different things out of their RPG system. But even for genre emulation, it's not always clear what the best variance is.

For heroic genres, I feel that high variance often fits even worse than reality. Say we're trying for a heroic genre like Conan. In swords and sorcery, does it make more sense for a kobold to defeat Conan in a contest of Strength? For me, the answer is generally no. It doesn't fit the genre for a kobold to beat him in a contest of strength.

GeekyBugle

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« Reply #78 on: May 13, 2020, 08:39:11 pm »
Quote from: jhkim;1129902
I think the debate is getting caught up some in specifics of arm-wrestling and/or kobolds, when it's really a broad thing about what die rolls are like.

First of all, this isn't some airy theoretical issue. There exist systems other than D&D that people play which have different probability distributions. Low-variance systems aren't common, but they also aren't unknown. I'd rate Unisystem as medium-variance, for example, and CORPS and Amber Diceless as low-variance.

So if you haven't played those - what's a low-variance system like? It means that expert PCs can really shine in their fields - often with guaranteed success. Conversely, though, if a PC doesn't have appropriate ability, then they more often have a guaranteed failure. It's a matter of personal taste whether one likes this, but it's neither impossible nor bizarre how they work. Now, those systems have other foibles and issues, so I don't purely pick those. But if we're talking about coming up with a new mechanic for a new system, I think it's worth considering what degree of variance you want.



The variance in the mechanics used affects *all* rolls. I'm picking an extreme example for illustration, but the mechanics just as strongly affect how a skill 4 vs skill 5 contest works.

Higher variance in the die roll leads to more upsets with the lower-stat figure outperforming the higher-stat figure. Lower variance in the die roll means that there's less variation relative to skill.



snip

So don't use a single die, use 2d6, 3d6 systems, the bell curve means that in a well built system the looser will be the lower stat most of the time.

The 3d6 bell curve is better for this since it groups most around 9-12 which you give 0 +/-, making the stat the relevant factor, if the difference is greater than that one will get either 0 or +1, +2 and the other 0 or -1. -2. Making the stat more relevant than in d20 systems.
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VisionStorm

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« Reply #79 on: May 13, 2020, 08:48:42 pm »
Quote from: mightybrain;1129843
I think we might have unreasonable expectations in the differentiation of abilities as well as difficulty grasping the probabilities. For example, here is Devon Larratt, a world champion arm wrestler, bench pressing about 255 lbs. That's a D&D equivalent of between 8 and 9 in raw strength terms (using the strength × 30 rule.) And here is Thor Björnsson, one of the world's strongest men, bench pressing 540 lbs. Appropriately, this is the D&D equivalent of an 18 strength.

And here is Devon beating Thor in an arm wrestle; with ease.

Even a 7 strength isn't weak. It's just lower than average; in a world were the average man can bench press around 345 lbs.


In fairness a lot of that has to do with D&D 5e simplifying things to make it simple to calculate carry weight capacity for "it's a game" purposes rather than attempting to model reality 1/1. It's not that the average D&D human is intended to be literally that strong as a reflection of reality, even within the context of D&D world(s), but that the designers opted to keep the mechanics used to calculate carry capacity simple for playability purposes. I even heard someone once mention that the designers expressly said this was so, but I didn't read the source, so I don't remember where it was from.

That being said I agree with the starting sentence of your post and I believe that it's impossible to perfectly model reality 1/1. The best that we can hope for are "good enough" approximations for game rules purposes, focused on playability, with simulation as a secondary focus, to the degree that it can realistically be achieved.

However, I also believe that jhkin brings a valid point and interesting type of scenario where established task resolution mechanics (at least in D&D) seem to fail, or at least come up short. I'm not sure what the most elegant or adequate solution is, other than maybe doubling the Strength modifier in that specific type of STR vs STR tests. But that seems like kind of an ad hoc solution, if it doesn't really apply to other types of tests outside of STR vs STR. I think that most general skill related tasks still function without problems outside of this specific instance or maybe a few other outliers.

VisionStorm

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« Reply #80 on: May 13, 2020, 09:22:51 pm »
Quote from: GeekyBugle;1129904
So don't use a single die, use 2d6, 3d6 systems, the bell curve means that in a well built system the looser will be the lower stat most of the time.

The 3d6 bell curve is better for this since it groups most around 9-12 which you give 0 +/-, making the stat the relevant factor, if the difference is greater than that one will get either 0 or +1, +2 and the other 0 or -1. -2. Making the stat more relevant than in d20 systems.


I've considered trying this as well, though, I'm stuck with my preference for fast single-die task resolutions. But 2d6 or 3d6 sound really tempting, since d6 is my favorite die type for rolling multiple dice, and 2 or 3 dice are relatively quick to add up (beyond 3 dice, I would rather go with Shadowrun style dice pools and count successes). I would probably go with 3d6 if I try this, since it's close enough to a d20 variable range that I could use modifiers intended for a system using a d20 (maybe reducing them by 1 or 2) and it could still work.

mightybrain

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« Reply #81 on: May 14, 2020, 10:13:25 am »
If you use 3d6 + 2 against random opponents rolling 3d6 with modifiers from -2 to +2 you'll win about 65% of contests
If you use d20 + 4 against random opponents rolling d20 with modifiers from -4 to +4 you'll win about 65% of contests

The only real difference is that you'll get more draws with 3d6. But neither begins to approach the 99% you'd get without randomness.

jhkim

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« Reply #82 on: May 14, 2020, 04:24:34 pm »
Quote from: GeekyBugle;1129904
So don't use a single die, use 2d6, 3d6 systems, the bell curve means that in a well built system the looser will be the lower stat most of the time.

The 3d6 bell curve is better for this since it groups most around 9-12 which you give 0 +/-, making the stat the relevant factor, if the difference is greater than that one will get either 0 or +1, +2 and the other 0 or -1. -2. Making the stat more relevant than in d20 systems.
Quote from: VisionStorm;1129910
I've considered trying this as well, though, I'm stuck with my preference for fast single-die task resolutions. But 2d6 or 3d6 sound really tempting, since d6 is my favorite die type for rolling multiple dice, and 2 or 3 dice are relatively quick to add up (beyond 3 dice, I would rather go with Shadowrun style dice pools and count successes). I would probably go with 3d6 if I try this, since it's close enough to a d20 variable range that I could use modifiers intended for a system using a d20 (maybe reducing them by 1 or 2) and it could still work.
Quote from: mightybrain;1129953
If you use 3d6 + 2 against random opponents rolling 3d6 with modifiers from -2 to +2 you'll win about 65% of contests
If you use d20 + 4 against random opponents rolling d20 with modifiers from -4 to +4 you'll win about 65% of contests

The only real difference is that you'll get more draws with 3d6. But neither begins to approach the 99% you'd get without randomness.
mightybrain is correct that linear vs bell-curve doesn't directly address this. The issue is *die roll variance* vs *stat range*. 3d6 has less variance than 1d20, but so does 1d10.

1d20 has standard deviation of 5.77
3d6 has standard deviation of 2.96
1d10 has standard deviation of 2.87
1d6 has standard deviation of 1.71

It's a question of the standard deviation of the roll versus the stat difference between master and weakling (i.e. Strength mod between Conan and a kobold, for example).

In terms of system design, you can get a less swingy system by any of (1) reducing the size of the die like using 1d10 instead of 1d20, (2) replacing the die with more smaller dice for a tighter bell curve, like 3d6 instead of 1d20; or (3) increasing the range of the stats. It's not like the only choices are 65% or 99%.

Pat

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« Reply #83 on: May 14, 2020, 07:15:57 pm »
Quote from: VisionStorm;1129782
...this whole thing begs the question. Even in the part I didn't specifically address (last sentence in the quote, above) you're still making the claim that using essentially the same mechanic across the entire system is somehow "harder to keep straight" when dealing actions that are different (combat, spellcasting, skills, etc.), which is fundamentally absurd. How can using the same task resolution mechanic across the entire system--meaning that you only have to remember ONE thing--make it more difficult to remember how to resolve tasks?
No, I'm not making that claim. It's not about arbitrary categorization of mechanics based on chapters in the book or some other arbitrary scheme. It's about mechanics that look and feel alike, but are fundamentally different. Mechanics are the user interface of the game. They're the buttons we press, and the knobs we turn. When you have two knobs right next to each other, and both are labeled "d20", it creates a point of uncertainty. Sure, people will eventually memorize the positions, but that doesn't mean it's a good interface. It creates confusion when it's being learned, and makes it easier for even the skilled to make mistakes. That dissonance also slows things down, requiring users to devote a few extra slivers of time on an arbitrary mechanic every time it comes up, instead of responding automatically. While that can sometimes be deliberate -- cf. civil engineers and deliberately confusing intersections that force people to pay attention, and thus theoretically reduce accidents -- that's not good for a smooth flow of intuitive responses, it's frustrating or annoying, and in RPGs can do things like break immersion.

Quote from: VisionStorm;1129782
...which is an example that applies ONLY to D&D, and ONLY because it's badly implemented unified mechanics--we're still dealing with nearly identical mechanics. But because YOU personally can't remember what number to add in ONE circumstance in ONE specific game that uses a mishmash of subsystems rather than truly unify the whole thing that's somehow a testament against the entire enterprise of unified mechanics.
I've already addressed this. No, it's not about badly implemented unified mechanics. It's a flaw in the concept of unified mechanics. Because unless you have a very simplistic system that only needs one resolution method, like some single-focused storygames with a dramatic resolution technique that applies to everything, you'll end up using mechanics to model disparate things that function in different ways. We discussed some of these, for instance how different types of skill work, and how that compares to arm wrestling, and so on. So any reasonably complex RPG will, necessarily, end up with a heterogeneous mix of resolution methods. If you disguise those differences and make them all look alike because you're using the same dice and applying modifiers in superficially similar ways, that's equivalent to having two buttons labeled "d20" sitting next to each other.

This is all pretty basic stuff, which is why I recommended looking into usability theory.

Quote from: VisionStorm;1129782
...
And to nip this in the bud while we're at it...


I never "assumed" things that you never said.
Look at your own words, in the post you quoted. You quote me, and then use the second person "you". In that context, that's a direct reference to me, and thus you're making statements about me. You also ascribe motivations to other people in the paragraph about the originals designers, which reinforces the idea.

I can accept you didn't intend it that way, but that's how it came across.
« Last Edit: May 14, 2020, 08:38:31 pm by Pat »

Pat

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« Reply #84 on: May 14, 2020, 08:27:51 pm »
Quote from: jhkim;1129902
For heroic genres, I feel that high variance often fits even worse than reality. Say we're trying for a heroic genre like Conan. In swords and sorcery, does it make more sense for a kobold to defeat Conan in a contest of Strength? For me, the answer is generally no. It doesn't fit the genre for a kobold to beat him in a contest of strength.
That's a very complex question, because RPGs are a very different genre from books and film. In narrative media, there are plot structures and patterns, that are lacking in RPGs. Which is why RPGs sometimes default more back toward realism, or more properly verisimilitude; or conversely, go full storygame and structure resolution based on dramatic structures and plot flow rather than on some kind of static assessment of capability in a specific area. That's why referencing characters like Conan is so fraught.
« Last Edit: May 14, 2020, 08:39:19 pm by Pat »

nDervish

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« Reply #85 on: May 15, 2020, 05:22:32 am »
Quote from: mightybrain;1129953
If you use 3d6 + 2 against random opponents rolling 3d6 with modifiers from -2 to +2 you'll win about 65% of contests
If you use d20 + 4 against random opponents rolling d20 with modifiers from -4 to +4 you'll win about 65% of contests

The only real difference is that you'll get more draws with 3d6. But neither begins to approach the 99% you'd get without randomness.

As jhkim pointed out, the modifier ranges you used are about a third less than the standard deviations of each roll (+/-2 vs. SD 2.96 for 3d6, +/-4 vs. SD 5.77 for 1d20), so it's no surprise that the results would be tilted in your favor, but still pretty random.  If you want the results to go 99% "the right way", then you need to use larger modifiers, so that the results will be shaped primarily by the modifiers, rather than by the randomness of the roll.

If you use 3d6 + 20 against random opponents rolling 3d6 with modifiers from -2 to +2 you'll win about 100% of contests
If you use d20 + 20 against random opponents rolling d20 with modifiers from -4 to +4 you'll win about 100% of contests

mightybrain

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« Reply #86 on: May 15, 2020, 06:00:40 am »
Ah, the old 50 strength ploy. Even the mighty Tarrasque only has a +10!

With 3d6 that's 100% with no chance of failure. With d20 there's still a slim chance that a character with +2 or more can win such a contest.
« Last Edit: May 15, 2020, 06:29:51 am by mightybrain »

Cloyer Bulse

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« Reply #87 on: May 15, 2020, 07:38:47 am »
Quote from: VisionStorm
....But Wisdom in particular was always an issue even back in the day, when the question would be "what is the real functional and fundamental difference between Intelligence and Wisdom?"....


The distinction between intelligence and wisdom is very real and appropriately represented in AD&D.

Religion is the means by which a culture stores its accumulated wisdom, not empirically, but through mythical story-telling.

When people practice the religion of their culture, they are embodying their ancestors' ancient knowledge without necessarily understanding it empirically. This is represented in AD&D by the fact that magic-users must learn their spells, whereas clerics are simply given their spells.

High wisdom provides some resistance to mental attack forms involving will force. This makes sense because people who practice religion are more resistant to despair, anxiety, and other attacks against the mind. That is because our ancestors learned long ago how to withstand these mental assaults, otherwise we would not be here.

Naturally, people who are irreligious do not understand wisdom, and the more empirically minded they are, the more this is true.

Our culture has had what is in essence a spiritual stroke because it has become too empirical. The problem is that the world is too complex for the human brain to understand in strictly empirical terms. Holistic apprehension is more complete but less specific -- a picture is worth a 1,000 words.

People have latched onto the corona virus hysteria largely because it's something that they can understand in empirical terms; everyone knows what a virus is and how it works. The corona virus is a stand-in for aspects of reality that trouble our culture, but which most can no longer understand, in the same way that demons were once stand-ins for diseases which people did not understand.

The two hemispheres of the brain are hard-wired differently:

Left hemisphere: Operation in Explored Territory
positive affect
activation of behavior
word processing
linear thinking
detail recognition
detail generation
fine motor action

Right hemisphere: Operation in Unexplored Territory
negative affect
inhibition of behavior
image processing
holistic thinking
pattern recognition
pattern generation
gross motor action

There is an obvious correlation between the hemispheres and intelligence/wisdom.

VisionStorm

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« Reply #88 on: May 15, 2020, 10:02:52 am »
Quote from: jhkim;1129985
mightybrain is correct that linear vs bell-curve doesn't directly address this. The issue is *die roll variance* vs *stat range*. 3d6 has less variance than 1d20, but so does 1d10.

1d20 has standard deviation of 5.77
3d6 has standard deviation of 2.96
1d10 has standard deviation of 2.87
1d6 has standard deviation of 1.71

It's a question of the standard deviation of the roll versus the stat difference between master and weakling (i.e. Strength mod between Conan and a kobold, for example).

In terms of system design, you can get a less swingy system by any of (1) reducing the size of the die like using 1d10 instead of 1d20, (2) replacing the die with more smaller dice for a tighter bell curve, like 3d6 instead of 1d20; or (3) increasing the range of the stats. It's not like the only choices are 65% or 99%.


I think that this is an outlier situation, though. I don't think that it necessarily applies to all types of actions that characters will perform. And this is also a D&D-specific issue dealing with Strength contests that might not apply to other systems.

Part of the issue is that Strength is essentially being used as a "Skill", but without having a skill (or Proficiency, whatever). So you don't get a Proficiency modifier for the roll, which is normally the only way to reach the upper limit in terms of ability roll modifiers in D&D 5e.

The issue is that this particular Strength function is essentially its own skill, but the game isn't accounting for that because there is no "Strength" proficiency (other than Strength saves). So you end up rolling low modifiers against each other, since it's just a plain ability check with no Proficiency. And since the system uses a die type with high variability that low modifier doesn't mean much. That's the reason why a kobold has such a high chance to beat Conan on a Strength check.

IMO, the best way to handle this in D&D is to double Strength modifiers for this type of check, specifically. That will give characters with higher scores the a significant edged without changing or complicating the game too much.

Another alternative could be to include a Strength proficiency, but then anyone could get it, which defeats its purpose. So the best alternative to truly give the contestant with the highest Strength a consistent edge is to double their Str modifiers for this type of rolls.

But this type of issue only happens when making plain ability score contests without Proficiencies. There's no need to adjust the entire task resolution mechanic to account just for this type of specialized scenario. I'm also not sure that Conan needs a 99% success rate in a Strength contest in the middle of combat, where lots of variables are in play. Specially when we consider that chimps are technically stronger than humans in real life, which means that just because a creature is small that doesn't mean that they're automatically weak.

VisionStorm

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« Reply #89 on: May 15, 2020, 10:04:53 am »
Quote from: Pat;1130006
No, I'm not making that claim. It's not about arbitrary categorization of mechanics based on chapters in the book or some other arbitrary scheme. It's about mechanics that look and feel alike, but are fundamentally different. Mechanics are the user interface of the game. They're the buttons we press, and the knobs we turn. When you have two knobs right next to each other, and both are labeled "d20", it creates a point of uncertainty. Sure, people will eventually memorize the positions, but that doesn't mean it's a good interface. It creates confusion when it's being learned, and makes it easier for even the skilled to make mistakes. That dissonance also slows things down, requiring users to devote a few extra slivers of time on an arbitrary mechanic every time it comes up, instead of responding automatically. While that can sometimes be deliberate -- cf. civil engineers and deliberately confusing intersections that force people to pay attention, and thus theoretically reduce accidents -- that's not good for a smooth flow of intuitive responses, it's frustrating or annoying, and in RPGs can do things like break immersion.


I've already addressed this. No, it's not about badly implemented unified mechanics. It's a flaw in the concept of unified mechanics. Because unless you have a very simplistic system that only needs one resolution method, like some single-focused storygames with a dramatic resolution technique that applies to everything, you'll end up using mechanics to model disparate things that function in different ways. We discussed some of these, for instance how different types of skill work, and how that compares to arm wrestling, and so on. So any reasonably complex RPG will, necessarily, end up with a heterogeneous mix of resolution methods. If you disguise those differences and make them all look alike because you're using the same dice and applying modifiers in superficially similar ways, that's equivalent to having two buttons labeled "d20" sitting next to each other.

This is all pretty basic stuff, which is why I recommended looking into usability theory.


Look at your own words, in the post you quoted. You quote me, and then use the second person "you". In that context, that's a direct reference to me, and thus you're making statements about me. You also ascribe motivations to other people in the paragraph about the originals designers, which reinforces the idea.

I can accept you didn't intend it that way, but that's how it came across.


We're fundamentally misunderstanding each other so this discussion is useless.