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Author Topic: Probability Theory and You  (Read 6129 times)

Spinachcat

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« Reply #15 on: May 10, 2020, 04:10:22 am »
All game mechanics totally suck!! :)

Quote from: Theory of Games;1129442
D20 aquired great Fame being as "swingy" as possible, but it can drive PC parties to TPKs like no other solid. It can "feel treacherous" at times.

THIS is exactly why I love using a D20 for RPGs. It's that absolute treachery of the damned die. Sometimes for the GM, sometimes for the players, sometimes for that one dude who can't roll over 10 all damn night! We've all been that dude.

I once ran a 4 hour dungeon with plenty of combat and I failed every attack roll. It was hysterical, but what made it even more fun is I ran that same event the next day and slaughtered the PCs. To me, that's a feature of the D20.

S'mon

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« Reply #16 on: May 10, 2020, 05:07:44 am »
Quote from: Libramarian;1129457
I like linear for binary pass/fail rolls. The effect of modifiers is more intuitive, and I don't understand what people mean when they say the d20 is "swingy", unless they're narrating attacks that miss by 8 as "worse" misses than attacks that miss by 1. Just stop doing that.

But this is often built into the d20 system, eg some iterations use "d20 + Athletics" as the number of feet your PC jumps, which can give ridiculous results. Or 5e opposed shove/grapple checks where the STR 20 Proficient guy rolls '1'+7 = 8 and the STR -2 kobold rolls 20-2 = 18. These kind of opposed checks and roll=result stuff would be far better done on multiple dice generating a plausible bell curve.

For old school D&D I went back to Tom Moldvay's suggestion of using multiple d6s roll-under for attribute checks, which generates a bell curve. For 3e-4e-5e the d20 is too hardwired in to the system, although I guess one could use 3d6 or 2d10 for Attribute checks (not attacks or saves).
BTW I find the BRP d% system's approach of treating success chances as Platonic ideals not floating DCs works ok with the flat 1-100 spread. The specific problem is with the 3e-5e d20 System's floating DCs & opposed checks. It takes OD&D's functional attack & save mechanic (both naturally highly variable) and uses it for skill/ability checks, where it's simply not appropriate. You can cludge it with generous use of "Take 10/Passive Score", but it's fundamentally not a good system IMO.
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mightybrain

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« Reply #17 on: May 10, 2020, 06:13:13 am »
Quote from: S'mon;1129468
5e opposed shove/grapple checks where the STR 20 Proficient guy rolls '1'+7 = 8 and the STR -2 kobold rolls 20-2 = 18. These kind of opposed checks and roll=result stuff would be far better done on multiple dice generating a plausible bell curve.


In 5e a kobold would more likely oppose with DEX+2. But even so, it's still not flat because you are using multiple dice. The chance of this scenario playing out as you've described it is 1/4 of 1%. Or as my group would call it, a million to one.

Chance of success: 73.75%

https://anydice.com/program/1b849
« Last Edit: May 10, 2020, 06:22:05 am by mightybrain »

nDervish

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« Reply #18 on: May 10, 2020, 08:07:29 am »
What I'm using at the moment is ye olde percentile dice, mainly because I'm currently running Mythras, which is BRP family.  I'm not really a big fan of "flat" dice curves in general, but I do like the classic BRP skill improvement mechanics (which I'm using, rather than doing it "the Mythras way"), which are only really implemented for percentile.  (Although there is a modified d20-based version of the advancement mechanic used in Pendragon, but I particularly dislike d20-based resolution, probably because of its strong association with D&D and, thus, with class-and-level and zero-to-demigod systems.)

As for what I actually like in dice mechanics, I seem to be a serious outlier - in most of these kinds of discussions, a lot of people will generally say "I like Dice Mechanic X because the exact probabilities are transparent", but I consider that a bug, not a feature.  Pre-4th edition Shadowrun is one of my favorite dice mechanics, mainly for the clear implicit model of complex situations (the number of dice rolled solely reflects your ability, the target number solely reflects the difficulty of the task, and the number of successes solely reflects the quality of the result), but also in part because very few people can look at "8 dice vs. target number 4" and immediately know the exact percentage chance of getting any specific number of successes - but anyone can easily see that, most of the time, you'll get roughly 4 of them.  This feels more true-to-life to me, given that, IRL, if I'm shooting at a target on the range, I don't know that I have a 37.48672% chance of a bullseye, but I do know that I'll usually hit within about 5 cm/2 inches of the center.  (Made-up numbers, not an actual statement of my personal ability with firearms.)

I also like EABA's "roll some number of d6s, and keep the 3 highest" mechanic, which pushes average results higher with increased skill, but doesn't change the range of possible results as skill levels become arbitrarily high.

And I've lately been really liking what I've read of the dice mechanic in Early Dark, where you roll a handful of d10s (usually 6-8 for starting characters), group them into sets such that the sum of each set is no more than a limit based on your base attributes (usually a limit of 7-8 for starting characters), and then each set is one effect from your attempt with the power of that effect being based on the number of dice in the set.  Unfortunately, because there's significant strategy in how you want to group your sets (lots of small sets to create many minor effects vs. big sets for big effects), it's not suitable for solo play, and seems unlikely to work that well for online play either (because, in an opposed roll situation, the other person's dice rolls are hidden information until after you're done grouping them and simultaneously reveal your sets), so I doubt I'll be able to actually play it until the covidpocalypse has passed.  But, here again, good luck seeing the percentages in that mechanic without using a calculator.

S'mon

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« Reply #19 on: May 10, 2020, 10:45:50 am »
Quote from: mightybrain;1129472
In 5e a kobold would more likely oppose with DEX+2. But even so, it's still not flat because you are using multiple dice. The chance of this scenario playing out as you've described it is 1/4 of 1%. Or as my group would call it, a million to one.

Chance of success: 73.75%

https://anydice.com/program/1b849

I was assuming the kobold grappled the fighter!
Yes 1& 20 is 1 in 400, but it there's a much bigger chance the kobold grapples the fighter. I can fluff it so it makes sense but it's harder with some static skill checks, or roll= result like 3e & 4e jumping. There are a bunch of cludges to make it work, eg Rogue Reliable Talent, but a better designed system would not need them.
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Pat

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« Reply #20 on: May 10, 2020, 11:37:03 am »
Probability matters, but the mechanics around the probabilities often matter more. For instance, do you have to roll every time a skill comes up, or do you automatically succeed barring exceptional circumstances? Is your chance based almost entirely on your raw aptitude and training matters very little (AD&D's method), or the other way around? When you roll, under what circumstances, what contributes to the roll, and what success and failure mean can matter a lot more than the odds.

HappyDaze

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« Reply #21 on: May 10, 2020, 01:19:13 pm »
Quote from: Cave Bear;1129438
What you're describing is a feature, not a flaw. It models the rise and fall of fortune in a way that's less prone to streaks than dice-based systems.


I call it flaw because "modeling the rise and fall of fortune" isn't what I'm trying to do. There is nothing wrong with streaks. Sometimes they are positive, sometimes negative, but I prefer independent randomness over cards.

mightybrain

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« Reply #22 on: May 10, 2020, 02:03:47 pm »
Actually more than that (I forgot the brackets): fighter grappling kobold probability of success: 86.25%

Quote from: S'mon;1129483
I was assuming the kobold grappled the fighter!
Yes 1& 20 is 1 in 400, but it there's a much bigger chance the kobold grapples the fighter.

Kobold grappling the fighter probability of success: 11.25%. That's about a 9 to 1 advantage to the fighter. Is that not enough?

If you do want more of an advantage, the easiest fix in 5e is to impose disadvantage on the kobold for trying to grapple a larger creature. Now its chance reduces to 3.56%.

Still not enough? Grant advantage as well to the fighter resisting a smaller creature. Now its chance is less than 1%.
« Last Edit: May 10, 2020, 02:52:36 pm by mightybrain »

VisionStorm

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« Reply #23 on: May 10, 2020, 03:15:53 pm »
Quote from: Pat;1129485
Probability matters, but the mechanics around the probabilities often matter more. For instance, do you have to roll every time a skill comes up, or do you automatically succeed barring exceptional circumstances? Is your chance based almost entirely on your raw aptitude and training matters very little (AD&D's method), or the other way around? When you roll, under what circumstances, what contributes to the roll, and what success and failure mean can matter a lot more than the odds.


One of the things I used to hate about old D&D was how probably of success for skill-related tasks seemed to rely almost entirely on a set of widely variable abilities that was rolled during character creation then set on stone. And if you got lucky and scored an 18 you would have a default 90% chance of success on any action based on that stat--Forever!

Fuck training! You got lucky during character creation, congrats!

I prefer systems where training and conditioning are a bigger factor for success than "natural" abilities, and opportunities for improvement exist across the board (for a cost) for basically all abilities, rather than crucial abilities necessary to handle common tasks being set on stone.

I'm also not entirely a fan of binary success. I tend to think of successes in degrees, with merely partial success (or failure) being the default and truly succeeding (or messing up) requiring high rolls (maybe 5+ above or below target number on a d20+Mod mechanic). That way skill and high modifiers become more relevant, even given the swingyness of a d20 roll.

Success generation Dice Pool mechanics also handle this pretty well, since degrees of success are baked into the system by the very nature of having to count ascending "successes" (the more the better!). Though, I think single dice +Mod mechanics run faster, but I have a soft spot for success generation Dice Pools, and prefer them over counting pips if I have to roll multiple dice to handle task resolution.

S'mon

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« Reply #24 on: May 10, 2020, 04:28:29 pm »
Quote from: VisionStorm;1129499
One of the things I used to hate about old D&D was how probably of success for skill-related tasks seemed to rely almost entirely on a set of widely variable abilities that was rolled during character creation then set on stone. And if you got lucky and scored an 18 you would have a default 90% chance of success on any action based on that stat--Forever!

I guess that'd be 2e AD&D? Maybe RC D&D? No other version had roll-under d20 proficiency checks as standard.
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VisionStorm

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« Reply #25 on: May 10, 2020, 05:21:46 pm »
Quote from: S'mon;1129502
I guess that'd be 2e AD&D? Maybe RC D&D? No other version had roll-under d20 proficiency checks as standard.


Yeah, I mostly played 2e, and briefly Basic before I quickly moved on to 2e. But I always figured older editions still used roll-under stats, since they had no skills/proficiencies, so ability checks defaulted to closest score based on whatever characters wanted to try at DM's discretion. At least from what I gathered from the times I played Basic with other DMs while still new to the hobby (I played 2e by the time I got my own books and started DMing).

Pat

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« Reply #26 on: May 10, 2020, 08:28:25 pm »
Quote from: S'mon;1129502
I guess that'd be 2e AD&D? Maybe RC D&D? No other version had roll-under d20 proficiency checks as standard.
No, 1st edition. The original proficiency system in Oriental Adventures had fixed rolls (each peaceful proficiency had its own target number), but that was quickly dropped. The version that appeared in the Dungeoneer's Survival Guide, and was expanded in the Wilderness Survival Guide, and then became part of the core in 2e, rolled against ability scores when making non-weapon proficiency checks.

And even Moldvay has that note in the back about using ability checks to resolve random tasks, which has the same problem sans a skill system.

Libramarian

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« Reply #27 on: May 11, 2020, 02:08:15 am »
Quote from: S'mon;1129468
But this is often built into the d20 system, eg some iterations use "d20 + Athletics" as the number of feet your PC jumps, which can give ridiculous results. Or 5e opposed shove/grapple checks where the STR 20 Proficient guy rolls '1'+7 = 8 and the STR -2 kobold rolls 20-2 = 18. These kind of opposed checks and roll=result stuff would be far better done on multiple dice generating a plausible bell curve.

For old school D&D I went back to Tom Moldvay's suggestion of using multiple d6s roll-under for attribute checks, which generates a bell curve. For 3e-4e-5e the d20 is too hardwired in to the system, although I guess one could use 3d6 or 2d10 for Attribute checks (not attacks or saves).
BTW I find the BRP d% system's approach of treating success chances as Platonic ideals not floating DCs works ok with the flat 1-100 spread. The specific problem is with the 3e-5e d20 System's floating DCs & opposed checks. It takes OD&D's functional attack & save mechanic (both naturally highly variable) and uses it for skill/ability checks, where it's simply not appropriate. You can cludge it with generous use of "Take 10/Passive Score", but it's fundamentally not a good system IMO.


Yes I agree, dice result = fictional result rolls should use a normal curve.

The D&D attack roll works because it's only one factor in a complex set of checks where the more skilled combatant not only is more likely to hit, but also has more hit points and probably does more damage. So they might only be 15% more likely to hit, but still have 10:1 odds to win the whole combat. To abstract a D&D combat into a single check, the appropriate mechanic would be hit dice vs. hit dice, a la Tunnels & Trolls. Something similar would probably give the results you're looking for in the kobold grappling a fighter example.

S'mon

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« Reply #28 on: May 11, 2020, 02:39:20 am »
Quote from: Pat;1129521
No, 1st edition. The original proficiency system in Oriental Adventures had fixed rolls (each peaceful proficiency had its own target number), but that was quickly dropped. The version that appeared in the Dungeoneer's Survival Guide, and was expanded in the Wilderness Survival Guide, and then became part of the core in 2e, rolled against ability scores when making non-weapon proficiency checks.

And even Moldvay has that note in the back about using ability checks to resolve random tasks, which has the same problem sans a skill system.

True re 1e, so it's there if you count DSG and WSG as standard/core - I certainly don't.

Moldvay & Mentzer optionally suggest d20 checks, but they also suggest multiple-d6 checks, which I eventually realised works much better.
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jhkim

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« Reply #29 on: May 11, 2020, 03:20:56 am »
Regarding probabilities like a contest of Strength in 5E D&D...

Quote from: mightybrain;1129492
Actually more than that (I forgot the brackets): fighter grappling kobold probability of success: 86.25%

Kobold grappling the fighter probability of success: 11.25%. That's about a 9 to 1 advantage to the fighter. Is that not enough?
For me, it really isn't.

The strongest possible human loses a contest of strength to an average kobold 10% of the time? That really stretches my suspension of disbelief.

In a test of raw strength, the strongest possible human should just always win a contest of strength with an average kobold. There shouldn't be any dice-rolling tension - it should just happen. And if we did look up the rules, the rules should tell us the same thing - that the strongest man in the world wins with no doubt whatsoever.

In RPGs, this regularly comes up when the expert PC tries their skill and fails. Then all the other PCs without training try it, and because they have five chances to roll high, one of them succeeds. For example, if you were dying -- what would be the best choice to save your life? Having a brilliant doctor come see you, or five average people with no medical training? In D&D (in the case 5E), a cleric with Wisdom 18 has a +6 in Medicine. That's an 85% chance of success of a DC10 Medicine check. But five people with +0 have a 98% chance to get a success among them.


Personally, I find that the vast majority of RPG rule systems have far too much variance for my suspension of disbelief. In the real world, the champion Olympic weightlifter is never going to lose to a below-average guy off the street. Particularly with skills, the range of ability goes much larger than roll variance. That is, the top mathematician in the world will be able to solve math problems that an undergraduate student has no hope of solving. But conversely, an undergraduate math major can also solve problems that a high school dropout can't even understand.

So if the range of roll is 1 to 20, then skill should go from 1 to 40 or more -- and that's just with real-world skill, let alone legendary or fantastic ability.

People who are experts in their field should always and reliably be able to outperform those with no particular skill.