A search for an optimal resolution mechanic

[A Man In Black]

Why not? It's definitely true for a normal distribution.

Because PhoneLobster and Frank Trollman have this years-ongoing argument about semantics WRT bellcurves.

Do not encourage it.

[Roog]

Averages in cases like this are used as a shortcut.

Your use of avaerages in the comparison distracts from your point. Any integer RNG will have the same average % increase per +1 bonus as any other. If the average is what matters then a curved RNG is just as good as a flat RNG. If the average is what matters, then "increases chance of success by approximatly +n%" is a good enough answer to the question "what does the bonus on my +2 magic sword do?".

But that's not what you point seems to be. If I understand correctly, then your point seems to be that only flat RNGs are simple enough to be intutivly understood in play.

But at that point you have effectively presented an argument stating that curved RNGs just plain aren't suitable for the vast majority of game designers, or even players.

Which is fine by me because that would be just one more of about a bajillion reasons why they should never ever be used ever.

If you follow that line of arguement, you should never have rerolls, contested checks, limited use bonuses, action points, take 10, take 20, or any other mecanical feature that disturbs the RNG. Any of those will change to effictive shape of the RNG and stop "what does the bonus on my +2 magic sword do?" being aswered in the specific simple format that you want.

[Blicero]

Dice Pools Roll NsMs, counting how many dice rolled X or better. Has the advantage of infinite extensibility in one direction (adding more dice) and incredibly easy calculations of averages (dice/chance pr die = average hits). Unfortunately, system breaks down completely at the low end (as you have no more dice to take away) and the calculation of the chances to get a specific number of hits with a single roll is a ghastly N-polynomial that is not normally doable at the table.[/list]

Could anyone possibly go into an explanation on how one calculates dicepool probabilites?

[PhoneLobster]

If I understand correctly, then your point seems to be that only flat RNGs are simple enough to be intutivly understood in play.

That's not what my point is, it is A point I am prepared to make and have made in the past but not at all what I was talking about here.

My point here was...
1) You do not measure bonuses on a curve at the Median and get to make statements about bonuses at other points on the curve with that measurement. (ie, no Frank's dice mechanic does NOT "go to 11")

2) As a design tool you would use averages rather than the measurement at the Median. Because that would be closer to being correct more often, which is what averages in such situations are for.

you should never have rerolls, contested checks, limited use bonuses, action points, take 10, take 20

About half your list shouldn't be on that list, but I get your point.

Thing is rerolls should not be the default standard mechanic. And due to their iterative nature in play at least players can relatively easily ask the question "If I reroll what are my chances of success?" if they are using a 1d20, but not so much if they are using three dice types in an exploding reverse double negative dice pool.

Contested checks perhaps shouldn't be used for anything much of great importance, but mostly fall into the next bit as a cost benefit situation that should be considered separately to the costs and benefits of rolling and tallying 3d6 for your basic mechanic.

Aaaaand the rest of your list isn't really the same sort of thing at all. But there certainly are other things which ARE the same sort of thing. Like making a roll for "hit vs dodge" followed by a roll for "damage vs armour" to resolve a single attack etc...

But those deserve discussion and consideration on their own. Is the complexity of a 2 roll attack mechanic worth it? It has real intuitive costs, but possibly benefits. Meanwhile the curved dice mechanic is pretty shallow in its so called "benefits" and has a wide array of costs, not the least of which is that when you combine it with other complexity costs (like the 2 roll attack mechanic) it's complexity costs become multiplicative.

And that's not nice at all.

[...You Lost Me]

There's a system called Hi/Lo Heroes (free pdf on Scribd) which has you assign your attributes (there were 6 of them) to "High" or "Low" values. When it comes time to make a check, you roll 2d6, and take the high one if your stat is "High", or the low one if your stat is "Low".

I enjoy it, though the game it was made for was very much a Magical Tea Party. The biggest problem with the system (in my opinion) is that you can never advance your base attributes--and advancing base attributes is what excites people in the most in TTRPG's.

[CatharzGodfoot]

Dice Pools Roll NsMs, counting how many dice rolled X or better. Has the advantage of infinite extensibility in one direction (adding more dice) and incredibly easy calculations of averages (dice/chance pr die = average hits). Unfortunately, system breaks down completely at the low end (as you have no more dice to take away) and the calculation of the chances to get a specific number of hits with a single roll is a ghastly N-polynomial that is not normally doable at the table.[/list]

Could anyone possibly go into an explanation on how one calculates dicepool probabilites?

[Username17]

If you follow that line of arguement, you should never have rerolls, contested checks, limited use bonuses, action points, take 10, take 20, or any other mecanical feature that disturbs the RNG. Any of those will change to effictive shape of the RNG and stop "what does the bonus on my +2 magic sword do?" being aswered in the specific simple format that you want.

Roog, seriously. You are wasting everyone's time. Stop trying to have a discussion about dice mechanics with PhoneLobster. If he was going to agree that adding "one standard deviation" or "half your current chance to succeed" was as valid a thing to add to your chance of success as "15% of the total possible outcomes" he would have stopped arguing two fucking years ago. But he won't. It is frustrating, but there it is. PhoneLobster does not believe that adding things to chances of success other than fixed percentages of the total possible outcomes is valid as a thing to do. So he has been accusing people who like non-flat random number generators of being foolish or deceptive for literally years.

Could anyone possibly go into an explanation on how one calculates dicepool probabilites?

Sure. The main strengths of dicepools are their infinite extensibility (you can always roll one more die) and their production of average values. While a flat number generator gives an equal chance of a high or a low result, a dicepool generates likely and unlikely numbers. And figuring out the most likely number is incredibly easy - just multiply the chance of a hit per die times the number of dice. With Shadowrun dice, one third of the dice are hits, so a dicepool of 12 gets 4 hits more often than any other number. And since you went to dicepools because you wanted things to normalize to average values, that's what you'll reach for most of the time.

However, if you want to calculate the exact probability of getting a specific number of hits, that's uglier. It's C^X*(1-C)^(Y-X)*(Y!)/(X!)/[(Y-X)!] where C is the chance of getting a hit per die, X is the number of hits, and Y is the number of dice. That equation is fucked. Easy enough to get it for any possible dicepool size in a spreadsheet, but very few people can calculate any but the most modest dicepool sizes in their heads on the fly.

But in all probability you reached for a dicepool system because it gives an answer to the question "what am I probably going to roll" which a flat RNG doesn't. And the answer to that question is simply C*Y, which anyone should be able to do.

-Username17

[Ganbare Gincun]

If he was going to agree that adding "one standard deviation" or "half your current chance to succeed" was as valid a thing to add to your chance of success as "15% of the total possible outcomes" he would have stopped arguing two fucking years ago.

The standard deviation for 3D6 would be +3, correct? So you could add two standard deviations to a roll before going off the range? And how would you easily apply "adding half your current chance to succeed" to your roll in a game where you use 3D6? That could range from add the equivalent of +1 to +4 on the number depending on what your target number is. Or do you just manipulate the target number directly?

[Shazbot79]

Separate dice for skill and stat (each ranging from d4 to d12) is exactly how the Cortex system works btw. The Supernatural and Firefly (or Serenity, whatever) RPGs both use the system, among others I'm probably not aware of.

You're right...I was thinking of Rolemaster. Runequest is the one that has opposed percentile rolls for some checks. Why they decided to do this, I don't know.

I don't have any experience with the Cortex system, alas. I'll have to try and find a copy to flip through.

I like the idea of die steps because I think that increasing an attribute or skill one level should be a greater leap than a mere +1 (Though statistically, it usually only means a mere +1) Also, I like the actual rolls to make for of a difference to the outcome of a challenge, rather than simply stacking static multipliers. I also like that the numbers wouldn't get too huge, meaning that epic level dragons can still take a beating from a peasant army.

I know that opposed rolls aren't a good idea with a curved roll resolution mechanics, but I wonder if anyone here has any experience with games where players make attack and defense rolls against static TN's, like in Icons. I have the game, but I haven't used it at the table as yet and I wonder how it plays out "in the shit" as it were.

[Surgo]

However, if you want to calculate the exact probability of getting a specific number of hits, that's uglier. It's C^X*(1-C)^(Y-X)*(Y!)/(X!)/[(Y-X)!] where C is the chance of getting a hit per die, X is the number of hits, and Y is the number of dice. That equation is fucked. Easy enough to get it for any possible dicepool size in a spreadsheet, but very few people can calculate any but the most modest dicepool sizes in their heads on the fly.

Also if you have a computer, you can use the pbinom() function in R or the handy Binomial Distribution Calculator.

Nowadays you can pop that kind of thing into most cell phones and get the result right in the middle of doing anything -- which is nice.

[PhoneLobster]

If he was going to agree that adding "one standard deviation" or "half your current chance to succeed" was as valid

You are mixing your definitions up again.

It is rather hard to take your arguments on the matter as serious when they largely consist of irrelevant non-sequitors like "Look! Standard Deviation, it's a... thing... and it... exists... therefore mine goes to 11!".

I mean hey, YOU could have just not spent the last "two fucking years" going on about how curved mechanics "go to 11" but you went and did it. And yeah, I'm going to "stubbornly" continue to point out that no, you don't get to go to 11. Because seriously what? I'm going to just live and let live and change the way math works just for you?

[CCarter]

Separate dice for skill and stat (each ranging from d4 to d12) is exactly how the Cortex system works btw. The Supernatural and Firefly (or Serenity, whatever) RPGs both use the system, among others I'm probably not aware of.

You're right...I was thinking of Rolemaster. Runequest is the one that has opposed percentile rolls for some checks. Why they decided to do this, I don't know.

I don't have any experience with the Cortex system, alas. I'll have to try and find a copy to flip through.

I like the idea of die steps because I think that increasing an attribute or skill one level should be a greater leap than a mere +1 (Though statistically, it usually only means a mere +1) Also, I like the actual rolls to make for of a difference to the outcome of a challenge, rather than simply stacking static multipliers. I also like that the numbers wouldn't get too huge, meaning that epic level dragons can still take a beating from a peasant army.

I know that opposed rolls aren't a good idea with a curved roll resolution mechanics, but I wonder if anyone here has any experience with games where players make attack and defense rolls against static TN's, like in Icons. I have the game, but I haven't used it at the table as yet and I wonder how it plays out "in the shit" as it were.

Well as far as Cortex goes there's always therpgsite for discussion of such things: someone there has probably played it, even if you won't be getting a designer-level view. My view from reading it was that perhaps the limited number of steps limit the system to more 'gritty' play - dragons might be past the scale that the system can find a big enough die for.

A die pool system is fairly 'granular' as well of course (a few big jumps rather than stacking a ton of piddly +1s) and its all 'actual rolls' too, although the more dice you roll the less variance you end up with in the outcome.

[Roog]

7th Sea - Roll and Keep
Additive dice pool with extra complexity. Roll nd6, add up the best m

Alternity
d20 +/- dn, where n depends on difficulty.
Roll under TN of stat + skill, or TN of a fraction of stat + skill for a higher degree of success

CthuluTech
roll nd10, take highest or add up runs or sets

Deadlands
Best of m dn, m based on skill level, n based on stat, each dice is open-ended
TN based on difficulty

Dogs in the Vineyard
Roll dice to generate a set of numbers and play a mini game with those numbers

Dying Earth
d6 TN 4, pay from a skill pool for re-rolls

Gumshoe
d6 TN based difficulty, pay from a non-regenerating skill pool for a bonus

In Nomine
2d6 roll low, degree of success determined by a 3rd d6

Marvel Universe RPG
No RNG, pay points from a regenerating pool to achieve effects

Torg
Open-ended d20, then lookup on table to generate a modifier

Unknown Armies
d100, but players can swap the digits under certain circumstances

Weapons of the Gods
Dice pool, result = 10 x size of largest matching set + face value of that set
players have a limited ability to set dice aside to use in later rolls

[tzor]

And now for something completely different: Time Lords RPG - Beat the Difference

Step one: assume that you have a system where the abilities and target levels are low (within the die type you are using, so in the case of Time Lords lower than 6.

Step two: determine attribute and target level, subtract the former from the latter. If < 0 assume auto success. (If > 4 walk away and cry.)

Step three: Take 2d6 roll them. Take the difference (not the sum) of the two dice (0-5).

Step four: If that difference is greater than the difference in step two you have "beaten the difference" and you succeed, otherwise you fail.

Here are the results:
Beat a 0 (1+) 30/36
Beat a 1 (2+) 20/36
Beat a 2 (3+) 12/36
Beat a 3 (4+) 6/36
Beat a 4 (5) 2/36

[CCarter]

WTF...? Does that actually do anything useful you couldn't in a less byzantine fashion?

A couple more weird ones:

Summerland: try to roll under your stat on 2d6 (easy tasks), 3d6 (moderate tasks) or 4d6 (hard tasks)... same mechanic is seen in HarnMaster damage rolls, though HM mostly uses d%.

Universal Tables: everywhere in the 80s (Marvel Super Heroes FASERIP, and I think Indiana Jones and Top Secret ?). Roll a d100 on your chart and read off a result, usually colour-coded. Marvel Super Heroes uses this so you can have attributes ranging from 2 to 5000 without having their RNG break. After its success TSR were using it for almost everything for awhile (e.g. 3rd edition Gamma World and a Conan game).

Full Light, Full Steam: roll 4d6 and arrange highest to lowest.
Stat and Skill are each ranked from 1 to 4 and determine which die you get to pick - the two are then added together. i.e. if you have Strength 3, Athletics 1 you would take the second-highest of the four and the lowest of the four and add them to get a result from 2 to 12.

[Orca]

Earthdawn uses the increasing dice size mechanic, though usually with 2 dice (2d6, d6+d8, 2d8, d8+d10, 2d10, d20+d4 - that jump always pissed people off)

[fectin]

If he was going to agree that adding "one standard deviation" or "half your current chance to succeed" was as valid

Stuff

You're mixing and matching too many things.

First off, you're talking about the median, but you should say the mean. Unless Frank is advocating use of non-linear dice, the mean and median are the same, but only one makes sense to talk about.

Second, you're (perhaps inadvertantly) pulling a slight of hand by comparing the before/after sucess rate ratio on the 3d6 (or NdM) to the bonus/RNG range ratio on the d20 (again, or whatever). In both cases, a given bonus increases sucess by a set amount. In both cases that amount depends on the other modifiers.

Third, so what? even assuming that 3d6 had uniquely unpredictable bonus effects, where's the Harm?


On topic:
Amber diceless is relevent after all: it's basically competing narratives, trying to play your strength aginst other characters' weaknesses. Like Magical Tea Party, but with agreements ahead of time about who is best at what. It's already a game about politics and navel gazing though, so that's actually not a bad thing.

Exalted had an edge case high in one Sidereal martial art that turned combat into purely competitive narration, in a paradigm of your choice ("We are each mountains, resisting the erosion of time..."). I don't even know how to describe that. Magical Drug Party?

Danger Patrol! has varying die sizes rolled against a fixed target number (either 4 or 5, depending how beaten up you are). Bonuses are in the form of extra dice. Works great for that system, but probably not for general use.

I haven't seen Rock Paper Scissors listed yet. It's basically flipping a coin, but more personal.

The Darksword RPG had a weird mechanic where R-P-S type handwaving between two people generated a number, and you added your bonuses to that against a target number. Or something. It's been a long time, and I never actually got a game together.

Any other mechanic plus "fate points" that let you buy successes. Especially the WEG Star Wars that let you spend XP to boost rolls.

Edit: Also, exploding dice probably count as different. especially if there's a mechanic to make them explode on more than one result (see: FantasyCraft is stupidly complex).

[Roog]

Blue Planet
nd10 take lowest, where n = aptitude (ranges from 1 to 3)
TN = Attribute + Skill - Difficulty

[PhoneLobster]

In both cases that amount depends on the other modifiers.

I don't think you are properly following or addressing the argument at all.

I never called that into question, rather I have been pointing that out to Frank and co, who's "mine goes to 11" argument rather strictly relies on ignoring that particular point in regards to "curved" RNGs.

Third, so what? even assuming that 3d6 had uniquely unpredictable bonus effects, where's the Harm?

You are kidding right?

I mean hell at that point you may as well use tea leaves as your RNG, or dice pools.

No wait. On second thought, stick to the tea leaves.

[Username17]

The standard deviation for 3D6 would be +3, correct? So you could add two standard deviations to a roll before going off the range?

Pretty much, yeah. If your chance to succeed requires you to roll better than -&#963;, then a 3 point shift one way means that you need to roll better than -2&#963;, and a 3 point shift the other way means that you have to beat the mean. That's true pretty much anywhere you are on the curve, except obviously at the very end where you get pushed off the curve entirely.

Using different sized piles of dice to generate a curve will change the value of &#963;. Using a flat RNG, the value of &#963; becomes variable. With percentile dice, if you're at -&#963;, it takes a 14 point shift to go -2&#963;, but a 31 point shift to go to even odds. So you can't set a single modifier to shift someone &#963; up or down in their chances of success. If you set the modifier to +14, it will fall short whenever the players are near the mean, and if you set it to +31, it will be too large and break the RNG if the players are not.

This basic reality is totally uncontentious to everyone except one person on this thread. People who want to add "10% of the total" to their chance of success gravitate towards flat RNGs because flat RNGs are good at giving you that output. If you get +4 on a d20, then 20% of the time you roll the die you will succeed instead of failing because of that modifier. People who want to add "one standard deviation of the total" to their chance of success gravitate towards curved RNGs because curved RNGs are good at giving you that output. If you get +4 on 3d8, there is one standard deviation of the data that would have beaten you that now does not.

And how would you easily apply "adding half your current chance to succeed" to your roll in a game where you use 3D6?

You wouldn't. That's what happens when you have 2 dice instead of 1 die in Mouseguard. Dicepool systems are inherently exponential, with additional dice having a multiplication effect on your current chances. Dicepool systems are there for you when you want to be able to scale up a lot and you still have average outputs that are comparable to one another.

-Username17

[tzor]

WTF...? Does that actually do anything useful you couldn't in a less byzantine fashion?

Well it is somewhat intitutively obvious to a casual observer; assuming the casual observer never plaed a role playing game in their life. The idea (which is common to a lot of gamers) is you have an attribute and a difficulty level (which could easily be the attribute of the creature you are trying to do something to). You then take the difference. This is something done automatically in most systems to determine if you need to roll the dice in the first place (yes I need to roll a -3 on this die to ... OK I succeed).

So with that in mind, the writers who had no previous role playing game experience went to the conclusion that given this difference you had to get something better than the difference, you have to beat the difference. How do you beat the difference? With another difference.

They really manage to smooth talk the procedure so it actually makes sense. If you weren't a gamer, you wouldn't think it was odd.

[tzor]

Here is a good argument for the Rock-Paper-Sizzors method.



Hey it worked for WWII.

[Dean]

So what about theoretical resolution methods? Ones that no one has used yet to my knowledge...

What if a system used a single die that was modeled to represent a rough bell curve thus giving the efficiency of the one die roll of a d20 system but the more centered result spread of a 3d6 roll. Here's what I'm thinking...

You take a 24 sided die
(http://upload.wikimedia.org/wikipedia/c ... px-D24.jpg)

And then label it's sides like so

1,2,3,3,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,10,10,11,12: Which is 24 sides

So it's bell curve for results would look something like this (using 0's as markers of results for this ad-hoc graph)

1....0
2....0
3....00
4....00
5....000
6....000
7....000
8....000
9....00
10..00
11..0
12..0

So it would be an approximate bell curve. I feel like this could be very solid. D24's already exist and since you're using a 12 base system you could just say "feel free to use d12's if you haven't ordered our dice for a swingier system" which would allow people to test out the game with regular dice. It also feels right to me to work with an 11 point numerical spread. That seems just right to make +1's statistically significant and honestly something you'll care about but it still feels less granular than die pool systems. Granted the odds for things are too hard for most people to mentally calculate which is a negative but all in all it seems feasible and like it might be a positive addition to gaming. What do you all think?

(Additional: I have never made a graph here, if that^ is too much of an eyesore someone PM me or whatever and I'll fix it.)

[tzor]

I have a table (I lovingly stole my typing it by hand) which I think was for the never released Cold Iron system that converts an open ended percentile roll into a linear negative to positive modifier. This would date the page to around 1983 and it may have been inspired by Rolemaster.

(Open ended means if you roll max, roll again, until you stop rolling max likewise if you roll min, roll again until you stop rolling min. Doing that to percentile dice is something only a deranged role player from an Engineering Institute would even consider doing. - Your honor I object, I was never "deranged" as I was never on the range to begin with.)

If you want I can give an example of this. The insanely open ended RNG.

[Judging__Eagle]

Dean, I rather like that idea.

Going from a dice pool; to a single dice roll is a lot better imo.

I'm considering using this as a method to show a "change" in tiers. Allowing a character to replacing a pool of 5 dice; with a single d12 on that "hit" spread would keep total dice pools small as creatures get more powerful.

Having pools of dice that the PCs can "rely on"; and other dice pools that they "can't always" (unless of sufficient power; 3 dice = 1 hit, but pools only go to 5 in my system, so most of the time you can only get 1 hit. I hate seeing dice pools go to numbers that are annoying to roll; an 18 or 24+ sized pool is awesome but annoying to ever have to roll.