View Full Version : Why dice pools? (Any system)

There seem to be lots of RPGs out there, that use dice pools. It's an interesting idea, but seems more troublesome to me than it's worth. Simply counting the numbers on the dice and adding a number seems much more intuitive to me than counting the number of successes you rolled.

But still lots of people make and play games using this system. Why?

(When using a dice pool, you check your relevant skills rank and then roll a number of d6 equal to it. Then you count all the dice that came up with a 4 or higher or a 5 or higher, and the number of these "successes" are your final value.)

The Rose Dragon

2011-01-09, 11:30 AM

That's not necessarily the only dice pool mechanic, but it is the most common.

The answer is usually that people like the probabilistics that the dice pool systems have. Each way of rolling dice has its own probabilities of results, and each are good for different games.

Has anyone ever made a statisic curve diagram for that? :smallbiggrin:

Somehow I'm one of the people who thinks they are really helpful for understanding such things.

Kurald Galain

2011-01-09, 11:38 AM

I find the mechanics of a dice pool system tend to be confusing. For example, in White Wolf, to jump over something you roll a number of dice equal to Dexterity plus Athletics, and each 7 or higher counts as a success.

So if the DM wants to make this harder, should he (1) remove a few dice as penalty, (2) increase the difficulty to 8, or (3) require more than one success? Each of these will make the roll harder to succeed, but it isn't clear what the relative effect of these measures are.

The Rose Dragon

2011-01-09, 11:44 AM

So if the DM wants to make this harder, should he (1) remove a few dice as penalty, (2) increase the difficulty to 8, or (3) require more than one success? Each of these will make the roll harder to succeed, but it isn't clear what the relative effect of these measures are.

Each extra success required is roughly equivalent to removing two dice from the pool, if the target number is 7. The target number changes are more complex, since they change that equivalency.

Xiander

2011-01-09, 12:02 PM

I find the mechanics of a dice pool system tend to be confusing. For example, in White Wolf, to jump over something you roll a number of dice equal to Dexterity plus Athletics, and each 7 or higher counts as a success.

So if the DM wants to make this harder, should he (1) remove a few dice as penalty, (2) increase the difficulty to 8, or (3) require more than one success? Each of these will make the roll harder to succeed, but it isn't clear what the relative effect of these measures are.

This is what made OWoD hell to work with because all three measures where a part of the rule system. NWoD has made the goto responce removing dice as a penalty, and further frozen the targetnumbers at 8 which makes everything much easier to understand. (The GM can however still requre several successes for an act to be successfull).

These dice mechanics seem simple and intuitive to me. This is one of the main reasons i find NWoD to be a simple and entertaning system to GM.

tahu88810

2011-01-09, 12:05 PM

It's a conspiracy to get people to buy more dice.

Knaight

2011-01-09, 12:09 PM

However, other systems (I would say better systems) have much more elegant mechanics. Take Burning Wheel, as a rule one needs to roll 4+ for a success, difficulty is a matter of successes needed. However, there is also a second dimension to skill and attribute, every skill and attribute has a number and a color, black, gray, or white. Black skills are the default, and need 4+, Grey needs 3+, white needs 1+. This creates an incredibly elegant method in which to model variation over a group, or exceptional talent, while maintaining a model of individual capacity that is entirely separate.

Blackfang108

2011-01-09, 12:13 PM

It's a conspiracy to get people to buy more dice.

No, that's rpgs in general. :smallbiggrin:

Side question: Assumed we have 6d2 that show the numbers 0 and 1. What's the formula to calculate how many possibilities there are to get a total of 2?

(Or: How many ways are there to arrange two 1s and four 0s?)

Xuc Xac

2011-01-09, 12:30 PM

Reasons I like dice pools:

Having more dice is better, but it's not completely clear how much better. I think it helps immersion to think "He's a little better at this than I am" rather than "He has a 7% greater chance of success than I do".

The numbers are more visceral. Human beings can see small numbers without counting. If you roll a handful of dice and get 3 successes, you know it at a glance. If you have 5 successes, you know it without having to say "1, 2, 3, 4, 5". But higher numbers (like comparing percentiles or rolling a D20 and adding a modifier than could be well into the double digits) can only be understood on an intellectual, abstract level. The smaller number of successes in a dice pool system is visceral. (If your system involves ridiculously large dice pools like Exalted, then you don't get this benefit.) This visceral attraction is a huge appeal for me. Using percentages offers finer granularity, but it feels "colder" because it only engages the higher brain functions and doesn't involve the "lizard brain". Also, I feel that the finer granularity is only apparent on paper. In actual play, you can only really recognize at most Critical Failure/Failure/Mediocre Success/Unqualified Success/Critical Success. If you can only really process it as one of those five levels of success, why not just have five levels of success in the first place? The extra granularity might be more accurate, but it's below the resolution that you're capable of discerning (it's like paying much more to buy a camera with better pixel resolution than your monitor, printer, or eyeball are capable of processing so the extra pixels are just wasted anyway).

Related to the first point, you have to make decisions based on information like "This action will be easy/really hard" instead of "This action has an 88%/21% chance of success". That's more like the way people make decisions in real life (except maybe insurance adjusters using actuarial tables or something).

Diminishing returns. Any bit of help is a big deal when you have a low level of skill, but those little bonuses don't matter as much at higher levels. At the low end, adding a bonus die for a positive modifier (or improving your skill) can change your chance of success from 50% to 75%. At a higher level, that same +1 die might change your chance of success from 92% to 94%. If each level of skill has the same cost (or an increasing cost), the higher levels become less and less cost effective and lower skill levels are much more enticing to pick up. This makes one-trick ponies possible, but really inefficient compared to ponies with a more varied repertoire (although they might have a signature trick among their variety of abilities). I hate enforced niche protection, so I like this effect.

Getting better doesn't just push the average of your roll higher and higher, it's makes your average roll more and more likely. The better your skill gets, the more predictable the roll will be due to the bell curve getting a higher peak. Professionals can reliably perform at a consistent level because the distribution of their rolls become more clustered around the average as they get bigger dice pools. A one-die-plus-mods system like D20 means that improving from a skill of 5 to 10 means that your rolls go from 15+/-10 to 20+/-10. Going from a 5 die pool to a 10 die pool can mean going from "Usually 2 or 3 successes but 1 or 4 aren't uncommon" to "5 successes almost all of the time".

Kurald Galain

2011-01-09, 12:33 PM

(Or: How many ways are there to arrange two 1s and four 0s?)

That would be 6! / 4! 2! ways out of a total of 2 ^ 6.

Or 15 out of 64.

The Big Dice

2011-01-09, 12:33 PM

(When using a dice pool, you check your relevant skills rank and then roll a number of d6 equal to it. Then you count all the dice that came up with a 4 or higher or a 5 or higher, and the number of these "successes" are your final value.)

That's the World of Darkness dice pool mechanic. L5R uses a dice pool in a very different way.

There, you have a Trait and a Skill, both ranked out of 10. You add the two together to find out how many D10s to roll, keeping a number equal to your Trait. You can never roll more than 10 dice, but you get bonuses if you would have rolled more than 10. Fans of L5R produced a probability chart (http://www.fileden.com/files/2006/6/6/52958/Roleplaying/L5R_/RnK_ProbabilityChart.pdf) that gives percentage chances of making a given Target Number.

L5R also allows the use of Raises, that is the player choosing to increase the Target Number of a given task. This allows for greater amounts of success, but has the greater risk of failure too.

Tengu_temp

2011-01-09, 12:33 PM

1. Rolling several dice is more fun than rolling one die.

2. The more complicated a system is, the harder it is to powergame in it. Dice pools are more complicated than rolling 1d20 or 1d100.

Radar

2011-01-09, 12:42 PM

Side question: Assumed we have 6d2 that show the numbers 0 and 1. What's the formula to calculate how many possibilities there are to get a total of 2?

(Or: How many ways are there to arrange two 1s and four 0s?)

For 6 elements in a row, there are 6! possible arrangements. Since we don't care about swiching two identical elements (two zeros or ones) we should divide it by all possible arrangements within those subsets (zeros only and ones only). With 4 zeros and 2 ones we get 6!/(4!*2!)=15. Now with only zeros and ones, you get a total of 2^6 arrangements possible. So the probability of getting a sum of 2 on your 6d2 is 15/2^6.

This site (http://anydice.com/) has a rather advanced dice roller. Unfortunately dice pool isn't implemented and would have to be coded manualy.

Personaly I prefer summing up dices from a pool rather then counting successes - much easier to handle and gauge probabilities.

Foryn Gilnith

2011-01-09, 12:49 PM

The more complicated a system is, the harder it is to powergame in it. Dice pools are more complicated than rolling 1d20 or 1d100.

Does that really matter? Powergaming is about getting more bonuses. Bonus dice in a dice pool aren't necessarily harder to acquire than bonus modifiers to a d20. Crunching the exact numbers is harder, but the fundamental will to power doesn't require that sort of cerebral analysis. They merely tend to coincide in roleplayers (and some powergamers more into that sort of analysis might even hypothetically be drawn to the challenge).

Arbane

2011-01-09, 12:56 PM

1. Rolling several dice is more fun than rolling one die.

2. The more complicated a system is, the harder it is to powergame in it. Dice pools are more complicated than rolling 1d20 or 1d100.

What's so complicated about powergaming "More Dice = GOOD"?

And I'd argue that's only true for a fairly limited band of complexity. It's fairly tough to powergame RISUS, at one end, and there's tons of "how do I optimize (x)?" threads here, and D&D can get pretty complicated.

----

Another oddball dicepool game is the Weapons of the Gods system - you roll 2 to 8 d10s, and look for matches. The number of dice in the match becomes the tens value of your roll, and the number on the dice is the ones. So a roll of (2,5,6) is a 16 (or a 12 or 15), a roll of (1,3,3,8) is 23, and a roll of (1,8,8,8,8) is a 48.

What makes it interesting is that you can 'store' some rolls to add to another roll later. (Store away 2 9s, to make a later roll go from 39 to 59, for example...)

It's a good thing it has a probability chart in the back of the book, because calculating it is a BEAR.

Tengu_temp

2011-01-09, 02:19 PM

What's so complicated about powergaming "More Dice = GOOD"?

More complex mechanics mean it's harder to count what is the most optimal way of doing things. For example, look at DND 3.5 Power Attack: there are rather easy formulas to calculate what amount of PA is the best in the chosen situation. Those formulas would be much more complex if the game used dice pools.

woodenbandman

2011-01-09, 02:26 PM

More complex mechanics mean it's harder to count what is the most optimal way of doing things. For example, look at DND 3.5 Power Attack: there are rather easy formulas to calculate what amount of PA is the best in the chosen situation. Those formulas would be much more complex if the game used dice pools.

yeah because world of darkness is notoriously balanced and difficult to power game :smallcool:

CarpeGuitarrem

2011-01-09, 02:28 PM

Xuc Xac, with the reasons he listed, hits it right on the head, at least in the areas I'd point out. If you know what to look for (like in nWoD or Mouse Guard), it's a snap to figure out if you succeeded or not.

The math is actually more intuitive and simpler, in my mind. I like counting up successes, instead of adding a bunch of numbers to get a result. To me, it's even more immersive. You're doing less math. If you know what you're looking for (here is where the oWoD with its changeable target number got really tricky) then you can figure it out easy. Heck, White Wolf even has nWoD dice which have the 8-10 colored differently, so you can easily see how many successes you got.

Not only that, but the concept of +1 in a skill or ability = one more die to roll is just very intuitive to understand. I'm all onboard with what Xuc Xac says about dice pools engaging the visceral, instead of the intellectual and abstract.

AyeGill

2011-01-09, 02:48 PM

2. The more complicated the probability calculations of a system is, the harder it is to powergame in it. Dice pools are more complicated than rolling 1d20 or 1d100.

Fixed it for ya.

Seriously, as a system acquires more options, and more types of options, the potential for optimization rises.

true_shinken

2011-01-09, 03:28 PM

2. The more complicated a system is, the harder it is to powergame in it. Dice pools are more complicated than rolling 1d20 or 1d100.

This is oh so very wrong.

GURPS is one of the most complicated systems ever and it's ridiculously easy to break. OWoD used dice pools and was also ridiculously easy to break.

Ernir

2011-01-09, 03:40 PM

I suppose dice pools are better for people who can count, but are bad/slow when it comes to adding and subtracting.

More complex mechanics mean it's harder to count what is the most optimal way of doing things. For example, look at DND 3.5 Power Attack: there are rather easy formulas to calculate what amount of PA is the best in the chosen situation. Those formulas would be much more complex if the game used dice pools.

Pff. You'd be using a probability formula rather than a strictly algebraic formula. Wouldn't bother anyone with a calculator.

true_shinken

2011-01-09, 03:43 PM

Pff. You'd be using a probability formula rather than a strictly algebraic formula. Wouldn't bother anyone with a calculator.

Or a hardcore Pokemon player, wethey calculate probabilities in their heads pretty easily.

AyeGill

2011-01-09, 03:45 PM

Or a hardcore Pokemon player, wethey calculate probabilities in their heads pretty easily.

yeah. i swear, if every kid played pokemon, and their parents played it with them, mathematics advancement would soar.

Tengu_temp

2011-01-09, 03:48 PM

This is oh so very wrong.

GURPS is one of the most complicated systems ever and it's ridiculously easy to break. OWoD used dice pools and was also ridiculously easy to break.

Well, GURPS is an open systemt that can be used for anything, and those games are easy to break by default. And oWoD is ridiculously badly designed.

Kurald Galain

2011-01-09, 03:54 PM

And oWoD is ridiculously badly designed.

Or perhaps it simply had different design goals. It is probably true that any (sufficiently complicated) system can be "broken" by a sufficiently dedicated munchkin, so it's not necessarily a benefit for a system to have "balance" as one of its main design goals. Indeed, near as I can tell, only a handful of RPGs consider balance one of their goals, and all of those clearly fail at achieving that goal.

Terraoblivion

2011-01-09, 04:13 PM

OWoD was pretty badly designed mechanically no matter how you look at it. A large number of rolls for mundane tasks, wildly differing power and usefulness of powers that were supposed to be equal, no system or XP cost for learning some of the most powerful and useful abilities and the list goes on. While balance was not a major concern, it honestly seems that the system in it mostly existed because someone thought that any new RP needs to have mechanics. Pretty much everything is arbitrary, clunky and mindbogglingly unbalanced. I mean, seriously, who thought that Pavise of Foul Presence was a good idea?

true_shinken

2011-01-09, 04:16 PM

OWoD was pretty badly designed mechanically no matter how you look at it.

I have to agree. Even then, it's still one of my favourite games. I never tried NWoD because I liked the mix-and-match nature of OWoD.

The old Storyteller system also graced us with Street Fighter StG, the best combat system ever for fantastic martial arts.

Trekkin

2011-01-09, 07:55 PM

I love dice pools as Shadowrun does them; each required hit needs, on average, three more dice in the pool, and i can work easily from there as a DM without having to stop and work through probabilities.

It also lets me accomplish amazing feats of dice-stackery while I wait for my players to get themselves fed, watered, and ready to play.

The Big Dice

2011-01-09, 08:16 PM

It also lets me accomplish amazing feats of dice-stackery while I wait for my players to get themselves fed, watered, and ready to play.

Which is possibly the most important ting you can do while waiting for players. and I'm glad 'm not the only one who does this.

valadil

2011-01-09, 09:28 PM

So if the DM wants to make this harder, should he (1) remove a few dice as penalty, (2) increase the difficulty to 8, or (3) require more than one success? Each of these will make the roll harder to succeed, but it isn't clear what the relative effect of these measures are.

There are plenty of charts out there showing how these changes can affect your expected result.

There seem to be lots of RPGs out there, that use dice pools. It's an interesting idea, but seems more troublesome to me than it's worth. Simply counting the numbers on the dice and adding a number seems much more intuitive to me than counting the number of successes you rolled.

Intuitive is not necessarily better. Addition may be your first reaction to calculating the value of rolling 4d10. But you can explain a dice pool in a few seconds. "Roll dice, count values over N as a success, return total successes." I'd argue that a dice pool is faster to count than D&D style. Try rolling 10d10. See how long it takes you to count the number of dice above 6. Now see how long it takes you to sum the results. Even if you're damn good at math, counting should be quicker. This means that in a dice pool system you can still throw around a bunch of dice, but won't spend as much time crunching numbers.

I'll also add that dice pools feel different than summation. Sometimes you have to break convention if you want to get players out of their old habits. D&D players are stereotyped as being dungeon crawlers who can't roleplay. If you're trying to play a new system, but don't want to carry old habits and assumptions, making the game feel mechanically different will help convey that you're in a new game.

The Big Dice

2011-01-10, 09:32 AM

But you can explain a dice pool in a few seconds. "Roll dice, count values over N as a success, return total successes." I'd argue that a dice pool is faster to count than D&D style. Try rolling 10d10. See how long it takes you to count the number of dice above 6. Now see how long it takes you to sum the results. Even if you're damn good at math, counting should be quicker. This means that in a dice pool system you can still throw around a bunch of dice, but won't spend as much time crunching numbers.

That's one type of dice pool, but it's far from the only one. If you go here (http://www.l5r.com/rpg/) you can ge the Free RPG Day adventure that AEG put out for L5R 4th edition. It's got quick start section for the rules and a bunch of sample characters you can use to play the module with. And try out a game with a different type of dice pool.

All a dice pool is, is rolling a lot of dice at once. Most RPGs you'll roll between 1 and 3 dice for tasks, with maybe more for damage or maybe not. In a dice pool you'll be rolling 5 or more, more often than not. Hence the name.

true_shinken

2011-01-10, 09:33 AM

I'll also add that dice pools feel different than summation. Sometimes you have to break convention if you want to get players out of their old habits. D&D players are stereotyped as being dungeon crawlers who can't roleplay. If you're trying to play a new system, but don't want to carry old habits and assumptions, making the game feel mechanically different will help convey that you're in a new game.

This, so much this. I'm redisigning an old RPG system and I've decided I'll use additions for combat and dice pools for skills and most other checks.

Kiero

2011-01-10, 09:43 AM

To get a bell curve of probabilities, rather than linear ones. Means a character's skill matters more than simple random chance, since results tend to group around an average.

Winterwind

2011-01-10, 09:49 AM

Beside the already mentioned reasons (of which especially the bell curve one is likely the most crucial), one major advantage of dice pools is, I find, that they tend to not only tell you whether you succeeded or not, but also how well you succeeded - a useful information many other systems don't give.

Moreover, when they tell you how well you succeeded, they do so with sufficiently little variance to make it easy to work with that result - in ShadowRun, whether you end up with one success or six of them is a pretty major difference, and even very advanced characters aren't that likely to score that much more successes, whereas with a mechanic like in, say, D&D, even if you would implement something like "for every point you rolled higher than you had to, you have succeeded better", you would run into trouble because of just how much these numbers would vary - the difference between a very good roll and a poor (but still successful) one might be something like 7 early on (so, a difference of 7 should already be quite significant), but something like 60 with high level characters who have lots of ranks and other stuff enhancing them later on. So, if you said something like "for every point you are over the necessary result, you get mechanical benefit X", this would very quickly lead to the system breaking - it's difficult to have information on how well you succeeded and make it work consistently if you have such big variations of your results in your system.

I actually asked this way back then first time I learned about... I think it's either Exalted or Cthulhutech. I think my friend's answer was with dice pool there are more variables. You can add or substract the dice, give static bonus or penalty, use opposite dice, and so on (I don't know all of them). Or something in that line, crunchs and maths are really not my strong suit.

edit:

There's a wikipedia article about dicepool that I think was what my friend told me.

http://en.wikipedia.org/wiki/Dice_pool

FelixG

2011-01-10, 09:52 AM

Its also highly psychological. some people judge their worth based on how many dice they roll. :smallbiggrin:

That werewolf or space marine commander feels like a big (wo)man when he is rolling 74,612d6! (exaggeration of course)

Person_Man

2011-01-10, 12:36 PM

It allows for greater statistical variance (http://en.wikipedia.org/wiki/Variance), and in some systems you have less math to do, because there are fewer modifiers (class, race, feat, item, magical, situational, etc) to add and subtract.

Also, you tend to roll a lot of dice. Some people enjoy rolling a ton of dice, simply for the sake of rolling.

Kurald Galain

2011-01-10, 12:41 PM

There are plenty of charts out there showing how these changes can affect your expected result.

Sure, but you're missing the point.

Answer me this in five seconds: assuming you've got +12 for a skill roll, what are the odds of you hitting DC 25?

Now answer me this in five seconds: assuming you've got six dice for a skill roll, what are the odds of you getting three successes at TN 7?

Foryn Gilnith

2011-01-10, 02:15 PM

For example, look at DND 3.5 Power Attack: there are rather easy formulas to calculate what amount of PA is the best in the chosen situation.

[Chance to Hit]*10 - [Average Damage]/2[Power Attack Multiplier] is the optimal amount to power attack for, with chance to hit and average damage being calculated before any power attack modifiers. At least, that's what it comes to if I ran the numbers properly. The more damage you do before power attacking, the less you should power attack for; the higher your multiplier or initial accuracy, the more you should power attack for.

Carry on with dice pool discussion.

valadil

2011-01-10, 02:48 PM

Sure, but you're missing the point.

Answer me this in five seconds: assuming you've got +12 for a skill roll, what are the odds of you hitting DC 25?

Now answer me this in five seconds: assuming you've got six dice for a skill roll, what are the odds of you getting three successes at TN 7?

I can't do that. I've only ever GMed D&D (and MERP, but that's d100 based). However, my friends who have only done WoD could tell you those odds off the tops of their heads. One of the WoD guys even finds d20 confusing because he doesn't grasp how adding +2 to a DC will affect the check.

I feel like dice pool scenarios work out so long as you know what a target difficulty should be. If climbing a ladder is diff 2 and a wall is diff 6, odds are a tree is going to be a 4 or 5 depending on the kind of tree. I'd rather set the difficulty based on the flavor of what's going on than on the expected rate of PC success.

Addition may be your first reaction to calculating the value of rolling 4d10. But you can explain a dice pool in a few seconds. "Roll dice, count values over N as a success, return total successes." I'd argue that a dice pool is faster to count than D&D style. Try rolling 10d10. See how long it takes you to count the number of dice above 6. Now see how long it takes you to sum the results.

Here's why I think this isn't a good point:

It really has to be "Roll X dice, count values over N as a success, return total successes."

With a "regular roll" you say "Roll 1 dice, add X". Either way, you have to determine X before you roll. Adding X to a roll or counting the number of dice that show a success don't seem that different in difficulty when it comes to basic math.

10d10 is a pain to count, but just because you use the numbers on the dice, doesn't mean such situations arise. Even in D&D, you usually roll 1d20 and one die for damage. Sneak Attack Damage and Spell Damage is something else, but that's the fault of D&D, not the idea of adding two numbers.

Answer me this in five seconds: assuming you've got +12 for a skill roll, what are the odds of you hitting DC 25?

65%?

Not that I ever, in my 12 years of playing, made such a calculation while playing. Ever.

valadil

2011-01-10, 04:25 PM

10d10 is a pain to count, but just because you use the numbers on the dice, doesn't mean such situations arise. Even in D&D, you usually roll 1d20 and one die for damage. Sneak Attack Damage and Spell Damage is something else, but that's the fault of D&D, not the idea of adding two numbers.

Fair enough. I'll concede that 1d20 + N is probably quicker than Nd10 count greater than X. But I think that D&D's lots of dice problem comes up pretty damn frequently. I've even seen players take 10s of seconds to add dice in GURPS (which is 3d6). Also, didn't NWoD get rid of the difficulty threshold? That would bring you back down to one variable. You still need to gather N dice, but the DC is always 6.

If you want a system that rolls a large number of dice at once (and that is not always a fair assumption to make), I maintain that counting above a threshold is faster than summing all those dice.

lesser_minion

2011-01-10, 04:39 PM

Sure, but you're missing the point.

Answer me this in five seconds: assuming you've got +12 for a skill roll, what are the odds of you hitting DC 25?

Now answer me this in five seconds: assuming you've got six dice for a skill roll, what are the odds of you getting three successes at TN 7?

I think that's probably one of the main arguments involved, at least for WoD -- with a d20 + modifiers roll, it's trivial to extract information such as the probability of success, which your character probably wouldn't have.

With a dice pool, it's trivial to get a rough idea of how confident you should be in the result -- which is information your character probably does have -- but harder to figure out the exact probability (but it's entirely trivial for the writers to figure out the probability if they want it).

Ravens_cry

2011-01-10, 04:41 PM

I've pretty much played d20 in some form or the other my entire career of gaming. That being said, once I got the hang of it, a 'count successes' dice pool sounds much more fast paced. I am terrible at mental math and putting me in front of a bung of d6's, plus assorted other die types, is a sure way to slow down the game. But I think even I could could count successes pretty rapidly.

CarpeGuitarrem

2011-01-10, 04:49 PM

Here's why I think this isn't a good point:

It really has to be "Roll X dice, count values over N as a success, return total successes."

With a "regular roll" you say "Roll 1 dice, add X". Either way, you have to determine X before you roll. Adding X to a roll or counting the number of dice that show a success don't seem that different in difficulty when it comes to basic math.

10d10 is a pain to count, but just because you use the numbers on the dice, doesn't mean such situations arise. Even in D&D, you usually roll 1d20 and one die for damage. Sneak Attack Damage and Spell Damage is something else, but that's the fault of D&D, not the idea of adding two numbers.

The thing is, Dice Pool systems often remove the math element when you're looking for the result. You're keeping your eyes peeled for those magic numbers which signal success. Instead of looking for dice with results greater than 7, you're looking for dice with 8s, 9s, and 10s. It changes it from a math skill to a number-reading skill, and number-reading is far more fundamental and simpler than math.

I believe that with a bit of play, anyone can be trained to read a dice pool far quicker than adding a number to a d20 roll.

TheEmerged

2011-01-10, 07:12 PM

My favorite dice mechanic was the one from Alternity. Based dice is a d20. Instead of the standard, constant penalty/bonus however you get a "step" penalty or bonus. It starts with d4, then goes up/down to d6, d8, and so forth. This gives the result a curve without involving insane numbers of dice.

It's a "roll low" system though - step penalties are added, step bonuses are subtracted. Your target number is your related attribute plus the number of skill ranks you have.

The part that compensated for being a "roll low" system is that there are degrees of success. Roll half of your target number and you've got a good success. Roll half of THAT and you've got an amazing success.

This lead to some oddities, of course (I didn't say it was perfect, I said it was my favorite). That first step penalty/bonus was worth a lot more than subsequent ones -- unless you got far enough to make the jump from d12 to d20. Similarly getting that target number to a multiple of 4 was pretty huge; going from 15 to 16 felt a lot larger than going from 16 to 17, for example.

Knaight

2011-01-10, 07:16 PM

I'm going to weigh in with a pro dicepool stance that I suspect isn't very common. I love math, use it intuitively, think easily in geometry, and am, in general, not someone who is going to have any issue with numbers. I consider the most natural methods of modeling resources (e.g. health) integrals, and what few written notes I have are liable to have set notation in them.

I'm also a very minimalist game designer. I consider any RPG I make that can't be easily memorized a failure, and prefer systems that act as elegant models, with relatively few fiddly bits each of which has plenty of utility. Dice pools lend themselves to this, among other benefits.

That said, I usually play heavily modified Fudge, which is a roll and add system. However, that is largely because of a few traits that work very well, rather than a general appreciation for the design. The small, zero centered skill and attribute ladder allows easy conception of capability and difficulty in standard deviation, the curved distribution makes benefits count, and the system is easy to memorize and requires no mechanical prep work. Interesting as math is, trivial arithmetic and algebra just gets old after a while. Elegant math behind the scenes is preferable.

Doug Lampert

2011-01-10, 09:46 PM

Reasons I like dice pools:

...

Getting better doesn't just push the average of your roll higher and higher, it's makes your average roll more and more likely. The better your skill gets, the more predictable the roll will be due to the bell curve getting a higher peak. Professionals can reliably perform at a consistent level because the distribution of their rolls become more clustered around the average as they get bigger dice pools. A one-die-plus-mods system like D20 means that improving from a skill of 5 to 10 means that your rolls go from 15+/-10 to 20+/-10. Going from a 5 die pool to a 10 die pool can mean going from "Usually 2 or 3 successes but 1 or 4 aren't uncommon" to "5 successes almost all of the time".

This last is wrong. The variance increases with increased numbers of dice.

If a die succeeds half the time then with 5 dice you'll get 2 or 3 successes over 60% of the time.

With 10 dice you'll get a 5 less than a quarter of the time. Not almost all the time.

Now, your chance of a 4-6 is actually slighly higher than the chances of the guy with 5 dice rolling a 2-3. But the uncertainty increased.

The standard deviation goes up SLOWER than the average number of successes, so the chances of a 0 or 1 go down, but the variance and standard deviation ARE increasing which they do not with a flat d20 + modifier system.

Xuc Xac

2011-01-11, 10:44 AM

This last is wrong. The variance increases with increased numbers of dice.

If a die succeeds half the time then with 5 dice you'll get 2 or 3 successes over 60% of the time.

With 10 dice you'll get a 5 less than a quarter of the time. Not almost all the time.

Exactly 5 successes on those 10 dice will only be 25% of the time. But "5 or more successes" (which is the same thing unless you're playing a bizarre game that punishes you for rolling too well), will happen over 60% of the time too (actually it's 62% according to my spreadsheet).

I don't know of any dice pool systems that ever require you to roll "exactly X successes". They are all of the "at least X successes" type.

AyeGill

2011-01-11, 10:48 AM

This last is wrong. The variance increases with increased numbers of dice.

If a die succeeds half the time then with 5 dice you'll get 2 or 3 successes over 60% of the time.

With 10 dice you'll get a 5 less than a quarter of the time. Not almost all the time.

Now, your chance of a 4-6 is actually slighly higher than the chances of the guy with 5 dice rolling a 2-3. But the uncertainty increased.

The standard deviation goes up SLOWER than the average number of successes, so the chances of a 0 or 1 go down, but the variance and standard deviation ARE increasing which they do not with a flat d20 + modifier system.

This is right. I think the misconception is that, as number of dice increases, the variance in the sum of all the dice decreases. But, as you say, with counting successes, it gets more variable. Which is not necessarily a bad thing, mind you.

Callista

2011-01-11, 10:50 AM

Has anyone ever made a statisic curve diagram for that? :smallbiggrin:

Somehow I'm one of the people who thinks they are really helpful for understanding such things.Of course they have. People who are nerdy enough to like tabletop RPGs are often also nerdy enough to like statistics too...

Now you're making me want to work out the distributions. And I'm supposed to be working on fluid dynamics problems. Darn you. :smallfurious:

AyeGill

2011-01-11, 10:53 AM

Of course they have. People who are nerdy enough to like tabletop RPGs are often also nerdy enough to like statistics too...

Now you're making me want to work out the distributions. And I'm supposed to be working on fluid dynamics problems. Darn you. :smallfurious:

'Tis the curse of all we math geeks, too easily do we fall into the trap that is probabilistic analysis of RPGs

Dingle

2011-01-11, 11:33 AM

The guy who runs our Vampire: the Masqerade game absolutely hates statistics and maths.

The more dice you roll, the more closely the results approximate a gaussian distribution, but large numbers are awkward.

The fact that dice pool systems are easy to use for people who don't like doing more maths than counting adding small numbers is a definite benefit compared to other systems with realistic gaussian probability distributions.

They're also complex enough to be interesting to people who like maths (I'm doing a Theoretical Physics degree)

I absolutely fail at math, a trait I have from my mother.

With the notable exceptions of geometry (that's not really math) and statistics. Never understood while anyone think it's hard. And trying to figure something out and ending up with rediscovering formulas that you could just have looked up if you knew there already is a formula for that, is certainly not what most people do.

But people have tried to explain logarithms to me at least 8 times and I still have no idea what the word means. I can't even multiply fractions. :smallbiggrin:

Tavar

2011-01-11, 11:57 AM

The fact that dice pool systems are easy to use for people who don't like doing more maths than counting adding small numbers is a definite benefit compared to other systems with realistic gaussian probability distributions.

There's also the fact that you tend to have less modifiers. Adding +1 or 2 to a roll is common in DnD, and it's easy to loose track of them. In Dice pool systems, there don't seem to be many effects that add or subtract dice to a roll, and those that exist seem to be based more on the individual roll and one time or permanent effects, not temporary modifiers.

Oh, and Cybrans forever!

Dingle

2011-01-11, 03:42 PM

as far as modifiers go, different ways of making tasks harder can affect different skill levels differently.

an increase in target number affects everyone evenly (possibly easier on low pools if 1s subtract (owod) or if there's an option to spend something for an auto-success (owod willpower), ), but reducing dicepools hit low pools harder, and higher required successes can easily make it nigh impossible for low skill charachters.

Oracle_Hunter

2011-01-11, 03:57 PM

Hmmm....

So, how do you figure out the relative impact on probable Successes between modifying DCs and adding/subtracting Dice from a pool?

For the sake of argument:

- Assume d10s with a base DC of 7.

- We're looking at the probability of rolling 1 Success starting with a Dice Pool of 1.

- Specifically, whether reducing the DC by 1 (i.e. DC 6) or adding another die (i.e. making a Dice Pool of 2) increases the likelihood of rolling 1 Success more.

If you can make a rate of exchange (i.e. adding X dice to a Dice Pool is equivalent to reducing the DC by Y) that'd be great.

The first question is: Why? If you know what Target Number has a 50% chance, I think that's all you ever really need.

But if you think you have to, dice pools have the really great advatnage, that a die can only say "success" or "failure". And since you usually count all the successes, you can say all successes are 1 and all failures are 0.

Transforming all possible rolls to 1 and 0 makes calculating probabilities infinetly simpler!

Basically, adding or substracting numbers from the final result only shifts the curve to the left or to the right when drawn on an axis. Increasing the number of rolls (or dice in this case) improves the chances of rolling close to the center of the distribution and reduces the chance to get to the extremes (like 0 and max.)

By saying 1d10, DC 7 I assume you need a 7 to have a success? That would mean the chance that a single die is a success is 0.4, the chance for a failure is 0.6.

lesser_minion

2011-01-11, 04:21 PM

Well, the general formula for the probability of getting r successes for a random variable X, where X ~ B(n, p) and q = (1 - p) is:

P(X=r) = nCr * (prqn-r)

Where n is the size of the dice pool, X is the actual number of successes, r is the desired number of successes, p is the probability of a success on any given die, and q is the probability of a failure on any given die.

nCr is the binomial coefficient, which we can either obtain using Pascal's triangle, or by using the formula:

nCr = n!/r!(n-r)!

Where y! is the factorial of y.

For exactly one success, the whole thing becomes:

P(X=1) = npqn-1

Which is a little easier.

Oracle_Hunter

2011-01-11, 04:25 PM

Does it change if we're looking for "at least" 1 Success rather than "exactly" 1 Success??

lesser_minion

2011-01-11, 04:28 PM

Does it change if we're looking for "at least" 1 Success rather than "exactly" 1 Success??

It doesn't change the general formula, but it does make things easier overall. If you're looking for at least one success, then you work out the probability of getting zero successes, which is given by:

P(X == 0) = qn

And then work out the probability of not getting that result, which leaves you with:

P(X >= 1) = 1 - qn

Second post vs. Ninjas:

For the sake of argument:

- Assume d10s with a base DC of 7.

- We're looking at the probability of rolling 1 Success starting with a Dice Pool of 1.

- Specifically, whether reducing the DC by 1 (i.e. DC 6) or adding another die (i.e. making a Dice Pool of 2) increases the likelihood of rolling 1 Success more.

Calculating the chance for a number of successes is a bit difficult. But for some reason calculating the chance for failure is much easier. Just substract that from 100% and you get your desired result. :smallwink:

1d10, DC 7: Chance for 6 or less = 0.6

1 die, chance for 0 successes: 0.6 = 60%

2 dice, chance for 0 successes: 0.6 * 0.6 = 36%

3 dice, chance for 0 successes: 0.6 * 0.6 * 0.6 = 22%

4 dice, chance for 0 successes: 0.6 ^4 = 13%

5 dice, chance for 0 successes: 0.6 ^5 = 8%

6 dice, chance for 0 successes: 0.6 ^6 = 5%

The other thing you said is the chance for 6, 5, 4, 3, 2, and 1 as a success while still roling 1d10.

1d10, DC 7: Chance for 6 or lower: 60%

1d10, DC 6: Chance for 5 or lower: 50%

1d10, DC 5: Chance for 4 or lower: 40%

1d10, DC 4: Chance for 3 or lower: 30%

1d10, DC 3: Chance for 2 or lower: 20%

1d10, DC 2: Chance for 1 or lower: 10%

And for direct compairison

Method 1/Method 2

60% / 60%

36% / 50%

22% / 40%

13% / 30%

8% / 20%

5%/ 10%

The chances for failure are always lower for the greater dice pool than for the reduced DC.

Oracle_Hunter

2011-01-11, 04:40 PM

And then work out the probability of not getting that result, which leaves you with:

P(X >= 1) = 1 - qn

Which expands to 1 - (1-p)n

So if p = 4/10 = 0.4 and n = 1 we get

P(X >= 1) = 1 - (1-(0.4))1

P(X >= 1) = 1 - 1 + 0.4

P(X >= 1) = 0.4

But if p = 5/10 = 0.5 and n = 1 we get

P(X >= 1) = 0.4

And if p= 4/10 = 0.4 and n = 2 we get

P(X >= 1) = 1 - (1-(0.4))2

P(X >= 1) = 1 - (0.6)2

P(X >= 1) = 0.64

Which seems to say that adding dice is worth more (+26% vs. +10%).

Now, if p= 5/10 = 0.5 and n = 2 we get

P(X >= 1) = 1 - (1-(0.5))2

P(X >= 1) = 1 - (0.5)2

P(X >= 1) = 0.75

Which is a +35% bonus. Provided I didn't screw anything up :smallredface:

Error in second spoiler. You didn't change 0.4 to 0.5.

Oracle_Hunter

2011-01-11, 04:42 PM

Error in second spoiler. You didn't change 0.4 to 0.5.

Damn!

Well, it looks like my questions have been answered. Good to know :smallbiggrin:

I'm also not sure what you're trying to do, but in the third spoiler the 0,6^2 seems odd to me. I think the bracets are not right.

Edit: I'm wrong: You're 0,64 is my -36%. Our results match.

Dingle

2011-01-11, 05:03 PM

The point is that different things affect different pools differently.

we'll, compare person 1 with 2 dice in his pool, and person 2 with 6 dice in his dice pool.

we'll also assume that we're using 10 sided dice with success on 7-10 (40% per die).

normally

person 1: 64%

person 2: 95.33

adding dice:

if we add 2 to everyone: person 1 is rolling twice as many dice, person 2 is rolling 1/3 more

probabilities:

person 1: 87.04%

person 2: 98.32%

subtracting dice:

if we subtract 2 to everyone: person 1 is rolling no dice, person 2 is rolling 1/3 fewer

probabilities:

person 1: 0%

person 2: 87.04%

increasing difficulty:

increase target number by 2 to 9 (20%)

probabilities:

person 1: 36%

person 2: 73.79%

increasing required successes:

increase by 1 (to 2):

probabilities:

person 1: 9%

person 2: 57.98%

increase by 2 (to 3)

probabilities:

person 1: 0%

person 2: 25.57%

I've been horribly ninja'd

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