# dice pool outcome probability calculator

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### #1 Yepesnopes

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Posted 20 January 2013 - 07:05 AM

I posted this on the beta forums also, I don't know which of the two are active right now, sorry for the duplicity.

Has anyone done a program, excel sheet, or similar that calculates the probabilities of success and/or possible outcomes of a given dice pool for SW EotE?

Cheers,

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### #2 Fiddleback

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Posted 20 January 2013 - 08:05 AM

Given what we now know about the design of the dice system from here and here from Jay, I'm not sure that this is an undertaking that will have any major payoffs.  The sheer numbers of potential outcomes and options make it difficult to nail down in a purely mathematical sense.  It is, afterall, intended to be a marrative rather than mechanical resolution system.  If you make choices purely based on the probability of one result over another (not that YOU are specifically), you might be missing the point.  Anyway, check out those two links; they, and the discussion they spark, might help explain what is going on with the dice and why calculating the probability of results is, perhaps, a more daunting task than it first appears.  Jay does a nice job of explaining how it all works.

Cheers!

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### #3 Yepesnopes

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Posted 20 January 2013 - 12:01 PM

Actually I am comming from Warhammer 3, so I am acquainted with the dice pool mechanic, outcomes and narrative purpouse. So far I have not played SW EotE yet, I am reading through the beta book, and I realize the dice pool builds a bit different than in Warhammer 3, but the outcomes are mainly the same.

In warhammer 3 we have an excel sheet that does a bit of probability calculations. Given a dice pool it tells you the percentage of obtaining a simple success or a 3+ success. It also tells you the probability of rolling at least two beneficial side effects, the probability of obtaining at least two detrimental side effects…well and many more.

Still you are right, it is not important for the game itself, but I like it. It helps when doing a bit of phylosophical / theoretical RPG discussion.

If nobody goes for it, I will try to convert the one we have in warhammer 3 to SW EotE.

Cheers,

Yepes

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### #4 Droma

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Posted 20 January 2013 - 05:22 PM

As long as you have the same amount of ability dice as difficulty dice or better you are likely to hit. The problem comes when you start including setback dice or challenge dice into the mix.

The most important calculation to figure out in my opinion is whether or not it's better to upgrade an ability dice to proficiency dice or gain an additional ability dice.

Example: I have 2 agility and 1 rank in ranged heavy do I get 3 agility or another rank in ranged heavy?

### #5 Voice

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Posted 20 January 2013 - 05:50 PM

It depends.  People with more time to spend on the statistics than I have claimed that adding an Ability die is better than upgrading to a Proficiency die.

If I want to put points into being good with a blaster rifle (ranged - heavy), I can do it by boosting my Agility from 2 to 3 (30 XP), or by buying two ranks in the skill (15-25 XP).  (I could, of course, do both; but we're comparing basic options here.)

The boosted Agility has broader payoff up front for Agility based skills, but it costs more (in some cases *significantly* more), and leaves me without any Proficiency dice to roll, so I'll never hit that Triumph with my blaster rifle, so my Advantages better come up hot enough to make up the difference.

Note: We'll assume that both characters have Ranged - heavy on their career skill list moving forward.  Assuming they both *don't* only changes the individual costs, and assuming that only 1 does just loads the deck against the other one.

After character creation, the Skill character only has to spend 35 XP to hit a pool of 4 dice (2c/4s).  That same 35 XP for the Agility character would only give them 3 dice (3c/3s) (30 XP spent, 5 'in the bank' for the next rank).  As the skill points get more expensive, that 15 XP 'lead' becomes smaller and if the two characters allocate equal XP toward boosting their raw dice pools in that skill, they will leapfrog each other in effectiveness.  (The Skill character will add an extra die first, but when their pools are of equal size, the Agility character will have 1 more Proficiency die.)

At maximum XP expenditure, the Agility character will be better by a single Proficiency die because any boost the Skill character can get to a Characteristic the Agility character can get as well, and for the same overall cost.  (But at the same post-creation cost, the Skill character will also have had 15 more XP to put into other Skills or Talents as well.)

The Skill option means 'topping out' lower than the Characteristic option, but it also means having more XP to allocate in other ways.  As a result, which is 'better' will depend on a *wide* range of questions.

### #6 LethalDose

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Posted 21 January 2013 - 10:56 AM

Yep.  Back at the start of EotE's beta, I wrote scripts for R to generate large pools of dice pool results, which was how I provided evidence for those claims (adding an ability is a bigger gain than upgrading a die, etc).  R (aka CRAN) is a free, command based statistical package and is downloable here.

The results of each roll are aggregated and the total number of net successes, net advantages, & number of despair and stored in a 4 x n matrix, where n is the number of times the pool is simulated.  I basically just wrote code to output whatever parameters I was specifically interested in estimating.  So if you're looking for a nice, pretty interface and clean output, it's probably not for you.  But, if you just want the numbers and a lot of flexibility and access to the results, it might be fine.  For the former, you'd need someone more savvy coding applications, where I just really cared about the latter.

So, If this DOES work for you, I can post or send the script code somehwere.

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #7 Kallabecca

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Posted 21 January 2013 - 12:26 PM

Part of the problem in setting this up is what exactly are you wanting to see in the output? With just two dice (1 Difficulty, 1 Ability) there are as many as 64 different possible outcomes. At the extreme other end, you could have 6 Proficiency against 6 Challenge with up to 6 Boost and 6 Setback which is on the order of 2*10^22 possible outcomes.

The simplest displays would be those that count > 0 Successes, > 0 Advantages, > 0 Triumphs or > 0 Despair

### #8 Kallabecca

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Posted 21 January 2013 - 01:33 PM

LethalDose said:

Yep.  Back at the start of EotE's beta, I wrote scripts for R to generate large pools of dice pool results, which was how I provided evidence for those claims (adding an ability is a bigger gain than upgrading a die, etc).  R (aka CRAN) is a free, command based statistical package and is downloable here.

The results of each roll are aggregated and the total number of net successes, net advantages, & number of despair and stored in a 4 x n matrix, where n is the number of times the pool is simulated.  I basically just wrote code to output whatever parameters I was specifically interested in estimating.  So if you're looking for a nice, pretty interface and clean output, it's probably not for you.  But, if you just want the numbers and a lot of flexibility and access to the results, it might be fine.  For the former, you'd need someone more savvy coding applications, where I just really cared about the latter.

So, If this DOES work for you, I can post or send the script code somehwere.

-WJL

When thinking this problem over last night I realized that you don't need to do a Monte Carlo type simulation. Just the combinitorix of the dice will get the actual distribution of the results.

### #9 Kallabecca

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Posted 21 January 2013 - 03:19 PM

So, starting from my dice roller, I was able to get it to do this work, but aside from counting Successes vs Failures or Advantages vs Threat, not sure what it should display.

### #10 LethalDose

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Posted 21 January 2013 - 07:52 PM

You're probably right, I didn't have to you Monte Carlo sampling, but I frequently prefer them for a few reasons:

1. I don't have to figure out the relative values of the terminal outcomes, and which are degenerate, which I suspect would be particularly difficult to figure out in all four dimensions.  Besides, with a large sample size, the outcome 'space' should be fully (or at least, reasonably) explored.
2. I can easily and directly find Probability/credibility intervals.  In simulations, confidence intervals in simulated results are, at best, completely f*cking useless, and at worst (and more likely) misleading.  This is because conf. intervals rely on sample size, which is arbitrarily large in simulations.  I don't think you can get PI's from the combinatorix method, but I could be wrong
3. The algorithm was much easier for me to code as a MC  because of how similar the algorithm was to an old project I worked on.
4. Since the process generating the results is perfectly understood, I think these results are more like what you'd see on the table.  I also have a lot of confidence that my method is giving me good answers because the steps involved are very simple:
• RNG to assign a face is just a modified unary generator
• Assign value to the face using the matrix of outcomes provided in the Beta book.
• Roll the die and add it to the previous total

I can look at individual rolls, instead of expected values of the rolls, and I can easily debug the simple code.

Admittedly, the combinatoric (is that a word?) would give you exact results, but man, what a headache that'd for me to make sense of the output, and I'd be concerned about making a mistake coding my algorithm.  I think both ways are perfectly valid.  I chose MC because it's familiar to me, and gives me data in a form I'm most familiar dealing with (a matrix with a column for each roll, and a line for each outcome axis), especially in the context of R and it's analysis functions.

If you've coded your combinatorial method, I'd be more than happy to see how my output compares to yours.  Thanks for the good input!

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #11 Yepesnopes

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Posted 21 January 2013 - 08:11 PM

LethalDose said:

Yep.  Back at the start of EotE's beta, I wrote scripts for R to generate large pools of dice pool results, which was how I provided evidence for those claims (adding an ability is a bigger gain than upgrading a die, etc).  R (aka CRAN) is a free, command based statistical package and is downloable here.

The results of each roll are aggregated and the total number of net successes, net advantages, & number of despair and stored in a 4 x n matrix, where n is the number of times the pool is simulated.  I basically just wrote code to output whatever parameters I was specifically interested in estimating.  So if you're looking for a nice, pretty interface and clean output, it's probably not for you.  But, if you just want the numbers and a lot of flexibility and access to the results, it might be fine.  For the former, you'd need someone more savvy coding applications, where I just really cared about the latter.

So, If this DOES work for you, I can post or send the script code somehwere.

-WJL

Yepes

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Dice statistics calculator for SW EotE

### #12 Kallabecca

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Posted 22 January 2013 - 03:06 AM

LethalDose said:

You're probably right, I didn't have to you Monte Carlo sampling, but I frequently prefer them for a few reasons:

1. I don't have to figure out the relative values of the terminal outcomes, and which are degenerate, which I suspect would be particularly difficult to figure out in all four dimensions.  Besides, with a large sample size, the outcome 'space' should be fully (or at least, reasonably) explored.
2. I can easily and directly find Probability/credibility intervals.  In simulations, confidence intervals in simulated results are, at best, completely f*cking useless, and at worst (and more likely) misleading.  This is because conf. intervals rely on sample size, which is arbitrarily large in simulations.  I don't think you can get PI's from the combinatorix method, but I could be wrong
3. The algorithm was much easier for me to code as a MC  because of how similar the algorithm was to an old project I worked on.
4. Since the process generating the results is perfectly understood, I think these results are more like what you'd see on the table.  I also have a lot of confidence that my method is giving me good answers because the steps involved are very simple:
• RNG to assign a face is just a modified unary generator
• Assign value to the face using the matrix of outcomes provided in the Beta book.
• Roll the die and add it to the previous total

I can look at individual rolls, instead of expected values of the rolls, and I can easily debug the simple code.

Admittedly, the combinatoric (is that a word?) would give you exact results, but man, what a headache that'd for me to make sense of the output, and I'd be concerned about making a mistake coding my algorithm.  I think both ways are perfectly valid.  I chose MC because it's familiar to me, and gives me data in a form I'm most familiar dealing with (a matrix with a column for each roll, and a line for each outcome axis), especially in the context of R and it's analysis functions.

If you've coded your combinatorial method, I'd be more than happy to see how my output compares to yours.  Thanks for the good input!

-WJL

You don't need a CI for known values. In the case of dice, what is on the sides is known and unless something is wrong with the physical die, then they are truly random and so you can just build up a table of combinations. Like in the case of an Ability + Difficulty, you get the following results.

 12 18.75% a 6 9.38% stt 2 3.13% faa 1 1.56% tt 1 1.56% sst 3 4.69% ss 1 1.56% sa 1 1.56% aa 1 1.56% f 5 7.81% t 7 10.94% ft 1 1.56% ff 1 1.56% st 8 12.50% fa 4 6.25% s 6 9.38% ffaa 1 1.56% sstt 1 1.56% ffa 2 3.13%

Each die has 8 sides, so the total combinations is 64 (8 * 8). As the number of dice increases the combinations keep going up. As I noted above about the worst case scenario of dice (6 Proficiency, 6 Challenge, 6 Boost and 6 Setback) that results in a fairly large pool of possible results. Originally I said it was on the order of 10^22. I realized that the Boost and Setback dice are really 3 choices not 6 (since 2 sides share the same result for each possible result) which reduces the table to 10^18. Doing an MC of something that large would require a very large number of runs. My original tests in the other thread was 10^5 samples for just 2 dice (max of 64 combinations) to get the final numbers that came really close to those listed in the table here. In comparison, that would barely scratch the surface of the possibilities of the largest pool.

### #13 Yepesnopes

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Posted 22 January 2013 - 03:22 AM

Wow!

Well, I was not looking into a program that tells you all possible outcomes. Something just more simple that tells you a few things, like

simple succes probability /failure

3+ successes

rolling 2+ disavantages

etc.

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### #14 Kallabecca

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Posted 22 January 2013 - 03:36 AM

Yepesnopes said:

Wow!

Well, I was not looking into a program that tells you all possible outcomes. Something just more simple that tells you a few things, like

simple succes probability /failure

3+ successes

rolling 2+ disavantages

etc.

That was why I'd asked earlier what you were looking to see. And it is hard to code for "etc…"

To figure out each of your things, the combinations are needed anyways, so all that changes is how the results are filtered for display.

### #15 LethalDose

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Posted 22 January 2013 - 06:39 AM

Kallabecca said:

You don't need a CI for known values. In the case of dice, what is on the sides is known and unless something is wrong with the physical die, then they are truly random and so you can just build up a table of combinations. Like in the case of an Ability + Difficulty, you get the following results.

 12 18.75% a 6 9.38% stt 2 3.13% faa 1 1.56% tt 1 1.56% sst 3 4.69% ss 1 1.56% sa 1 1.56% aa 1 1.56% f 5 7.81% t 7 10.94% ft 1 1.56% ff 1 1.56% st 8 12.50% fa 4 6.25% s 6 9.38% ffaa 1 1.56% sstt 1 1.56% ffa 2 3.13%

Each die has 8 sides, so the total combinations is 64 (8 * 8). As the number of dice increases the combinations keep going up. As I noted above about the worst case scenario of dice (6 Proficiency, 6 Challenge, 6 Boost and 6 Setback) that results in a fairly large pool of possible results. Originally I said it was on the order of 10^22. I realized that the Boost and Setback dice are really 3 choices not 6 (since 2 sides share the same result for each possible result) which reduces the table to 10^18. Doing an MC of something that large would require a very large number of runs. My original tests in the other thread was 10^5 samples for just 2 dice (max of 64 combinations) to get the final numbers that came really close to those listed in the table here. In comparison, that would barely scratch the surface of the possibilities of the largest pool.

On confidence intervals, no, you don't need them for known exact parameter values (as compared to estimated parameter values).  But probability intervals are NOT confidence intervals.  Even if you know the exact parameter value, e.g you knew exactly what the mean or median of a random process was (in which case you don't need a confidence interval to estimate uncertainy about said parameter), it still doesn't describle how the outcomes (not the parameter) are distributed.  Probability/credible intervals do provide you with an easily intepreted summary of where the values fall. For example, if a distibution (not a mean or median, the WHOLE distribution) has a 90% probaility interval of (-1, 3), then 90% of the results will have fall between -1 and 3.

For example, lets say we KNOW the median of success on some roll is 2.  Well, cool, but we could have this from an infinite number of distributions where the median is two, some examples of which have the following 90% probability intervals:

• (-4,3)
• (1, 5)
• (-1,3)

To me, those are very very different distributions.  Notice there's chance of failure for the second one is less than 10% (no guarantee of symettric distribution) , but appears to be higher on the others since their intervals include 0 and negative values.  It doesn't give ALL the information about a distribution, but it is a quick way of providing information abut it, just like confidence interval does.  Also, the PI's from an MC simulation don't rely on or require defined distributions.

On exploration of the event space, okay, you're right, it would take a very large MC simulation to get, or even have a chance of getting every outcome.  But I don't need to observe every possible outcome to get good information, for several reasons.  First, Probability intervals are independant of sample size.  After a certain point, say 100 or so simulations (and this number is based on personal experience), the PI's don't change much and I'm mostly using >10k simulations (typically 50k). Empirically my PIs are very very stable between simulations.  Second, thanks to the WLoLN, I know my calculated means do approach the real means.

To compare to observational studies, you don't have to observe every possible configuration of predictors and outcomes (in fact to do so, you would probably not have a random sample, which screws up inference).  Similarly, I don't need to observe every possible outcome from a MC simulation for it to be valid.  See the method of pi calculation on wiki's MC site.  I don't need every possible observation, I only need a representative sample.  Explicitly, I'm addressing the 3 goal listed int he MC method's site: generation of samples from a probability distribution when a deterministic algorithm is infeasible (I think the combinatorial method is infeasible).

Now contrast with your combinatorial method, where you DO have to calculate all possible outcomes (which you've pointed out is along the 18th order of magnitude), also takes a very long time.  The aggregation of that many individual results into a usable form, I would think, would be difficult, especially to do things like calculate correlation and PI's.

So, sum up: There are some short-comings of the MC method that your combinatorial method solves.  Personally, I don't think that increased complexity of the combinatorial method is worth said complexity, but if you do, by all means please code it so we can compare results.

-WJL

"All models are wrong, but some models are useful."  - George E. P. Box

### #16 Kallabecca

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Posted 22 January 2013 - 09:09 AM

LethalDose said:

So, sum up: There are some short-comings of the MC method that your combinatorial method solves.  Personally, I don't think that increased complexity of the combinatorial method is worth said complexity, but if you do, by all means please code it so we can compare results.

-WJL

I already did code it up. The chart was from running it for 1 Ability + 1 Difficulty.

From that table comes the question of what is desired. If this was most other systems (like Savage Worlds or D&D or Shadowrun) I'd know what was desired, namely success (or success and a raise for Savage Worlds) given my bucket of dice. For SWEotE it isn't as simple. What should be collected into which buckets?

One suggestion was 1 Success, 3+ Successes, 1 Advantage, 3+ Advantages, etc… which is fine, not they they really have much direct meaning in and of themselves (since different abilities require different amount of Advantages to activate and such).

### #17 Yepesnopes

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Posted 01 February 2013 - 02:33 AM

I have adapted the dice probability calculator from Warhammer 3 to EotE, here is the link. It calculates a very limited amount of outcomes, yet enough to have an idea. While not very useful for the game experience itself, it allows some numerology. For those GM and players who like these sort of things.

Cheers,

Yepes

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Dice statistics calculator for SW EotE

### #18 Emirikol

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Posted 25 May 2013 - 09:31 AM

I think this is what you're looking for:  https://dl.dropboxus...b/diceprob.html

Now, if someone has any ability greater than mine (which is none), they should be able to simply put the sides of the SW dice into the same system.

jh

### #19 Yepesnopes

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Posted 25 May 2013 - 01:53 PM

I will look into it, but the one I posted (though a bit more limited in resulsts out come) works equally well.

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### #20 Masque

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Posted 25 May 2013 - 04:07 PM

The web app found here can be used as a dice roller or to calculate probabilities.  http://waveyourgeekf...-of-empire.html

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