Formulae for calculating Storyteller / Exalted d10 probabilities?

[vicky_molokh]

Greetings, all!

I've searched the web, and I can't find a transparent calculation of probabilities for Storyteller-derived Exalted dice pool successes. The results I've found seem inconsistent, and I don't think I can figure which ones are more correct. I've considered writing a brute-force calculation, but this isn't a good idea, as dice pools can easily go all the way past 20×d10.

The basic rules of dice are as follows:
Each d10 is rolled once. A result of 7,8,9 adds one success to the roll, while a result of 10 on the die adds two successes. There are no rerolls, and no subtractions.

How do I calculate the probability of each number of successes for a given dice pool?

Thanks in advance!

[Anthony]

http://anydice.com/program/5e8a (that's for 5d, but should be easy to adjust)

[vicky_molokh]

Originally Posted by Anthony

http://anydice.com/program/5e8a (that's for 5d, but should be easy to adjust)

Oh, cool: I did use that site before, but it timed out on calculations of 21-30 dice. But your variant of the request seems to calculate much faster than the one I used (counting 7,8,9s, and double-counting 10s). Thanks!

[cptbutton]

Not sure this is what you want, but this has tables, I don't know if it covers Exalted:

The distribution of World of Darkness dice rolls
Ralf H¨uls
(huels@amadeus.statistik.uni-dortmund.de)
August 21, 1996

http://www.scribd.com/doc/46230301/d...ability#scribd

[Anthony]

Originally Posted by vicky_molokh

Oh, cool: I did use that site before, but it timed out on calculations of 21-30 dice. But your variant of the request seems to calculate much faster than the one I used (counting 7,8,9s, and double-counting 10s). Thanks!

By the time it's any large number of dice you've got a curve that's essentially indistinguishable from a normal curve with mean = 0.5 * dice and std deviation = sqrt(0.45*dice). However, Anydice with my setup seems fine at 100d, which should be more than you ever need.

[vicky_molokh]

Originally Posted by Anthony

By the time it's any large number of dice you've got a curve that's essentially indistinguishable from a normal curve with mean = 0.5 * dice and std deviation = sqrt(0.45*dice). However, Anydice with my setup seems fine at 100d, which should be more than you ever need.

Yeah, I don't think even Primordials go over 50d.
I did find StDev, but couldn't meaningfully convert it to actual probabilities of X successes.

And I wonder why your setup is so much faster than counting 7's-10's on dice. It feels as if the 7s-counting op is extremely inefficient.

[whswhs]

I did that many years ago on Excel, getting exact odds for every outcome. But it was a rather complicated iterative algorithm to implement. It would be a lot of work to set up and I'm not sure I could verbalize it.

[ericthered]

Vicky, you can program, right?

var single = [];
single[0]=.6;
single[1]=.3;
single[2]=.1;

function combine(a,b){var result=[]; for(var i=0;i<a.length;i++)for(var j=0;j<b.length;j++){var x = i+j; if(!result[x])result[x]=0; result[x]+=a[i]*b[j];} return result;}
var pool = function (x){var result = single; for(var i=1;i<x;i++) result = combine(result,single); return result;}

Its javascript, designed to be run from the console log in developer tools. calling pool(5) will give you the probabilities for rolling five dice. pool(31) will do the same. The index of the array is the number of successes.

The algorithm is fast, relying on probability rather than brute force.

[Anthony]

Originally Posted by vicky_molokh

And I wonder why your setup is so much faster than counting 7's-10's on dice.

Probably because AnyDice understands what I'm doing and can optimize it well (it's not a hard optimization problem; erikthered's code could do with formatting and comments but is probably correct). Might I ask what you tried to give it?

Spreadsheet version: https://docs.google.com/spreadsheets...it?usp=sharing

[vicky_molokh]

Originally Posted by ericthered

Vicky, you can program, right?

To a certain extent. I'm at least half self-taught, and working in a somewhat peculiar narrow subset of C#, so might not know some things. Still, Java seems readable, being of a related family or something.

Originally Posted by ericthered

var single = [];
single[0]=.6;
single[1]=.3;
single[2]=.1;

function combine(a,b){
 var result=[]; 
 for(var i=0;i<a.length;i++)
  for(var j=0;j<b.length;j++)
   {
    var x = i+j; if(!result[x])result[x]=0; result[x]+=a[i]*b[j];
   } 
return result;}
var pool = function (x){var result = single; for(var i=1;i<x;i++) result = combine(result,single); return result;}

Its javascript, designed to be run from the console log in developer tools. calling pool(5) will give you the probabilities for rolling five dice. pool(31) will do the same. The index of the array is the number of successes.

The algorithm is fast, relying on probability rather than brute force.

I think I got it. I stumbled for some while with adding a[i]*b[j], but now it seems clear and neat. Thanks: even though I already have my tables, the whole line of logic is quite interesting in its own right!