Steve Jackson Games - Site Navigation
Home General Info Follow Us Search Illuminator Store Forums What's New Other Games Ogre GURPS Munchkin Our Games: Home

Go Back   Steve Jackson Games Forums > Roleplaying > Roleplaying in General

Reply
 
Thread Tools Display Modes
Old 05-26-2015, 01:37 AM   #1
vicky_molokh
GURPS FAQ Keeper
 
vicky_molokh's Avatar
 
Join Date: Mar 2006
Location: Kyv, Ukraine
Default Formulae for calculating Storyteller / Exalted d10 probabilities?

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 20d10.

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!
__________________
Vicky 'Molokh', GURPS FAQ and uFAQ Keeper
vicky_molokh is offline   Reply With Quote
Old 05-26-2015, 01:45 AM   #2
Anthony
 
Join Date: Feb 2005
Location: Berkeley, CA
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

http://anydice.com/program/5e8a (that's for 5d, but should be easy to adjust)
__________________
My GURPS site and Blog.
Anthony is offline   Reply With Quote
Old 05-26-2015, 03:17 AM   #3
vicky_molokh
GURPS FAQ Keeper
 
vicky_molokh's Avatar
 
Join Date: Mar 2006
Location: Kyv, Ukraine
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
Originally Posted by Anthony View Post
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!
__________________
Vicky 'Molokh', GURPS FAQ and uFAQ Keeper
vicky_molokh is offline   Reply With Quote
Old 05-26-2015, 03:32 AM   #4
cptbutton
 
cptbutton's Avatar
 
Join Date: Jul 2007
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

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 Huls
(huels@amadeus.statistik.uni-dortmund.de)
August 21, 1996

http://www.scribd.com/doc/46230301/d...ability#scribd
cptbutton is offline   Reply With Quote
Old 05-26-2015, 12:22 PM   #5
Anthony
 
Join Date: Feb 2005
Location: Berkeley, CA
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
Originally Posted by vicky_molokh View Post
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.
__________________
My GURPS site and Blog.
Anthony is offline   Reply With Quote
Old 05-26-2015, 12:28 PM   #6
vicky_molokh
GURPS FAQ Keeper
 
vicky_molokh's Avatar
 
Join Date: Mar 2006
Location: Kyv, Ukraine
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
Originally Posted by Anthony View Post
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.
__________________
Vicky 'Molokh', GURPS FAQ and uFAQ Keeper
vicky_molokh is offline   Reply With Quote
Old 05-26-2015, 01:06 PM   #7
whswhs
 
Join Date: Jun 2005
Location: Lawrence, KS
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

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.
__________________
Bill Stoddard

I don't think we're in Oz any more.
whswhs is offline   Reply With Quote
Old 05-26-2015, 05:40 PM   #8
ericthered
Hero of Democracy
 
ericthered's Avatar
 
Join Date: Mar 2012
Location: far from the ocean
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Vicky, you can program, right?

Code:
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.
__________________
Be helpful, not pedantic

Worlds Beyond Earth -- my blog

Check out the PbP forum! If you don't see a game you'd like, ask me about making one!
ericthered is offline   Reply With Quote
Old 05-26-2015, 06:39 PM   #9
Anthony
 
Join Date: Feb 2005
Location: Berkeley, CA
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
Originally Posted by vicky_molokh View Post
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
__________________
My GURPS site and Blog.

Last edited by Anthony; 05-26-2015 at 06:53 PM.
Anthony is offline   Reply With Quote
Old 05-27-2015, 01:43 AM   #10
vicky_molokh
GURPS FAQ Keeper
 
vicky_molokh's Avatar
 
Join Date: Mar 2006
Location: Kyv, Ukraine
Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
Originally Posted by ericthered View Post
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.

Quote:
Originally Posted by ericthered View Post
Code:
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!
__________________
Vicky 'Molokh', GURPS FAQ and uFAQ Keeper
vicky_molokh is offline   Reply With Quote
Reply

Tags
dice, dice pool, exalted, probability, storyteller, theorycraft

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Fnords are Off
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -6. The time now is 12:38 AM.


Powered by vBulletin® Version 3.8.9
Copyright ©2000 - 2024, vBulletin Solutions, Inc.