05272015, 02:51 AM  #11  
GURPS FAQ Keeper
Join Date: Mar 2006
Location: Kyïv, Ukraine

Re: Formulae for calculating Storyteller / Exalted d10 probabilities?
Quote:
output [count {7,8,9,10,10} in 9d10] But it times out at higher pools. I'm guessing their ability to check whether a die result equals a given number is very slow . . . which seems odd to me, as we aren't parsing strings or something like that. 

05272015, 11:15 AM  #12 
Join Date: Feb 2005
Location: Berkeley, CA

Re: Formulae for calculating Storyteller / Exalted d10 probabilities?
No, the problem is likely that they have to actually generate the output of 9d10 when doing that, so the problem grows exponentially, as opposed to doing a simple expansion that grows quadratically.

05282015, 11:47 PM  #13 
Computer Scientist
Join Date: Aug 2004
Location: Dallas, Texas

Re: Formulae for calculating Storyteller / Exalted d10 probabilities?
This sounds very likely; I have always needed to iteratively expand die roll results when ever working with more than a handful. The expansion allows work into the hundreds of dice even in environs like Excel.

05312015, 10:02 PM  #14  
Join Date: Sep 2006
Location: SF Bay Area, CA

Re: Formulae for calculating Storyteller / Exalted d10 probabilities?
An alternative approach would be to use generating functions. Specifically, one can think of rolling n dice as you've described as the generating function (6+3x+x^2)^n and therefore the number of ways of getting exactly k successes is given by the coefficient of x^k in the expansion of the above polynomial. For instance, Wolfram Alpha will give the coefficients for 10 dice as:
Quote:


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