Steve Jackson Games Forums Formulae for calculating Storyteller / Exalted d10 probabilities?
 Register FAQ Calendar Mark Forums Read

05-27-2015, 02:51 AM   #11
vicky_molokh
GURPS FAQ Keeper

Join Date: Mar 2006
Location: Kyïv, Ukraine
Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
 Originally Posted by Anthony 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
I was using
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.
__________________
Vicky 'Molokh', GURPS FAQ and uFAQ Keeper

05-27-2015, 11:15 AM   #12
Anthony

Join Date: Feb 2005
Location: Berkeley, CA
Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
 Originally Posted by vicky_molokh I was using 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.
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.
__________________
My GURPS site and Blog.

05-28-2015, 11:47 PM   #13
jeff_wilson
Computer Scientist

Join Date: Aug 2004
Location: Dallas, Texas
Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

Quote:
 Originally Posted by Anthony 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.
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.
__________________
.

The Campaigns of William Stoddard

05-31-2015, 10:02 PM   #14
thulben

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:
 x^20+30 x^19+465 x^18+4860 x^17+38070 x^16+236196 x^15+1199610 x^14+5093280 x^13+18325845 x^12+56358990 x^11+148853781 x^10+338153940 x^9+659730420 x^8+1100148480 x^7+1554694560 x^6+1836660096 x^5+1776193920 x^4+1360488960 x^3+781021440 x^2+302330880 x+60466176
Which says that there is one way to get 20 successes, 465 ways to get 18 successes, and 302330880 ways to get only one success.

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

 Thread Tools Display Modes Linear Mode

 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 Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Illuminati Headquarters     SJ Games Discussion     Daily Illuminator     Forum Feedback and Help Warehouse 23     Warehouse 23 General Discussion     Warehouse 23 Digital     Pyramid Munchkin     Munchkin 101     Munchkin     Munchkin Collectible Card Game     Other Munchkin Games Roleplaying     Dungeon Fantasy Roleplaying Game         DFRPG Resources     GURPS         GURPS Resources         GURPS Character Assistant     Transhuman Space     Traveller     The Fantasy Trip         The Fantasy Trip: House Rules     In Nomine     Roleplaying in General     Play By Post Board and Card Games     Car Wars         Car Wars Old Editions     Ogre and G.E.V.         Ogre Video Game         Ogre Scenarios     Board and Dice Games     Card Games     Miniatures The Gnomes of Zurich     The Industry     Conventions     Trading Post     Gamer Finder

All times are GMT -6. The time now is 09:59 AM.

 -- Default Style ---- Classic Forum Colors Contact Us - Steve Jackson Games - Privacy Statement - Top