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Old 05-26-2015, 01:37 AM   #1
vicky_molokh
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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!
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Old 05-26-2015, 01:45 AM   #2
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Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

http://anydice.com/program/5e8a (that's for 5d, but should be easy to adjust)
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Old 05-26-2015, 03:17 AM   #3
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Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

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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!
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Old 05-26-2015, 03:32 AM   #4
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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
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Old 05-26-2015, 12:22 PM   #5
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Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

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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.
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Old 05-26-2015, 12:28 PM   #6
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Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

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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.
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Old 05-26-2015, 01:06 PM   #7
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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.
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Old 05-26-2015, 06:39 PM   #8
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Default Re: Formulae for calculating Storyteller / Exalted d10 probabilities?

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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
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Last edited by Anthony; 05-26-2015 at 06:53 PM.
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