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### World of Darkness 20th Anniversary Probability Function

Posted: Tue Dec 22, 2015 4:58 am UTC
Heya everyone. A number of years ago, while I was in school, I designed a function to calculate the probability and degree of success on dice pools in the World of Darkness roleplaying game line, specifically Vampire the Masquerade. Well, that was quite a few years ago, and since then White Wolf has released the 20th anniversary of the games, and with it a rule twerk.

In the WoD, players assemble dice pools ranging from 1 to 10 ten-sided dice. The ST assigns a number as the difficulty. Each die that comes up with that number as greater is a success. Each die that comes up as a 1 subtracts 1 success from the total (and if no successes are rolled, that results in a botch, indicating a spectacular failure).

Years ago, this is the function I created to model that probability. p for dice pool, s for number of successes, d for difficulty:

((p-s)/2)
P(S=s)= ∑ ((11-d)/10)^(s+i)∙(1/10)^i ∙((d-2)/10)^(p-s-2i)
i=0

The big change in the 20th anniversary edition is that certain skills can be designated as "specialty" skills. When such a skill is rolled, any roll of 10 counts twice for success. It's been too many years since I sat for a probability class to take my function apart and change it to reflect the rules update. Would anyone here by able to assist me?