### 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?

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?