White Wolf's World of Darkness Probability Tables

White Wolf's game mechanics typically look as though they were created by coked-up baboons.  I experienced a lot of frustration creating the probability tables for their 2004 version of the World of Darkness because of the mechanic of re-rolling 10s.  The whole game is like rolling damage for the arquebus in old D&D.  Technically, it is possible to roll forever, so I set some limits.  I stop calculating when the probability of an outcome drops below 0.001, or after the third roll.  It was relatively easy to find the probabilities of up to three successes with one die, then much more complicated for two dice, then after some struggles I noticed a pattern in how many separate equations must be solved and combined for each possible outcome (that meets my criteria) for a given number of dice:

So, instead of trying to solve over two thousand equations or trying to figure out how to write a computer program that would do it for me, I brute forced the problem.  I used Excel to whip up 10,000 sets of 3 rolls, then mixed them up twenty different ways, then averaged the occurrences of each number of successes.  The values in the following tables should be correct to about +/- 0.002.  (Click on the pictures to see bigger versions. I'm annoyed with blogspot's layouts.)

And, of course, by adding from the right we can find the probabilities of rolling at least any specific number of successes.  Remember that these probabilities include up to two re-rolls of 10s.

I hope that these tables will be useful to game masters (storytellers) in determining difficulty levels of challenges for characters in their campaigns.  They may also be helpful to players in deciding how much to increase a skill or attribute.

Shadowrun 4th Edition Probability Tables

This is a straightforward post of dice tables for 4th edition Shadowrun.  A player rolls a number of d6s equal to the sum of the character's relevant attribute and skill.  Dice that come up 5 or 6 count as successes.  If at least half of the dice come up 1, a Glitch occurs (something bad) even if there are also successes.  A Glitch with no successes is a Critical Glitch (something very bad).  These tables assume that players do not spend edge.  The first table shows the probability of each outcome for up to 15 dice.

What I find particularly interesting here is that the likelihood of both types of Glitch actually increases from 1 die to 2 dice, and that pattern continues for each even number of dice.  There is a kind of mechanical penalty for being better at a task half of the time, though probabilities of successes always increases.  This bizarre feature of the Glitch system does not make any sense from a simulation or game balance perspective.

This table may help game masters determine task difficulties based on characters' dice totals and the probabilities of success the GM wants in each situation.