EccentricCircle

2017-05-25, 11:17 AM

As many of you will be aware, various systems use some variation on the "dice pool" mechanic, where you roll a number of dice determined by the stats of your character. The result is *usually* determined by the number of "successes"; how many of the results exceed a target threshold.

I've been trying to figure out how to calculate the probability of certain results, but it turns out that my probability skill is a bit rusty, so hopefully some of the you have more experience working this sort of stuff out.

So first, the bit I *think* I can do:

To work out the chances of a dice within the pool equaling or exceeding a target:

p = (1 - (((t-1)/d) ^n)) x 100

Where:

p = probability expressed as a percentage.

t = target number

d = size of dice (e.g. d6, d10, d20 etc.)

n = number of dice in the pool

So we are essentially working out the probability that you don't beat t and subtracting that from one and multiplying it by 100 to get a percentage.

To get this probability we divide the number one lower than the DC by the number of possibilities on the dice, and multiply it by itself a number of times equal to the number of dice in the pool.

However most dice pool systems need you to get multiples, rather than just one number that beats the DC. For example you might need to get three numbers above seven on a d10, or two above sixteen on a d20.

So how can I expand this equation to work out the probability of getting x number of successes in a given dice pool? (assuming I've got the initial calculation correct that is...).

I've been trying to figure out how to calculate the probability of certain results, but it turns out that my probability skill is a bit rusty, so hopefully some of the you have more experience working this sort of stuff out.

So first, the bit I *think* I can do:

To work out the chances of a dice within the pool equaling or exceeding a target:

p = (1 - (((t-1)/d) ^n)) x 100

Where:

p = probability expressed as a percentage.

t = target number

d = size of dice (e.g. d6, d10, d20 etc.)

n = number of dice in the pool

So we are essentially working out the probability that you don't beat t and subtracting that from one and multiplying it by 100 to get a percentage.

To get this probability we divide the number one lower than the DC by the number of possibilities on the dice, and multiply it by itself a number of times equal to the number of dice in the pool.

However most dice pool systems need you to get multiples, rather than just one number that beats the DC. For example you might need to get three numbers above seven on a d10, or two above sixteen on a d20.

So how can I expand this equation to work out the probability of getting x number of successes in a given dice pool? (assuming I've got the initial calculation correct that is...).