To start with dice pools (target number variety). This is when you roll a pool of dice (usually the same but not necessarily) and you count "successes" or "hits" rather than using the numerical values. Usually some set value on the dice counting as success (5 or better on a d6, 4 or better on a d6, 8 or better on a d10 are all common varieties) while others count as failures. The number required to count as a success is often called a target number. Sometimes the target number varies, but this seems to be becoming less common because it's very hard to intuit whether changing a target number or the number of dice is more advantageous. You compare the number of successes rolled to the number required for the specific challenge and if you beat it you have succeeded.

How you model this. This is actually a binomial distribution if you want to do it in excel, I suggest you read the wikipedia page on binomials and use the built in excel functions.

In Anydice, there are several ways to model target number based dice pool systems.

The easiest is to just define a new dice (which will be useful later for fudge dice):

\Put in the number of dice you want for N\

\Change the number of ones to the number of values that count as successes and the number of zeroes to the number of values that count as failures\

output Nd{0,0,0,0,1,1}

You can also use the count function, which seems to be one of its primary purposes. (note this assumes you are counting on the high side as successes)

\N is the number of dice rolled\

\Y is the target number\

\D is the dice size\

\Replace those with the numbers you want to determine the probability of\

output [count {Y..D} in NdD]

If you want to compare the number of dice in the pool you can use the Loop function

\X is the variable that changes, do not put in a number there\

\b is the lowest number of dice\

\B is the highest number of dice in the pool, replace b and B with numbers\

loop X over {b..B} {

output [count {Y..D} in NdD]

}

Variants

In FATE you roll a pool of 4 dice and they count as plus or minus, this isn't really a target number system dice pool but mathematically and Anydice wise it's similar enough to just explain here.

On a Fudge dice there are two -1 sides, two 0 sides, and two +1 sides. You roll 4 and some the results.

Define a fate dice by (note you could also just do three values because the sides repeat, i.e. 2/6 = 1/3}

output d{-1,-1,0,0,1,1}

To get 4 dice, you put the 4 in front of the new dice.

output 4d{-1,-1,0,0,1,1}

In this variant the dice explode on the highest value, (i.e. you can roll dice that come up 6 on a d6 again for the chance to add another success on top of the one you got for a 6, theoretically out to infinity)

\This is set up for shadowrun where 5 and 6 are success and with edge you can reroll 6s\

\The top part is an Anydice function, R represents the values for which the die explodes, N >= 5 is the range for which things count as success\

function: nwod R:n again N:n {

if N >= R { result: 1 + [nwod R again d6] }

result: N >= 5

}

\This part is setting up the function to act as a dice so that you can loop X dice and have each one potentially explode\

NWOD: [nwod 6 again d6]

loop X over {2..10} {

output XdNWOD named "[X]d"

}

Sometimes instead of a fixed number of success required, two pools of dice are rolled against one another. This is often what happens when facing an NPC in many games.

For this simply pick on pool to be positive and one to be negative. So a pool with X dice(positive) goes against a pool with Y dice (positive). Here assumed to have a target number of 4 on a d6.

\Put in the size of your dice pools\

output [count {4,5,6} in Xd6] - [count {4,5,6} in Yd6]

\Positive means X had that many more successes than Y, negative means Y had that many more successes than X\