Functions

AnyDice allows you to define functions, which you can then invoke using any values you like. The name of a function can consist of any amount of lowercase words and variables. You invoke a function by writing its name between brackets, replacing the variables in its name with whatever you want it to operate on.

Inside the block of a function, you can define its result at any time. Whenever a function's result is defined, its execution is finished. If you do not define the result of a function then it will be the empty die.

function: add A to B {
 result: A + B
}

output [add 1 to 2] named "3"
output [add d4 to 1] named "d4 + 1"
output [add d4 to d6] named "d4 + d6"

The variables that are defined inside a function only exist while that function is being invoked. If a variable with the same name already existed, then its old value will become available again after the function invocation is finished.

It is not possible to provide output or to configure AnyDice while inside a function.

Parameter types

The variables inside a function's name are the parameters it operates on. It is possible to constrain these parameters to a specific type. You do this by following a variable with a colon, then a character indicating its type. Use n for numbers, d for dice, and s for sequences. The behavior of a function depends on what type of value it expects and what type of value it actually receives.

Expecting a number: If a sequence is provided, then the sequence will be summed. If a die is provided, then the function will be invoked for all numbers on the die – or the sums of a collection of dice – and the result will be a new die.
Expecting a die: If a number is provided, then it will be converted to a die that can roll only that number. If a sequence is provided, then the sequence will be summed and treated the same as a number.
Expecting a sequence: If a number is provided, then it will be converted to a sequence containing only that number. If dice are provided, then the function will be invoked for all possible sequences that can be made by rolling those dice. In that case the result will be a new die.

function: double A:n if above B:n {
 if A > B { result: A + A }
 result: A
}

output [double d6 if above 3] named "1, 2, 3, 8, 10, 12"

function: ROLL:s count fives and above and subtract ones {
 result: (ROLL >= 5) - (ROLL = 1)
}

output [3d6 count fives and above and subtract ones] named "-3 .. 3"

While it is possible to assign a value to a variable used as a parameter, you should not do so yourself.

Recursion

It is possible to invoke a function inside another function. It is even possible to invoke a function inside itself. Theoretically, it is possible to make a function invoke itself indefinitely. However, AnyDice is only able to support a limited number of nested function calls. Whenever this limit is exceeded, the invoked function's result will automatically be the empty die and a warning will be issued.

If you want to, you can adjust the maximum nesting level – called the maximum function depth – to any number you want. However, this might cause AnyDice to fail as it tries to claim more machine resources that it is allowed to.

function: depth { result: 1 + [depth] }

output [depth] named "default maximum function depth"

set "maximum function depth" to 5
output [depth] named "custom maximum function depth"