AnyDice

Dice

You can define dice using the d operation, which has the highest precedence. The simplest dice are of the form 1d6 or d6, which represents a single die that can produce the numbers 1 through 6. You can perform operations on dice as if they were numbers, in which case the operation gets applied to all individual numbers on the dice.

output d6 named "1, 2, 3, 4, 5, 6"

output d6 + 10 named "11, 12, 13, 14, 15, 16"

output d6 * 10 named "10, 20, 30, 40, 50, 60"

output d6 / 2 named "0, 1, 1, 2, 2, 3"

output d6 > 3 named "0, 0, 0, 1, 1, 1"
When you perform such an operation on two dice, each number of the first die will be combined with each number of the second die.
output d2 + d3 named "2, 3, 4, 3, 4, 5"

output d2 * d3 named "1, 2, 3, 2, 4, 6"

output d2 / d3 named "1, 0, 0, 2, 1, 0"

output d2 > d3 named "0, 0, 0, 1, 0, 0"

Dice collections

3d6 represents a collection of three d6. Usually, you want to sum all rolled numbers, so that is what AnyDice does before performing any of the mathematical operations like addition. Effectively, the collection of dice is converted into a single die.
output 2d2 named "2, 3, 3, 4"

output 2d2 + 10 named "12, 13, 13, 14"

output 2d2 > d3 named "1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1"