Numeric.Probability.Game.Dice

A module containing various definitions of dice as random events, and a few associated helper functions. See DieRoll, which is really a synonym for EventM Int.

Main die roll type

type DieRoll = EventM Int

A type synonym for events with an integer outcome (i.e. all standard die rolls).

The Num instance for EventM Int allows you to add the results of two die rolls, or subtract them (if it helps, (+) = liftA2 (+)).

Multiplication works as follows. d * e evaluates the first die roll, then sums that many rolls of the second. So 2 * d6 rolls two d6 and adds the outcomes. However, this definition means that d6 * 2 rolls one d6, then effectively scales the result by 2. And d6 * d4 rolls one d6, then rolls that number of d4, adding their results together. The simple rule when one of the terms is a constant is: use the constant on the left-hand side to get more dice, and use the constant on the right-hand side to scale the result.

roll :: DieRoll -> IO Int

A nice synonym for enact: actually rolls the die and produces a single result according to the probabilities in the EventM a parameter.

Dice definitions

d4 :: DieRoll

A die with an equal chance of rolling 1, 2, 3 or 4.

d6 :: DieRoll

A die with an equal chance of rolling 1, 2, 3, 4, 5 or 6.

d8 :: DieRoll

A die with an equal chance of rolling 1, 2, 3, 4, 5, 6, 7 or 8.

z10 :: DieRoll

A die with an equal chance of rolling 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.

d10 :: DieRoll

A die with an equal chance of rolling 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10.

d12 :: DieRoll

A die with an equal chance of rolling 1 to 12 inclusive.

d20 :: DieRoll

A die with an equal chance of rolling 1 to 20 inclusive.

d100 :: DieRoll

A die with an equal chance of rolling 1 to 100 inclusive.

z100 :: DieRoll

A die with an equal chance of rolling 0 to 99 inclusive.

d :: Int -> DieRoll

Makes a die that has an equal chance of achieving the numbers 1 through the number given. d 4 has an equal chance of producing the outcomes 1, 2, 3 and 4, d 1 is equivalent to return 1 (a certain result of 1), and d is undefined for any number below 1. For convenience, all the standard dice are provided, e.g. d6 = d 6.

z :: Int -> DieRoll

Makes a die that has an equal chance of achieving the numbers 0 through the one less than the number given. z 4 has an equal chance of producing the outcomes 0, 1, 2 and 3, while z 1 is equivalent to return 0 (a certain result of 0), and z is undefined for any number below 1. For convenience, several standard dice that can be interpreted with a lower result of 0 are provided, e.g. z10 = z 10.

Dice helper functions

rerollOn :: DieRoll -> [Int] -> DieRoll

Rerolls the die when the specified outcome(s) occur. This has the effect of removing the outcomes from the set of outcomes and rescaling all the other probabilities linearly to sum to 1. For example:

 d6 `rerollOn` [5,6] == d4
 chancePred (== 12) ((2*d6) `rerollOn` [7]) == 1/30

With the latter example, the standard chance of 12 on 2d6 is 1/36, which is rescaled by 36/30, the reciprocal of the chance of not hitting a 7.