Functional Dice Rolling

dice.ex

defmodule Dice do
  def sum_probability(dice, target) do
    prob  = :math.pow(6, dice) |> round
    total = 6 * dice

    "#{sum_probability(dice, target, total)} / #{prob}"
  end

  defp sum_probability(dice, target, _total) when target < dice do
    0
  end
  defp sum_probability(_dice, target, total) when target > total do
    0
  end
  defp sum_probability(1, _target, _total) do
    1
  end
  defp sum_probability(dice, target, _total) do
    perform_rolls(dice, target, 0)
  end

  defp perform_rolls(_dice, target, acc) when acc > target do
    0 # Prevents further rolls if accumulator result is higher then target
  end
  defp perform_rolls(0, target, acc) do
    if target == acc, do: 1, else: 0
  end
  defp perform_rolls(rolls_left, target, acc) do
    1..6
    |> Enum.to_list
    |> List.foldl(0, fn(roll, odds) ->
      perform_rolls(rolls_left - 1, target, acc + roll) + odds
    end)
  end
end

dice_test.exs

defmodule DiceTest do
  use ExUnit.Case
  import Dice

  test "sum_probability with valid values" do
    assert sum_probability(1, 5) == "1 / 6"
    assert sum_probability(2, 2) == "1 / 36"
    assert sum_probability(2, 4) == "3 / 36"
    assert sum_probability(3, 5) == "6 / 216"
  end

  test "sum_probability with invalid values" do
    assert sum_probability(1, 15) == "0 / 6"
    assert sum_probability(3, 1)  == "0 / 216"
  end
end