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(defn cross
([f xs] xs)
([f xs ys] (for [x xs y ys] (f x y)))
([f xs ys & more] (apply cross f (cross f xs ys) more)))
(defn dice-distn
[number sides]
(frequencies (apply cross + (take number (repeat (range 1 (inc sides)))))))
(defn prob
[pete colin prob]
(if (seq pete)
(let [pete_roll (first (first pete))
pete_count (second (first pete))
roll_beat (reduce + (for [[v c] colin :when (> pete_roll v)] c))
roll_prob (/ roll_beat (Math/pow 6 6))]
(recur (rest pete) colin (+ prob (/ (* pete_count roll_prob) (Math/pow 4 9)))))
(prob (dice-distn 9 4) (dice-distn 6 6) 0)
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