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(defn dice-probability-spread [sides rolls]
(let [sr (range 1 (inc sides))]
(->> sr
(iterate #(flatten (for [i sr] (map (partial + i) %))))
(drop (dec rolls))
((comp frequencies first)))))
(def rolls (dice-probability-spread 3 3))
(defn advance-pos [pos roll] (let [n (+ pos roll)] (if (> n 10) (- n 10) n)))
(defn add-roll [state roll p1-turn]
(let [pos (if p1-turn :pos1 :pos2)
score (if p1-turn :score1 :score2)
new-pos (advance-pos (state pos) roll)]
(-> state
(assoc pos new-pos)
(update score + new-pos))))
(defonce wins (atom [0 0]))
(loop [turn 0 states {{:pos1 4 :score1 0 :pos2 8 :score2 0} 1}]
(if (empty? states)
(println (apply max @wins))
(recur
(if (= 0 turn) 1 0)
(reduce
#(let [kvp (first %2)]
(if (< ((key kvp) (if (= 0 turn) :score1 :score2)) 21)
(if (contains? %1 (key kvp))
(update %1 (key kvp) +' (val kvp))
(conj %1 kvp))
(do (swap! wins update turn +' (val kvp)) %1)))
{}
(for [s states r rolls]
{(add-roll (first s) (key r) (= 0 turn)) (*' (second s) (val r))})))))
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