Monty Hall problem

monty-hall.clj

(defn monty-hall
  ""
  []
  (let [prize-idx (rand-int 3)
        doors [false false false]
        doors (assoc doors prize-idx true)
        random-pick (rand-int 3)
        monty-pick (first
                     (remove nil? (map-indexed
                                    (fn [idx val]
                                      (if (or
                                            val
                                            (= idx random-pick))
                                        nil
                                        idx))
                                    doors)))
        other-door (first (clojure.set/difference #{0 1 2} #{monty-pick random-pick}))
        strategy (first (shuffle ["stay" "switch"]))]
    [strategy
     (nth doors (if (= strategy "stay")
                  random-pick
                  other-door))]))

(defn run-a-bunch-o-games [x]
  (let [games (for [n (range x)]
                (monty-hall))
        grouped-games (group-by first games)
        stay-games (get grouped-games "stay")
        switch-games (get grouped-games "switch")
        calc-percent-wins (fn [games]
                            (let [total-games (count games)
                                  won-games (count (filter second games))]
                              (* 100.0 (/ won-games total-games))))]

    (do (println "Percent of total games won" (calc-percent-wins games))
        (println "Percent of stay games won" (calc-percent-wins stay-games))
        (println "Percent of switch games won" (calc-percent-wins switch-games)))))

results

(run-a-bunch-o-games 100)
Percent of total games won 51.0
Percent of stay games won 33.33333333333333
Percent of switch games won 69.38775510204081
=> nil
(run-a-bunch-o-games 1000)
Percent of total games won 49.9
Percent of stay games won 31.72690763052209
Percent of switch games won 67.92828685258964
=> nil
(run-a-bunch-o-games 10)
Percent of total games won 30.0
Percent of stay games won 0.0
Percent of switch games won 50.0
=> nil
(run-a-bunch-o-games 100000)
Percent of total games won 49.889
Percent of stay games won 33.13117969656939
Percent of switch games won 66.62136776050201
=> nil