Monty Hall

gistfile1.clj

(defn delete [items l]
  (remove (set items) l))

(defn monty-hall 
  [switch?]
  (let [doors     (range 3)
        car       (rand-nth doors)
        guess-1   (rand-nth doors)
        hint      (rand-nth 
                     (delete [guess-1 car] doors))
        guess-2   (if switch?
                      (rand-nth (delete [hint guess-1] doors))
                      guess-1)]
    (if (= guess-2 car)
        :win
        :lose)))

(defn win-ratio [reps switch?]
  (let [trials (repeatedly reps #(monty-hall switch?))
        wins   (count (filter #{:win} trials))]
    (float (/ wins reps))))

;; (win-ratio 1000 true) => 0.671
;; (win-ratio 1000 false) => 0.334