montyhall.clj

(import [clojure.set])

(defn make-doors []
  (rand-nth [[true false false]
             [false true false]
             [false false true]]))

(defn reveal-door [choice doors]
  (let [choices (filter #(not (= choice %)) [0 1 2])]
    (rand-nth (filter #(not (doors %)) choices))))

(defn change [choice revealed-door]
  (first (clojure.set/difference #{0 1 2} #{choice revealed-door})))

(defn no-change [choice revealed-door]
  choice)

(defn montyhall [approach doors]
  (let [choice (rand-int 3)]
    (doors (approach choice
                     (reveal-door choice doors)))))

(defn simulate [n approach]
  (float (/ (count (filter identity
                           (repeatedly n #(montyhall approach (make-doors)))))
            n)))

; user> (simulate 1000000 no-change)
; 0.33387

; user> (simulate 1000000 change)
; 0.667118