(defn win? [hold-the-door?]
  (let [doors (set (range 3))
        $$-door (rand-int 3)
        contestant-init-sel (rand-int 3)
        monty-sel (-> doors
                      (disj contestant-init-sel $$-door)
                      first)
        final-sel (if hold-the-door?
                    contestant-init-sel
                    (-> doors
                        (disj contestant-init-sel monty-sel)
                        first))]
    (= final-sel $$-door)))

(defn win-stats [hold-the-door? n]
  (let [freqs (frequencies
               (for [_ (range n)]
                 (win? hold-the-door?)))
        wins (get freqs true 0)
        losses (get freqs false 0)]
    {:win% (-> (/ wins (+ wins losses))
               (* 100)
               float)
     :wins wins
     :losses losses}))

(def holdin-dat-door (partial win-stats true))
(def i-prefer-another-door (partial win-stats false))

(comment
  (time (i-prefer-another-door 1e6))
  "Elapsed time: 1843.44821 msecs"
  {:win% 66.6149, :wins 666149, :losses 333851}

  (time (holdin-dat-door 1e6))
  "Elapsed time: 1415.997953 msecs"
  {:win% 33.4201, :wins 334201, :losses 665799})