Monty Hall Simulation in Racket

monty.rkt

#lang racket

(define (simulate strategy)
  (define car (random 3))
  (define goats (list (modulo (add1 car) 3)
                      (modulo (sub1 car) 3)))
  (define guess (random 3))
  (define reveal (list-ref goats (random 2)))
  (define final (strategy guess reveal))
  (if (= final car) 'win 'lose))

(define (const guess r) guess)

(define (flip guess r)
  (car (filter
        (λ (x) (not (or (= x guess) (= x r))))
        (range 3))))

(define (game rounds strategy)
  (define won 0)
  (for [(i (range rounds))]
    (if (eq? (simulate strategy) 'win)
        (set! won (add1 won))
        (void)))
  (exact->inexact (/ won rounds)))

(define rounds 1000000)

(define const-results (game rounds const))

(define flip-results (game rounds flip))

;; Print results
;;
(displayln (format "Win percent for staying with same door: ~a%"
                   const-results))

(displayln (format "Win percent for always flipping door: ~a%"
                   flip-results))