(define (game1a)
  (game1 (list-ref '(0 1/2 1) (random 3))))

(define (game1b)
  (game1 (random)))

(define (game1 q)
  (let ([coin (if (< (random) q) 'head 'tail)])
    (display "Bet head, tail, or none: ")
    (let ([bet (read)])
      (let ([payoff (case bet
                      ((none) 1/2)
                      (else (if (eq? coin bet) 1 -1)))])
        (display "The coin was ") (display coin) (newline)
        (display "Your payoff in this round is ") (display payoff) (newline)
        (game1 q)))))

(define (game2a)
  (game2 (list-ref '(-1 0 1) (random 3))))

(define (game2b)
  (game2 (normal 0 2)))

(define (game2 q)
  (let ([amount (normal q 1)])
    (display "Want to bet? ")
    (let ([bet (read)])
      (let ([payoff (if bet amount 1/2)])
        (display "The amount was ") (display amount) (newline)
        (display "Your payoff in this round is ") (display payoff) (newline)
        (game2 q)))))

; (normal mean stdev) samples a number from the normal distribution with the
; specified mean and standard deviation.
(define (normal mean stdev)
  (+ mean (* stdev (sqrt (* -2 (log (random)))) (cos (* 8 (atan 1) (random))))))