Problem Statement

(Given an equal-probability generator of one of the integers 1 to 5 as dice5),   create dice7 that generates a pseudo-random integer from 1 to 7 in equal probability using only dice5 as a source of random numbers,   and check the distribution for at least one million calls using the function created in   Simple Random Distribution Checker.

Implementation suggestion: dice7 might call dice5 twice, re-call if four of the 25 combinations are given, otherwise split the other 21 combinations into 7 groups of three, and return the group index from the rolls. (Task adapted from an answer here)

Let's start with the solution:

#lang racket
(define (dice5) (add1 (random 5)))

(define (dice7)
  (define res (+ (* 5 (dice5)) (dice5) -6))
  (if (< res 21) (+ 1 (modulo res 7)) (dice7)))


-> (require math/statistics)
-> (samples->hash (for/list ([i 700000]) (dice7)))
'#hash((7 . 100392)
       (6 . 100285)
       (5 . 99774)
       (4 . 100000)
       (3 . 100000)
       (2 . 99927)
       (1 . 99622))