Seven-sided dice from five-sided dice

Seven-sided dice from five-sided dice
You are encouraged to solve this task according to the task description, using any language you may know.

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 1000000 calls using the function created in Simple Random Distribution Checker.

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)

AutoHotkey

<lang AutoHotkey>dice5() { Random, v, 1, 5

  Return, v

}

dice7() { Loop

  {  v := 5 * dice5() + dice5() - 6
     IfLess v, 21, Return, (v // 3) + 1
  }

}</lang>

Distribution check:

Total elements = 10000

Margin = 3% --> Lbound = 1386, Ubound = 1471

Bucket 1 contains 1450 elements.
Bucket 2 contains 1374 elements. Too far off.
Bucket 3 contains 1412 elements.
Bucket 4 contains 1465 elements.
Bucket 5 contains 1370 elements. Too far off.
Bucket 6 contains 1485 elements. Too far off.
Bucket 7 contains 1444 elements.

C

<lang c>#include <stdio.h>

1. include <stdlib.h>
2. include <math.h>

void distcheck(int (*)(), int, double);

int dice5() {

 return 1 + (int)(5.0*rand() / (RAND_MAX + 1.0));

}

int dice7() {

 int d55;
 do {
   d55 = 5*dice5() + dice5() - 6;
 } while(d55 >= 21);
 return d55 % 7  + 1;

}

int main() {

 distcheck(dice5, 1000000, 1);
 distcheck(dice7, 1000000, 1);
 return 0;

}</lang>

Common Lisp

Translation of: C

<lang lisp>(defun d5 ()

 (1+ (random 5)))

(defun d7 ()

 (loop for d55 = (+ (* 5 (d5)) (d5) -6)
       until (< d55 21)
       finally (return (1+ (mod d55 7)))))</lang>

> (check-distribution 'd7 1000)
Distribution potentially skewed for 1: expected around 1000/7 got 153.
Distribution potentially skewed for 2: expected around 1000/7 got 119.
Distribution potentially skewed for 3: expected around 1000/7 got 125.
Distribution potentially skewed for 7: expected around 1000/7 got 156.
T
#<EQL Hash Table{7} 200B5A53>

> (check-distribution 'd7 10000)
NIL
#<EQL Hash Table{7} 200CB5BB>

OCaml

<lang ocaml>let dice5() = 1 + Random.int 5 ;;

let dice7 =

 let rolls2answer = Hashtbl.create 25 in
 let n = ref 0 in
 for roll1 = 1 to 5 do
   for roll2 = 1 to 5 do
     Hashtbl.add rolls2answer (roll1,roll2) (!n / 3 +1);
     incr n
   done;
 done;
 let rec aux() =
   let trial = Hashtbl.find rolls2answer (dice5(),dice5()) in
   if trial <= 7 then trial else aux()
 in
 aux

</lang>

Python

Follows the method suggested in the task description for creating dice7, and uses a function creator for dice7, to calculate the binning of the two calls to dice5. <lang python>import re, random

onetofive = (1,2,3,4,5)

def dice5():

   return random.choice(onetofive)

def dice7generator():

   rolls2answer = {}
   n=0
   for roll1 in onetofive:
       for roll2 in onetofive:
           rolls2answer[(roll1,roll2)] = (n // 3) + 1
           n += 1
   def dice7():
       'Generates 1 to 7 randomly, with equal prob. from dice5'
       trial = rolls2answer[(dice5(), dice5())]
       return trial if trial <=7 else dice7()
   return dice7

dice7 = dice7generator()</lang> Distribution check using Simple Random Distribution Checker:

>>> distcheck(dice5, 1000000, 1)
{1: 200244, 2: 199831, 3: 199548, 4: 199853, 5: 200524}
>>> distcheck(dice7, 1000000, 1)
{1: 142853, 2: 142576, 3: 143067, 4: 142149, 5: 143189, 6: 143285, 7: 142881}

Ruby

Translation of: Tcl

Uses distcheck from here. <lang ruby>require './distcheck.rb'

def d5

 1 + rand(5)

end

def d7

 loop do
   d55 = 5*d5() + d5() - 6
   return (d55 % 7 + 1) if d55 < 21
 end

end

distcheck(1_000_000) {d5} distcheck(1_000_000) {d7}</lang>

output

1 200478 2 199986 3 199582 4 199560 5 200394 
1 142371 2 142577 3 143328 4 143630 5 142553 6 142692 7 142849 

Tcl

Any old D&D hand will know these as a D5 and a D7... <lang tcl>proc D5 {} {expr {1 + int(5 * rand())}}

proc D7 {} {

   while 1 {
       set d55 [expr {5 * [D5] + [D5] - 6}]
       if {$d55 < 21} {
           return [expr {$d55 % 7 + 1}]
       }
   }

}</lang> Checking:

% distcheck D5 1000000
1 199893 2 200162 3 200075 4 199630 5 200240
% distcheck D7 1000000
1 143121 2 142383 3 143353 4 142811 5 142172 6 143291 7 142869