How many matches are left in the non-empty box?

simulate-match-picks.pl

#! /usr/bin/perl

# Simulates the distribution of the age-old question: when matches are
# picked randomly out of two matchboxes each of which initially has 40
# matches in it until one of them is empty, how many matches are left
# in the other one?

use 5.010;
use strict;
use warnings;

my $MATCHES = 40;
my $RUNS    = 1_000_000;
my $WIDTH   = 70;

my @hist;
for (1..$RUNS) {
    my @boxes = ($MATCHES) x 2;
    while ($boxes[0] && $boxes[1]) {
        --$boxes[int(rand() * 2)];
    }
    ++$hist[ $boxes[0] + $boxes[1] ];
}

sub max { my $max = shift // 0; for (@_) { $max = $_ if $max < $_ }; $max }
my $max = max(@hist);
for my $n (1..@hist-1) {
    my $v = $hist[$n] // 0;
    say sprintf "%2d %5s %s", $n, $v, '*' x ($WIDTH * $v / $max);
}

some-output

 1 89805 *********************************************************************
 2 90285 **********************************************************************
 3 88995 ********************************************************************
 4 86558 *******************************************************************
 5 82928 ****************************************************************
 6 78896 *************************************************************
 7 72912 ********************************************************
 8 67099 ****************************************************
 9 60645 ***********************************************
10 53407 *****************************************
11 46289 ***********************************
12 39566 ******************************
13 33564 **************************
14 27338 *********************
15 21916 ****************
16 16808 *************
17 12990 **********
18  9656 *******
19  6905 *****
20  4918 ***
21  3181 **
22  2158 *
23  1349 *
24   871 
25   461 
26   261 
27   132 
28    52 
29    32 
30    16 
31     7