Empirical proof of the Monty Hall problem

The purpose of the following Perl program is to prove the result to the Monty Hall problem. It performs a set number of games and keeps track of how often a sticker (someone who sticks to their first choice) and a switcher (someone who switches to another door) would win the game. The results are (within the tolerance of coincidence) close to a sticker/switcher ratio of 1:2, proving the hypothesis that the switcher has twice as much chance of winning the prize than the sticker.

#!/usr/bin/perl

# Empirical test of the Monty Hall problem

# Use -v to see each game. (default: off)
# Use -i # to set number of iterations. (default: 3000)

use strict;

my $iterations = 3000;    # How many games to play
my $verbosity = 0;

while (@ARGV) {
    my $param = shift @ARGV;
    $verbosity = 1 if $param eq '-v';
    $iterations = int (shift @ARGV) if $param eq '-i';
}

sub verbose {
    print $_[0]."\n" if $verbosity;
}

my $stickers;
my $switchers;

print "Playing $iterations games...\n\n";

for(1..$iterations) {
    my @items = qw(goat goat prize);     # two goats, one prize
    my @door;

    while (@items) {            # this puts the @items into the @door array in random order
        push (@door, splice (@items, int rand @items, 1));
    }

    verbose ("Door 0: $door[0];  Door 1: $door[1];  Door 2: $door[2]");

    my $contestant = int rand 3;
    verbose ("Contestant chooses door $contestant.");

    my $monty;

    # If the contestant picked the prize, Monty picks another door by random.
    if ($door[$contestant] eq 'prize') {
        $monty = ($contestant + (int rand 2) + 1) % 3;
    }

    # Otherwise, he picks the other goat.
    else {
        $monty = $door [ ($contestant+1) % 3 ] eq 'goat' ? ($contestant+1) % 3 : ($contestant+2) % 3;
    }

    verbose ("Monty opens door $monty.");

    # Now only two doors are open. If the sticker wins, the switcher loses and vice versa.
    if ($door[$contestant] eq 'prize') {
        verbose ("Sticker wins.  Switcher loses.");
        $stickers++;
    } else {
        verbose ("Sticker loses.  Switcher wins.");
        $switchers++;
    }
}

print "Grand totals:
Sticker  has won  $stickers  times
Switcher has won  $switchers  times
";

See also: Monty Hall problem