Re: [math-fun] best published explanation of the Monty Hall Paradox?

28 Oct 2009

      In August 2001, I argued stridently on the fledgling Wikipedia that switching 
was irrelevant, and wrote code to prove it, only to be proven wrong by my own 
code.  I posted the code as an "empirical example" subpage off the main 
article.  Unfortunately, the current article no longer includes an executable 
demonstration.

!/usr/bin/perl

# Here's a Perl script with which to empirically test
# the Monty Hall problem.
# I'll admit that the results completely blew me away
# the first time I ran the program, and I still wonder
# if there isn't some odd bug which just happens to
# make the numbers look the way they do...

# 9 Aug 2001
# -J

# Empirical test of the Monty Hall problem
# Run with -v to see each game.

$iterations = 10; # How many games to play

@items = ("goat1", "goat2", "car"); #We'll number the items 0-2

$verbosity = 1 if $ARGV[0] eq "-v";

sub verbose {

     if($verbosity == 1) {
         print($_[0]);
     }

}

for(1..$iterations) {

     $door[0] = int rand 3;  # What's behind door #1?

     if($door[0] == 0) {
         $door[1] = 1 + (int rand 2); # Door #2 gets 1 or 2
         if($door[1] == 1) { $door[2] = 2; } else { $door[2] = 1; }
     }

     if($door[0] == 1) {
         $door[1] = 2 * (int rand 2); # Door #2 gets 0 or 2
         if($door[1] == 0) { $door[2] = 2; } else { $door[2] = 0; }
     }

     if($door[0] == 2) {
         $door[1] = int rand 2; # Door #2 gets 0 or 1
         if($door[1] == 0) { $door[2] = 1; } else { $door[2] = 0; }
     }

     verbose( "Door 1: $items[$door[0]]  Door 2: $items[$door[1]]  Door 3: 
$items[$door[2]]

" );

     $contestant = int rand 3;
     verbose( "Contestant chooses door " . ($contestant+1) . ".

" );

     # If the contestant picked the car, Monty picks either other door
     if($items[$door[$contestant]] eq "car") {
         $coinflip = int rand 2;
         if($contestant == 0) { $monty = ($coinflip ? 1 : 2); }
         if($contestant == 1) { $monty = ($coinflip ? 0 : 2); }
         if($contestant == 2) { $monty = ($coinflip ? 0 : 1); }
     }

     # Otherwise, he picks the other goat
     if($items[$door[$contestant]] eq "goat1") {
         if($contestant == 0) { $monty = ($items[$door[1]] eq "goat2" ? 1:2); }
         if($contestant == 1) { $monty = ($items[$door[0]] eq "goat2" ? 0:2); }
         if($contestant == 2) { $monty = ($items[$door[0]] eq "goat2" ? 0:1); }
     }

     if($items[$door[$contestant]] eq "goat2") {
         if($contestant == 0) { $monty = ($items[$door[1]] eq "goat1" ? 1:2); }
         if($contestant == 1) { $monty = ($items[$door[0]] eq "goat1" ? 0:2); }
         if($contestant == 2) { $monty = ($items[$door[0]] eq "goat1" ? 0:1); }
     }

     verbose( "Monty opens door " . ($monty+1) . ".

" );

     $sticker = ($items[$door[$contestant]] eq "car") ? "wins" : "loses";
     $switcher = ($items[$door[$contestant]] eq "car") ? "loses" : "wins";

     verbose( "Sticker $sticker.  Switcher $switcher.

" );

     if($sticker eq "wins") { $stickers++ }
     if($switcher eq "wins") { $switchers++ }

}

print " Grand totals: Stickers: $stickers Switchers: $switchers ";

Re: [math-fun] best published explanation of the Monty Hall Paradox?

Jason