#!/usr/bin/perl
#
#Monty Hall's Hall Of Doors v2.0 19991026
#by Leonard Richardson leonardr@ucla.edu
#
#"And you may ask yourself, where is that large automobile?" 
#             - Talking Heads, 'Once in a Lifetime'
#

use CGI qw/:standard/;

$max_games = 10000;
$disable_logging_at = 100;

#preliminaries prints out the usual suspects and gets the input.
preliminaries();

#Initialize data structures.
foreach $a ("switch","stick")
{
    $wins{$a} = 0;
    $losses{$a} = 0;
}

#Play a bunch of games.
$switch_counter = 1;
for ($counter = 1; $counter <= $times; $counter++)
{
    play_game();
}

#Let's tabulate those scores!
print_statistics();

###########################################

sub play_game()
#Plays one round of the Monty Hall game of fun.
{
    $mega_door = int(rand(3)) + 1;
    @door_stats[$position]++;

    if ($same_door_always)
    {
	$first_choice = 1;
    } else {
	$first_choice = int(rand(3))+1;
    }

    #Figure out which door Monty opens. The door that neither the
    #player nor Monty picked is our choice if we want to switch.
    $opened = monty_decision($first_choice, $mega_door);
    $switch_choice = other_door($first_choice,$opened); 

    #Now we need to figure out if we're going to switch or not.
    #
    #We can switch randomly rather than with a counter, to exchange
    #experimental error (eg., 40% switching on 30 games) for random
    #error.
    if ($random)
    {
	if (int(rand(100))+1 <= $percent_switch)
	{
	    $action = "switch";
	} else {
	    $action = "stick";
	}
    } else {

	#Or, we can switch with a counter, to exchange random error for
	#experimental error. This is the default.
	if ($switch_counter <= $percent_switch)
	{
	    $action = "switch";
	} else {
	    $action = "stick";
	}
	$switch_counter++;
	if ($switch_counter > 100) { $switch_counter = 1; }
    }

    if ($action eq "switch")
    {
	$new_choice = $switch_choice;	
    } else {
	$new_choice = $first_choice;
    }

    #Now we see whether or not we won, and increment the appropriate variables.
    if ($mega_door == $new_choice)
    {
	$wins{$action}++;
    } else {
	$losses{$action}++;
    }

    if ($log)
    {
	print "<p><b>Log for round $counter:</b><br>\n";
	print "I chose door $first_choice.<br>\n";
	print "Monty opened door $opened.<br>\n";
	print "I decided ";
	if ($action eq "stick") {print "not ";}
	print "to switch";
	if ($action eq "switch") {print " to door $new_choice"};
	print ".<br>\n";
	if ($mega_door == $new_choice)
	{
	    print "Woohoo!";
	} else {
	    print "Damn!";
	}
	print " The mega prize was behind door $mega_door";
	if ($action eq "switch" && $mega_door ne $new_choice) { print " after all";}
	print "!<br>\n</p>\n";
	
	if ($counter == $disable_logging_at) 
	{
	    print "<p>$counter rounds played, disabling log.</p>\n";
	    $log = 0;
	}

    }
}


sub print_statistics #See also print_lies and print_damn_lies
{
%past = ("switch" => "switched",
	 "stick" => "stuck",);

#First, using only the starting conditions, we will predict the total
#percentage of rounds that should be won.
%theoretical_win_chance = ("switch" => 2/3,
			   "stick" => 1/3,);

$theoretical_win_chance = ($theoretical_win_chance{switch} * $percent_switch) +
    ($theoretical_win_chance{stick} * (100-$percent_switch));

#Now we print them out.
print "<h1>Monty Hall's Hall Of Doors<br>";
print "Stats on $times games, switching $percent_switch% of the time:</h1>";

foreach $a ("switch","stick") {
    #Need to do this crap to avoid division by zero errors
    $percentage{$a} = ($losses{$a} + $wins{$a} == 0 ? "0":
		      $wins{$a}/(($losses{$a} +
		      $wins{$a})) * 100);

    $total_percentage{$a} = ($wins{$a} / $times) * 100;

    $total = $wins{$a}+$losses{$a};
    print "<p><b>".ucfirst($a)."ing:</b> ";
    
    print "You $past{$a} $total times (" . $total/$times * 100 ."% of the time)<br>".
    "Wins on $a: $wins{$a}<br>".
    "Losses on $a: $losses{$a}<br>".
    "You won $percentage{$a}% of the time you $past{$a}.<br>";
}

print "<p><b>The Bottom Line:</b><br>";

print $total_percentage{stick}+$total_percentage{switch} . 
    "% of all rounds were won.<br>";
print "Theory predicts $theoretical_win_chance%.\n</p>";
}

sub monty_decision
{
    ($player_chosen_door, $mega_door) = @_;
    #Monty can't open the door you picked, and he can't open the mega
    #door.  If these doors are the same door, we pick
    #randomly. Otherwise, his hand is forced. 

    #This function isn't very understandable.
    if ($first_choice == $mega_door)
    {
	#There are two unopened doors. We pick one at random and then
	#see which actual doors they correspond to.
	$chosen_unopened_door = int(rand(2))+1;
	if ($mega_door == 1 || 
	    ($mega_door == 2 && $chosen_unopened_door == 2))
	{
	    return $chosen_unopened_door+1;
	} else {
	    return $chosen_unopened_door;
	}
    } else {
	#We pick the door that's neither the chosen door nor the mega
	#door. 
	return other_door($first_choice,$mega_door);
    }
}

sub other_door
{
    #Give this puppy two doors and it returns the door that's not the
    #one you gave it.
    @doors = (1..3);
    @invalid_doors = @_;
    foreach $door (@invalid_doors)
    {
	for ($i = 0; $i < scalar(@doors); $i++)
	{
	    if ($doors[$i] == $door)
	    {
		splice(@doors,$i,1);	    
		last;
	    }
	}
    }
    return $doors[0];
}

sub preliminaries
{
    print header;
    
    $times = param("times");
    $percent_switch = param("percent");
    $random = param("random");
    $same_door_always = param("same_door_always");
    $log = param("log");

    if ($times > $max_games)
    {
	print "<p>Can't play $times games, playing $max_games games instead.</p>";
	$times = $max_games;
    }
}