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Path: utzoo!linus!decvax!genrad!grkermit!masscomp!kobold!tjt
From: tjt@kobold.UUCP (T.J.Teixeira)
Newsgroups: net.math
Subject: Re: Let's Make a Deal
Message-ID: <165@kobold.UUCP>
Date: Sat, 8-Oct-83 11:50:21 EDT
Article-I.D.: kobold.165
Posted: Sat Oct  8 11:50:21 1983
Date-Received: Tue, 11-Oct-83 05:13:01 EDT
References: <169@mi-cec.UUCP>
Organization: Masscomp, Littleton, MA
Lines: 43

Having read Dave Martindale and Dan Klein's responses (always switching
doors gives you a 2/3 chance of winning), I don't believe it.

Firstly, if you hypothesize a second contestant who will win what is
behind the other door, both contestants can increase their chance of
winning to 2/3 by swapping doors!

Secondly, I did my own simulation:
================================================================================
int wins;	/* number of times I win by switching doors */
int losses;	/* number of times I lose after switching */
int monty;	/* number of times Monty shows me the good door */
int doors[3];	/* count how often each doors is a winner */
		/* to verify the random number generator */

main()
{
	register int i, door, mydoor, montysdoor;
	for (i = 0; i < 10000; i++) {
		/* pick a winning door at random */
		door = rand() % 3;
		doors[door]++;
		/* I pick a door at random */
		mydoor = rand() % 3;
		/* Monty picks a door, but not mine! */
		while ((montysdoor = rand() % 3) == mydoor);
		if (montysdoor == door)
			monty++;/* Monty shows me the car */
		else if (mydoor != door)
			wins++;	/* I win by switching */
		else
			losses++;/* I feel like a sap! */
	}
	printf("monty %d wins %d losses %d\n", monty, wins, losses);
	printf("door #1 %d #2 %d #3 %d\n", doors[0], doors[1], doors[2]);
}
================================================================================
monty 3302 wins 3258 losses 3440
door #1 3330 #2 3419 #3 3251
================================================================================
If Dave and Dan are right, why are the wins and losses roughly equal,
and what's wrong with my simulation (no flames please on coding style
-- it's just a 60-second hack)?  I showed you mine, now show me yours!