The Monty Hall Problem is a problem in probability theory derived from the game show Let's Make A Deal. On the show the contestents have a choice of doors to open. Behind one door is a prize, behind the other two is something less desirable. After the player makes their original choice, Monty opens one of the remaining doors exposing one of the losers. Then Monty asks the player if they want to trade their door for the remaining door. The question is how does this decision effect the odds. Almost everyone's intuition tells them it's 50/50 so trading or not does not matter but in fact switching doubles the odds of winning overall form 1/3 to 2/3.
Here's a Video discribing the problem
There is a good discussion on Wikipedia
Enter the number of trials and the number of doors and click run to to see the effect of switching or not switching doors. The simulation run by this window randomly selects which door wins and randomly selects the player's ( Alice or Bob ) initial choice. Monty Hall then opens one of the remaining doors which is a loser. Then Alice always stays with her original door and Bob always switches.
You can down load the Java Archive (.jar) which runs the above sim. The jar file is executable so it can be run direcetly on machines with java installed. It also contains the applet version which is running the above dialogDownload