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.

Try it out click a door to make you initial choice, then click again to make
your final choice

Not Convinced - Try it a few hundered thousand times

Monte Carlo Simulation

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.

Java Source

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 dialog