Hi Rick,
Lawry is wrong.
Let's look at it from Gerhardt's point of view. (He'd explain it again but
he's out scamming people with it now. Probly calls it 3-door-Monty.)
When you make your first pick you either guess it right or wrong.
If you guess it right and switch you lose, but this only happens 1 out of 3
times because the chance of guessing right is only 1/3.
If you guess it wrong and switch you win, but this happens 2 out of 3
times because the chance of guessing wrong is 2/3.
So your odds of winning are 2:1 with the switching strategy.
If you stick with your original pick you only have a 1 in 3 chance of winning.
The chance of this guess being right do not zoom to 1 in 2 when Monty
reveals a door because you made the pick BEFORE Monty revealed a door,
at a time when you had less information (this is what the 100 door
version blatantly illustrates).
It's also critical that Monty knows what's behind every door (and that the
contestant knows that Monty knows). If Monty is guessing when he reveals a
door, and he is lucky enough to reveal a booby prize, there is no advantage
in switching. Anyone who can explain the reason for *this* gets extra
credit. Jonathan? Gerhardt? If no one succeeds I'll explain it Monday.
Glenn
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