Hi Glenn and others,
> 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.)
I've only tried scamming my old dad, who is a stubborn man and always
stick to his first choice. But this game made him wonder a little ...
:-)
> 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
This example may help to understand the thinking in this problem. If
Monty does not know where the prize is, he will have a 50% chance of
finding the prize in the cases where you (or I) did not select the
correct door. So again, if the prize is in door A, there is 2/3 chance
that I select the wrong door first, and there is 1/2 a chance that Monty
in this case selects the prize. Assuming that the game then is over, and
that you do not win the prize if Monty finds the price, there is a 1/3
(2/3 * 1/2) chance that Monty finds the prize.
If Monty is not allowed to select the door with the prize, this 1/3
chance is for your benefit !!!
Looking at it as I showed yesterday:
The original problem (prize is in door A):
Your choice: Monty's Choice Strategy
Door A Door B Change looses / Stay wins
Door C Change looses / Stay
wins
Door B Door C Change wins / stay looses
Door C Door B Change wins / stay looses
Here change wins in 2/3 of the cases, and stay wins in 1/3 of the cases.
If Monty does not know the location of the price, he can select between
both remaining doors in all cases:
Your choice: Monty's Choice Strategy
Door A Door B Change looses / Stay wins
Door C Change looses / Stay
wins
Door B Door C Change wins / stay looses
Door A Monty gets prize
Door C Door B Change wins / stay looses
Door A Monty gets prize
Here you can see that change wins 1/3 of the cases, stay wins 1/3 of the
cases, and Monty gets the prize in 1/3 of the cases.
Hope this is understandable.
Best regards
Gerhard (with no t :-)
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