On May 18, 6:44*am, "David" wrote:
"Don Pearce" *wrote in message

...



The host acts as a leak of information. It might help to imagine
an
alternate game, where the host does not know the contents of the
doors,
and the game is void if the host reveals the car. This version
puts you
back to 50/50 when the host reveals a goat, whether you switch
doors or
not.
***
Not true. When the host reveals a goat whether he guessed or
knew
it was there makes absolutely no difference. You should still
switch doors.

David

If the host does not know, he might quite as easily reveal the
car.
You then can't win it. Do you guarantee yourself 2/3 odds by
switching
then? No. If the host reveals a goat by chance, the odds do
indeed
drop to 50/50.

d
***
Sorry, I disagree. *Yes the host could reveal a car if he is
unaware of the situation. If this happens, the game was defined
as void. If the host instead reveals a goat, there is no
difference whether he guessed or knew the goat was there.


Let's look at the case of the ignorant host.

There are three possibilities at the start of the game. The
probability of each is 1/3

_1 2 3_
aCGG
bGCG
cGGC

Let us say door 1 represents the contestant's pick. The host can pick
either door 2 or door 3
Case a: Host picks Door 2. Result: Goat. Contestant switches to Door
3, loses.
...............Host picks Door 3 Result Goat. Contestant switches to
Door 2, loses.
Case b: Host picks Door 2. Result Car. Contestant loses
...............Host picks Door 3. Result Goat. Contestant switches to
Door 2, wins
Case c: Host picks Door 2. Result Goat. Contestant switches to Door 3,
wins
...............Host picks Door 3 Result Car. Contestant loses.

Of the six possible scenarios, the contestant loses four times. If the
contestant does not switch after the ignorant host opens a door, the
contestant loses four times. If we discard the times the host opens a
door with a car behind it, the contestant wins two out of four times
when he switches, and two out of four times when he doesn't switch.
Therefore, switching picks has no effect on the odds when the host
randomly opens one of the other doors.