[Bill Graham]

Carey Carlan wrote:
spamtrap1888 wrote in
news:88df2861-f695-449b-
:

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.

Then go back to the original where the host knows where the car is and
the contestant switches.

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 3. Result Goat. Contestant switches to Door 2,
wins
Case c: Host picks Door 2. Result Goat. Contestant switches to Door 3,
wins

Or the contestant doesn't switch.

Case a: Host picks Door 2. Result: Goat. Contestant keeps Door 1,
wins. ..............Host picks Door 3 Result Goat. Contestant keeps
Door 1, wins.
Case b: Host picks Door 3. Result Goat. Contestant keeps Door 1, loses
Case c: Host picks Door 2. Result Goat. Contestant keeps Door 1, loses

After the Host opens the door the odds are even. Makes no difference
if the contestant changes doors or not. This is the same as there
only being two doors.

The original claim was that the odds remained 1 in 3 even after the
Host opened the door. I still don't see it.

I claqim there are two games. In the first game, you go to the studio, pick
a door, and then go home to wait and see if they call you and tell you that
you either won or lost. Your odds are only 1/3 of winning this game. But if
you play the second game, then you go to the studio and mess around until
the host opens up a door and shown you the donkey behind it. then you can
play the game with 50-50 odds of winning. The only thing I have trouble
explaining is why, in order to play this second game with the better odds,
you have to switch doors. But, in fact, you do have to switch in order to
switch games and take advantage of the better odds.