Re: Deal or No Deal - Monty Hall paradox applies?

On Mon, 03 Nov 2008 14:25:56 -0600, russotto@xxxxxxxxxxxxxxxxxxx
(Matthew Russotto) wrote:

In article <o6ung49vfb44iga8krhj0eo7ihi7g8abpc@xxxxxxx>,
Patrick Hamlyn <path@xxxxxxxxxxxxxxxxxxxxxxx> wrote:
Richard Heathfield <rjh@xxxxxxxxxxxxxxx> wrote:

I choose Door No 1. You choose Door No 2.
Monty opens Door No 3. So we both gain
by swapping. I don't think so!

You're playing a different game. Monty Hall is a one-player game.

It can be easily seen that the two-player game is different.

In the one-player game Monty can always find a goat to show you. In the
two-player game, one in three games he would be forced to open the last door
showing the car. And that can only lead to a fight between the two players.

In at least one actual two-player variant used on the show, he opened
a losing player's door. In that case, the remaining player should NOT
switch to the remaining door.


Well, it probably depends on what policy he was following when he
opened that door.

LET'S ASSUME that Monty's allowed to open or not open as many doors as
he wants, and give or not give either player a chance to switch.

Then, you really have to know Monty's motivation.

IF Monty's number one concern is trying to save money and avoid giving
out cars, then the remaining player should be very wary of switching
at that point. After all, in this scenario, Monty wouldn't offer any
switching opportunities; he would just show that both contestants
picked goats and pat himself on the back.

HOWEVER...

IF we can somehow know that Monty's number one concern is trying to
give away a car at the end of every single episode -- that he would
never take a chance that might result in ending up with both players
picking goats, then the opposite reasoning applies. The only reason
for Monty to do any door-opening or switch-offering is if it would
increase the chances of giving away that car. And the remaining
player should switch.
.

Relevant Pages

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