09 Oct '09 02:452 edits

If you switch, you win two out of three games...so yes, you should switch.

For example:

Assume the car is behind door #1.

If you pick (and then switch):

Door #1, the host opens, say #2. If you switch (to #3), you lose.

Door #2, the host opens door #3, if you switch (to #1) you win

Door #3, the host opens door #2, if you switch (to #1) you win.

If you switch, you will win if the car is behind EITHER one of the other two doors (2 out of 3 chance). But if you DON'T switch, you only win if the car is behind your original choice (1 out of 3 chance).

You can apply the exact same logic to any of the 3 doors you would originally choose regardless if the car is behind #1, #2 or #3.

The key is that the host knows where the car is, and ALWAYS opens a losing door after your choice.

For example:

Assume the car is behind door #1.

If you pick (and then switch):

Door #1, the host opens, say #2. If you switch (to #3), you lose.

Door #2, the host opens door #3, if you switch (to #1) you win

Door #3, the host opens door #2, if you switch (to #1) you win.

If you switch, you will win if the car is behind EITHER one of the other two doors (2 out of 3 chance). But if you DON'T switch, you only win if the car is behind your original choice (1 out of 3 chance).

You can apply the exact same logic to any of the 3 doors you would originally choose regardless if the car is behind #1, #2 or #3.

The key is that the host knows where the car is, and ALWAYS opens a losing door after your choice.