chipmunk stew
Philosopher
- Joined
- Jun 6, 2005
- Messages
- 7,448
The first pick is quite relevant.From Wikipedia: "Once the host has opened a door, the car must be behind one of the two remaining doors."
Wouldn't this statement mean that the first pick is irrelevant.
If your first pick is the car, Monty can eliminate either the first goat or the second goat. (If you switch, you lose. If you stay, you win.)
If your first pick is the first goat, Monty MUST eliminate the second goat. (If you switch, you win. If you stay, you lose.)
If your first pick is the second goat, Monty MUST eliminate the first goat. (If you switch, you win. If you stay, you lose.)
So if you switch, you have a 2/3 chance of winning, and if you stay, you have a 2/3 chance of losing.
Think of a roulette wheel with an electornic sign displaying the last 20 numbers that popped up. Those last numbers are still irrelvant in determinbing the next number the ball lands on. However, I do see your point mathematically. Monty has eliminated a wrong answer, thus increasing your odds if you make a switch. The assumption is that you will pick the wrong door the first time since it is one in three. I'll try your suggested experiment. Thanks.

