Uccisore wrote:someoneisatthedoor wrote:I understand the mathematical proof, I just place no stock in mathematical proofs concerning probability.

Likewise, a lot of people do this intuitively. As such, it isn't that they 'don't get' the answer, it's that they don't believe in it.

Be simple enough to test with 2 people and a deck of cards, wouldn't it? The stats aren't just numbers in space, if the example is right, switchng really should get you the car (or ace) 66% of the time.

You don't even need two people. You can do it yourself.

Just shuffle two deuces and an ace (the deuces represent the "goats" and the ace, the "car"), and deal them face down in front of you. Pick one of the three cards, being sure to keep it face down. Turn over one of the two cards that you didn't pick. Then:

A) if the card revealed is an ace (i.e., "the car"), start over because in the "Monty Hall problem," remember, the host never reveals the car when he opens one of two doors that weren't picked by the contestant. He always opens a door with a goat behind it.

B) if the card revealed is a deuce (i.e., "a goat"), then either keep your original card OR switch to the other face down card.

By switching, you'll switch to the ace close to 67% of the time. By keeping your original card, you'll keep the ace about 33% of the time . . . guaranteed.

If you don't believe it now, do the experiment and you'll believe it then.