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Tom replied:
>This would be true if the pick was random. But it is not. So we now do not have a chance of 2 empty choices. We have only a choice of one empty and one full because of Monty's non random choice.
>

Luc gave an excellent explanation, but let me try again in the form of a card game, which I will call Three Card Monty.

It is played with a deck of only 3 cards, an Ace and a pair of deuces.
Monty shuffles the cards and deals them out face down. You get to pick one, but it remains face down. If it proves to be the Ace, you will win. Your chances are 1/3.

Monty takes a look at the remaining two cards. They could be Ace-2, 2-Ace, or 2-2. He discards a 2 and places the remaining card face down in front of me. Whoever has the Ace wins the pot.

I really like these odds. I still maintain that the chances of you winning with that first card remain at 1/3. The chances of my holding the Ace are 2/3.

Don Seltzer
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