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    Re: The Darn Old Cocked Hat - the sequel 1
    From: Tom Sult
    Date: 2013 Mar 17, 19:01 -0500
    I would like to say I did not understand the problem. The issue is this represents the grad I got in stats. I yield.  

    Tom Sult
    Sent from my iPhone

    On Mar 17, 2013, at 18:44, Brad Morris <bradley.r.morris---.com> wrote:

    Hi Tom

    This problem comes around (and around, and around) so often, there are posted explanations of the counter-intuitive answer.  Here's one:



    On Mar 17, 2013 7:21 PM, "Tom Sult" <tsult---com> wrote:

    In this game we have three cards. A, 2, 2. Since Monty never takes the A. The second game is A, 2. 

    If Monty took a card at random the condition you describe would be true. 

    I have been know to get locked into my thinking but as I deal the card and peek to always take a 2 and not an ace. The second guess can not have a probability of 2, 2. Only A, 2 and 2, A. It is the condition of the fact that Monty will not reveal the A that changes the result. 

    Perhaps I am not understanding the game. On Monty's show he reveals the contents behind the curtain.  Is this a game different?  

    Tom Sult
    Sent from my iPhone

    On Mar 17, 2013, at 16:22, Don Seltzer <timoneer---COM> wrote:

    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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