Quote:
Originally Posted by HarryT
Please look at the maths in my original answer. You will see that you are incorrect.
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I see it as being more like the prison puzzle where everyone is logical.
Lets suppose that the dealer and player are both logical. The dealer knows that he has a 2/3 advantage of winning and only has to pay out even money. Most of the time he will turn over the cup where the coin is and take the money.
However he would like to get some more money into the game so he turns over an empty cup and makes an offer to let the player switch cups for the price of doubling down.
Remember the dealer knows where the coin is. He knows if the player guessed right the first time or not. Now let us suppose that the player is ever so logical and will always switch his bet when this offer comes up because mathematically it's too his advantage. But the dealer has the knowledge of where the coin actually is. By the rules of this game the dealer is not cheating if he uses that knowledge.
The dealer being ever so logical will make the offer every time he knows that the player guessed right the first time.