It's a law of restricted choice, question, but as phrased I think it's difficult to be certain that my instinctive answer ("the chance is the same as far as you are aware whether you pick the card or he does) is correct.
The famous example of this, of course, was when a player offered his opponent to pick one of his hole cards for $25. The player who paid the $25 thought that seeing one of the hole cards would give him more information about his opponent's hand, whereas in fact it did not. I'll dig out the example when I have time. I'm fairly sure that it is in Al Alvarez's first book on poker. "The Biggest Game In Town".
This does bring up a minor philosophical point. Suppose I am drawing to a flush with one card to come. We casually say that "your chance of hitting is 9/46", but, since the order of the cards is predetermined, we could (if we knew the order of the cards still in the deck) say that "your chance is 1" or "your chance is 0".
Both of us could be "right" simultaneously, simply because we (who know the order of the cards) are essentially inhabiting a different universe (in probabilistic terms) than the person who does not know the order of the cards. This has a large number of real-world applications, obviously.
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Date: 2010-07-10 02:34 pm (UTC)The famous example of this, of course, was when a player offered his opponent to pick one of his hole cards for $25. The player who paid the $25 thought that seeing one of the hole cards would give him more information about his opponent's hand, whereas in fact it did not. I'll dig out the example when I have time. I'm fairly sure that it is in Al Alvarez's first book on poker. "The Biggest Game In Town".
This does bring up a minor philosophical point. Suppose I am drawing to a flush with one card to come. We casually say that "your chance of hitting is 9/46", but, since the order of the cards is predetermined, we could (if we knew the order of the cards still in the deck) say that "your chance is 1" or "your chance is 0".
Both of us could be "right" simultaneously, simply because we (who know the order of the cards) are essentially inhabiting a different universe (in probabilistic terms) than the person who does not know the order of the cards. This has a large number of real-world applications, obviously.
PJ