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Medium: Paradox

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Release Message: A wager between two people seems to favor them both.

Description: The necktie paradox is a puzzle or paradox within the subjectivistic interpretation of probability theory. It is a variation (and historically, the origin) of the two-envelope paradox. Two men are each given a necktie by their respective wives as a Christmas present. Over drinks they start arguing over who has the cheaper necktie. They agree to have a wager over it. They will consult their wives and find out which necktie is more expensive. The terms of the bet are that the man with the more expensive necktie has to give it to the other as the prize. The first man reasons as follows: winning and losing are equally likely. If I lose, then I lose the value of my necktie. But if I win, then I win more than the value of my necktie. Therefore the wager is to my advantage. The second man can consider the wager in exactly the same way; thus, paradoxically, it seems both men have the advantage in the bet. This is obviously not possible. The paradox can be resolved by giving more careful consideration to what is lost in one scenario ("the value of my necktie") and what is won in the other ("more than the value of my necktie"). If we assume for simplicity that the only possible necktie prices are $20 and $30, and that a man has equal chances of having a $20 or $30 necktie, then four outcomes (all equally likely) are possible: