Two men bet on whose necktie cost less — and both talk themselves into the bet
Two men agree: whoever has the cheaper necktie has to give it to the other as a prize. Each reasons the same way — "If I lose, I lose the value of my tie; if I win, I gain more than that, since the other man's tie must be worth more than mine." Both men expect to profit from the very same bet. What's wrong with the reasoning?
Reveal the answer
The error is treating "the value of my tie" as a fixed reference point while also treating it as the random variable being wagered — the same quantity is smuggled into the comparison twice, in incompatible roles, which is what makes a genuinely zero-sum bet look profitable for both sides at once. The paradox is a close cousin of the two-envelope problem, and both show how easily symmetric-looking reasoning can hide a contradiction.