Your opponent will make more money in this game if he chooses to behave irrationally and pick "yes" or "no" at random. If you know that's his strategy, you're better off changing your answer to "no." In that case, half the time you'll get 4 points and half the time you'll get 5, for an expected payoff of 4.5. If you said "yes," your expected payoff would be only 3 (the average of 6 and 0).
Then, because your strategy makes your move fixed, his expected payoff will be the average of 5 and 6, or 5.5. If he had played rationally, on the other hand, you would have gotten 6 and he would have gotten 1. So you'll get less money, and he'll get more.
Credit: Adapted from a graphic by David H. Wolpert
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