Guess 2/3 of the Average
In this game, we ask you to pick a number from 0 and 100, but not just any number. The goal of the game is to pick the number that is closest to 2/3 of the average of the numbers picked by everyone else without going over. So, if everyone else picked 100, you should pick 2/3 of 100 without going over, which is 66. If everyone else picked 50, you should pick 33. Guess correctly and you will have the satisfaction of being smart enough to guess what everyone else is guessing.
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The great economist John Maynard Keynes had this to say about figuring out the average opinion of the average opinion:
Professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not the faces which he himself finds the prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one's judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree when we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practise the fourth, fifth and higher degrees.