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In the case where every player has to make a guess, but they are free to choose when to guess, there is a cooperative strategy that allows every player to guess correctly unless all the hats are the same colour. Each player should act as follows: Count the numbers b of blue hats and r of red hats that you see.
If a player guesses correctly, he immediately gets to guess again. Guessing correct on the second try wins the game. If a player makes an impossible guess, (e.g. guessing 20 but only putting in a fist and a palm for 5 points) then that person gets a strike. Two strikes would result in a point for the other player.
In game theory, "guess 2 / 3 of the average" is a game where players simultaneously select a real number between 0 and 100, inclusive. The winner of the game is the player(s) who select a number closest to 2 / 3 of the average of numbers chosen by all players.
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Guessing is the act of drawing a swift conclusion, called a guess, from data directly at hand, which is then held as probable or tentative, while the person making the guess (the guesser) admittedly lacks material for a greater degree of certainty.
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