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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.
With his strategy, the player has a win-chance of at least 2 / 3 , however the TV station plays; with the TV station's strategy, the TV station will lose with probability at most 2 / 3 , however the player plays. The fact that these two strategies match (at least 2 / 3 , at most 2 / 3 ) proves that they form the ...
Sequential game: A game is sequential if one player performs their actions after another player; otherwise, the game is a simultaneous move game. Perfect information : A game has perfect information if it is a sequential game and every player knows the strategies chosen by the players who preceded them.
The Guess 2/3 of the average game shows the level-n theory in practice. In this game, players are tasked with guessing an integer from 0 to 100 inclusive which they believe is closest to 2/3 of the average of all players’ guesses. A Nash equilibrium can be found by thinking through each level: Level 0: The average can be in [0, 100]
Speed is essential, as getting the opportunity to answer more clues first and right allows a player to pick more clues, thus increasing their chances of finding the Daily Doubles. [8] Winning contestants have a "just go for it" mentality and often push the buzzer before they know if they can answer correctly, trusting that they probably can.
The problem is to find a strategy for the players to determine the colours of their hats based on the hats they see and what the other players do. In some versions, they compete to be the first to guess correctly; in others, they can work out a strategy beforehand to cooperate and maximize the probability of correct guesses.
With perfect play, if neither side can force a win, the game is a draw. Some games with relatively small game trees have been proven to be first or second-player wins. For example, the game of nim with the classic 3–4–5 starting position is a first-player-win game. However, Nim with the 1-3-5-7 starting position is a second-player-win.
Game theory offers two strategies for this game that rely on different principles: the expected utility principle and the strategic dominance principle. The problem is considered a paradox because two seemingly logical analyses yield conflicting answers regarding which choice maximizes the player's payout.