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> You know everything about the state of the game

Is that fully accurate? Do players know how fast the other teams players run? The frequency with which they can catch the ball? How successful their blocking will be?

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Random elements do not interfere with perfect information. Adding a coin toss to chess won't make it a game of imperfect information. It will make it a game that is less deterministic than chess-without-the-coin-tossing. The opposite of "perfect information" is "hidden information", not "fallibility".

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