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I have one die. It has six sides marked 2, 4, 8, 16, 32 and 64. Does anyone know what game uses this?

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Backgammon uses a die like that; it's known as a doubling cube. It's used, when playing a multi-game match or for money, to track the current stakes of the game. Note that in this capacity it's not really rolled as a die; it's just a cube with the necessary numbers on the faces.

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