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I can think of two mathematical measures that might be useful, both based around Elo ratings. Is the correct Elo distribution function. Let's suppose Player B beats Player A 64% of the time, and Player C beats Player B 64% of the time. How often does Player C beat Player A? Generally, speaking, the higher the number, the less of a role luck plays, though ...


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Compare the Expected value to the Standard Deviation. The higher the luck factor in the game, the higher S.D(X) - E(X). For example, assume you play Cribbage or Poker a bit better than the other players at the table (meaning that your expected value is larger than zero) . Now, if you play just a single hand, the Standard Deviation will be way bigger than ...


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