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How about suggesting players play chess, where the winner loses! It would only take an hour instead of a full game, and the players themselves would participate! High, no offense, but your suggestion sounds a bit absurd.
P.S. If you really need to see a result, you can ask a judge to flip a coin while in a trance, and offer the choice of which side of the coin to pick to the player who tried harder to find the time and opportunity for the match. And randomness is randomness, no matter how hard you try to change it.