[EasilyFound]

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A double elimanation match does work where the player from the losing side has to beat the player from the winners side twice. IN your example where you are playing best out of three for the last match, that I would
A Consider it that the winner has already won one game of the best out of three so the player from the losing side has two win 2 games straight and the player from the winning side only has to win 1 game.

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OK. This makes sense, but this is not different than if the last match was not 2 of 3. Right? If this was just a single elimination, one game per match format, the loser's bracket would have to win two in a row, and the winner's bracket player would have to win just once. So this solution isn't really a true best 2 of 3 format, is it? To have a true best two of three, you have to have a second two of three match if the winner's bracket lost the first such match.