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Although, as I see it, wagering is introduced to weed out the weak.

Then wouldn't it be simpler to just say you only want to play against the best? Many people do that. There used to be an old forum, I don't remember the name, where almost all games were played for money, and what did it lead to? Newcomers would show up, watch, maybe lose a small amount, and leave, and eventually the forum withered.