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You could also suggest a game with a handicap, but I'm almost certain they won't agree to it.

No, but why not? Let's say a 100-point rating difference adds +1 to the return bet. For example, if players with ratings of 1900 and 1700 are playing, the match would be 1 to 3, meaning the stronger player receives 1 ruble if they win and lose 3 if they lose. This incentive could attract weaker opponents. However, as I see it, betting is introduced to weed out weaker players.