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If it is an online game, how can someone be 100% sure that his opponent will pay? It is always possible to abandon account and run away if you lose. Or there is someone who escrow funds? I think as you play it low bet, you havent experience cases when someone refuse to pay. Since the games itself are costly today, paying $2-$10 is something affordable. But if someone loses $1000 in best of 3 fight in just 3 minutes, winner might get problems of receiving his money.
From what the OP described, they have a group of probably reliable players who always play matches
When a community is formed, the users are usually reliable
Also, from what he described, the stakes are around 2 to 10 dollars, so there's no reason for anyone to take a hit for that amount
You described a bet of 1000 dollars, and I think it would be difficult for someone to bet that amount in a community aimed at fun and not professional, but in this case it would be easy to solve, probably the creator of the group, or community administrator could receive the amount in advance and be responsible for paying the winner