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Players can prove to outside observers whenever the lottery coordinator cheats
Can you explain this in more detail? What would happen if a coordinator cheats?
It's all detailed here. Specifically:
This lottery protocol is not entirely trustless, as the market maker has the sole ability to determine which of the players receives the jackpot money. However, all the complexity described above is designed to assure players that, in the event of cheating by the market maker, they can construct an irrefutable proof that the market maker cheated. The market maker can similarly prove irrefutably that a lottery was executed honestly and fairly.
The market maker can also cheat by going offline (not awarding the jackpot at all), but I also describe how they can commit to revealing at least one winner
To prove his intent to cooperate, the market maker can commit extra collateral to the lottery, forcing himself to reveal one of the outcome secrets shortly after the settlement height h, or else forfeiting his collateral. The satoshi value of this collateral can vary, but to be a worthwhile incentive, it should be enough to put the market maker at a meaningful net loss if surrendered.
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