设计最优在线赔率机制，确保庄家在最坏情况下仍能保本。
Optimal Online Bookmaking for Binary Games
- 提出基于双平衡树的新策略，动态调整赔率以应对投注变化。
- 在二元事件中实现理论最优，保证所有决定性投注序列下庄家损失相同。
- 适合研究在线博彩、风险控制与博弈论的学者与从业者。
在线投注中，庄家可在事件发生前多次更新赔率，且新赔率可依赖已积累的投注情况。本文研究最大化庄家最坏情况回报的在线赔率问题，将其形式化为最优在线赔率博弈，并给出了二元情形下的精确解。为此，我们提出了基于双平衡树的最优赔率策略，确保在所有决定性投注序列（即赌徒每轮将全部资金押注单一结果）下，庄家的亏损保持一致，从而实现风险最小化。
原文摘要 · Abstract (English)
In online betting, the bookmaker can update the payoffs it offers on a particular event many times before the event takes place, and the updated payoffs may depend on the bets accumulated thus far. We study the problem of bookmaking with the goal of maximizing the return in the worst-case, with respect to the gamblers' behavior and the event's outcome. We formalize this problem as the \emph{Optimal Online Bookmaking game}, and provide the exact solution for the binary case. To this end, we develop the optimal bookmaking strategy, which relies on a new technique called bi-balancing trees, that assures that the house loss is the same for all \emph{decisive} betting sequences, where the gambler bets all its money on a single outcome in each round.
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