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Optimal Online Bookmaking for Binary Games

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arxiv 2501.06923 v1 pith:HWXQ4U23 submitted 2025-01-12 cs.GT cs.ITcs.LGmath.ITmath.OC

Alankrita Bhatt , Or Ordentlich , Oron Sabag This is my paper · ORCID
classification cs.GTcs.ITcs.LGmath.ITmath.OC
keywords bookmakingeventonlineoptimalbetsbettingbinaryemph
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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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  1. Optimal Online Bookmaking for Any Number of Outcomes

    cs.LG 2025-06 accept novelty 7.0 of 10

    The optimal worst-case bookmaking loss for K outcomes and T rounds is the largest root of an explicit polynomial, with regret scaling as sqrt(T) times the largest Hermite root.

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