Optimal Online Bookmaking for Any Number of Outcomes
Hadar Tal, Oron Sabag

TL;DR
This paper introduces an optimal online bookmaking strategy that minimizes worst-case loss across any number of outcomes and rounds, using a novel dynamic programming approach linked to Hermite polynomials.
Contribution
It provides the first explicit characterization of the optimal online bookmaking strategy for any number of outcomes and rounds, connecting regret minimization with Hermite polynomials.
Findings
The optimal loss is the largest root of a simple polynomial.
The developed algorithm achieves optimal loss against an optimal gambler.
The approach unifies dynamic programming with Pareto frontier analysis in vector repeated games.
Abstract
We study the Online Bookmaking problem, where a bookmaker dynamically updates betting odds on the possible outcomes of an event. In each betting round, the bookmaker can adjust the odds based on the cumulative betting behavior of gamblers, aiming to maximize profit while mitigating potential loss. We show that for any event and any number of betting rounds, in a worst-case setting over all possible gamblers and outcome realizations, the bookmaker's optimal loss is the largest root of a simple polynomial. Our solution shows that bookmakers can be as fair as desired while avoiding financial risk, and the explicit characterization reveals an intriguing relation between the bookmaker's regret and Hermite polynomials. We develop an efficient algorithm that computes the optimal bookmaking strategy: when facing an optimal gambler, the algorithm achieves the optimal loss, and in rounds where…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Bandit Algorithms Research · Auction Theory and Applications · Sports Analytics and Performance
