Publications

Under Review

Log-Optimal Portfolio Construction for Binary Options with Combinatorial Constraints

Under Review at Management Science, 2025 (Previously Reject-and-resubmit from Operations Research)

Abstract: We study the problem of optimal wealth allocation across independent binary options with known payouts, aiming to maximize log utility under practical constraints. This general framework arises in settings such as prediction markets (e.g., Kalshi and Polymarket), financial event contracts (e.g., Nadex), and sports betting (e.g., Draftkings and FanDuel). The Kelly Criterion provides a classical solution for the bet sizing of a single binary option, and numerous papers have explored extensions to multiple binary options. Our work expands on this body of research by investigating how to incorporate combinatorial constraints into the model, including limits on the number of binary options to select in a portfolio, a requirement that arises in many settings. These constraints considerably increase the computational complexity of the problem, thereby necessitating advanced solution methodologies. To address this challenge, we develop a logic-based Benders decomposition algorithm that provides a scalable and computationally efficient solution framework. Although broadly applicable, we focus on sports betting due to its market scale and unique inclusion of parlay options. We also study how sportsbooks can make slight modifications to parlay pricing so that optimal allocations do not include parlay options, even though such options may remain attractive to bettors.

Recommended citation: Jeff Decary, David Bergman, Bin Zou (2025). "Log-Optimal Portfolio Construction for Binary Options with Combinatorial Constraints".
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Simplifying the Madness of March Madness

Under 2nd round Major Revision at Production and Operations Management, 2025

Abstract: This paper investigates the effectiveness of maximizing the expected value of the best-performing entry in multi-entry betting pools for single-elimination tournaments, with a particular focus on March Madness. In such betting pools, participants select winners for each game, and their score is a weighted sum of the correct selections. Due to the top-heavy payout structures in these pools, we study whether maximizing the expected score of the highest-scoring entry, which has been successfully adopted in the sports betting literature, is a suitable modeling approach for March Madness betting pools. Unlike traditional methods that require modeling how other participants make their selections - an especially challenging task given that March Madness only occurs annually - this approach only requires win probability estimates for teams as input, and inherently provides a diversified position across multiple entries. We present an exact dynamic programming approach for calculating the expected maximum score of any fixed set of entries. Additionally, we explore the structural properties of this approach to develop several solution techniques. Using insights from one of our algorithms, we design a simple yet effective heuristic which delivers high-quality results when tested against high-roller betters in a real-world March Madness betting pool. In particular, our results demonstrate that the best 100-entry solution identified by our approach had a 2% likelihood of winning a $1 million prize in a real-world betting pool, showing that the proposed heuristic is competitive even against the best professional bettors.

Recommended citation: Jeff Decary, David Bergman, Carlos Cardonha, Jason Imbrogno, and Andrea Lodi (2025). "Simplifying the Madness of March Madness"; URL https://arxiv.org/abs/2407.13438.
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