The Parlay Puzzle: Expected Utility and Multi-Leg Betting

Karl Whelan

No 202610, Working Papers from School of Economics, University College Dublin

Abstract: Multi-leg parlay bets have become hugely popular in the US despite loss rates on stakes that are four times higher than regular bets. This paper shows that even if bettors believe they have an edge, maximization of subjective expected utility requires placing separate bets when per-leg win probabilities are below one-third and combining at most two legs for probabilities between one-third and one-half. These thresholds are largely independent of risk aversion and edge size. With average leg counts of five, and component bet win probabilities typically below one-half, the popularity of parlays presents a new puzzle for expected utility theory.

Keywords: Parlays; Expected utility theory; Kelly criterion (search for similar items in EconPapers)
JEL-codes: D81 G11 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2026-05
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http://hdl.handle.net/10197/32468 First version, 2026 (application/pdf)

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