The Economics of Free Bets

Karl Whelan

No 22016, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: Sportsbooks offer promotional ``free bets'' that return profits if the bets win, but not the stake provided. These bets can be hedged to produce guaranteed profits. This paper shows how to value the guaranteed profit from these stake-not-returned free bets under a simple constant-margin pricing rule in which sportsbooks, on average, keep a fraction m of the money staked. The guaranteed hedged value is a nonlinear function of the free bet's probability of winning, reaching a maximum when this probability is the square root of m time 1-m. Empirical evidence from odds on tennis bets confirms this prediction.

Date: 2026-10
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