{"title":"The economics of free bets","authors":"Karl Whelan","doi":"10.1016/j.econlet.2026.113289","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mi>m</mi></math></span> 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 <span><math><msqrt><mrow><mi>m</mi><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>m</mi><mo>)</mo></mrow></mrow></msqrt></math></span>. Empirical evidence from odds on tennis bets confirms this prediction.</div></div>","PeriodicalId":11468,"journal":{"name":"Economics Letters","volume":"269 ","pages":"Article 113289"},"PeriodicalIF":2.0000,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economics Letters","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165176526004854","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2026/10/9 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
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 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 . Empirical evidence from odds on tennis bets confirms this prediction.
期刊介绍:
Many economists today are concerned by the proliferation of journals and the concomitant labyrinth of research to be conquered in order to reach the specific information they require. To combat this tendency, Economics Letters has been conceived and designed outside the realm of the traditional economics journal. As a Letters Journal, it consists of concise communications (letters) that provide a means of rapid and efficient dissemination of new results, models and methods in all fields of economic research.