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Evaluating betting odds and free coupons using desirability

Nakharutai, Nawapon; Caiado, Camila C.S.; Troffaes, Matthias C.M.

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Nawapon Nakharutai


In the UK betting market, bookmakers often offer a free coupon to new customers. These free coupons allow the customer to place extra bets, at lower risk, in combination with the usual betting odds. We are interested in whether a customer can exploit these free coupons in order to make a sure gain, and if so, how the customer can achieve this. To answer this question, we evaluate the odds and free coupons as a set of desirable gambles for the bookmaker. We show that we can use the Choquet integral to check whether this set of desirable gambles incurs sure loss for the bookmaker, and hence, results in a sure gain for the customer. In the latter case, we also show how a customer can determine the combination of bets that make the best possible gain, based on complementary slackness. As an illustration, we look at some actual betting odds in the market and find that, without free coupons, the set of desirable gambles derived from those odds avoids sure loss. However, with free coupons, we identify some combinations of bets that customers could place in order to make a guaranteed gain.


Nakharutai, N., Caiado, C. C., & Troffaes, M. C. (2019). Evaluating betting odds and free coupons using desirability. International Journal of Approximate Reasoning: Uncertainty in Intelligent Systems, 106, 128-145.

Journal Article Type Article
Acceptance Date Jan 7, 2019
Online Publication Date Jan 16, 2019
Publication Date Mar 31, 2019
Deposit Date Jul 9, 2018
Publicly Available Date Jan 16, 2020
Journal International Journal of Approximate Reasoning
Print ISSN 0888-613X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 106
Pages 128-145
Related Public URLs


Accepted Journal Article (388 Kb)

Copyright Statement
© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license

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