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Evaluating betting odds and free coupons using desirability.

Nakharutai, Nawapon and Caiado, Camila C. S. and Troffaes, Matthias C. M. (2019) 'Evaluating betting odds and free coupons using desirability.', International journal of approximate reasoning., 106 . pp. 128-145.


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.

Item Type:Article
Full text:Publisher-imposed embargo until 16 January 2020.
(AM) Accepted Manuscript
First Live Deposit - 09 January 2019
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
File format - PDF
Publisher Web site:
Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Record Created:09 Jan 2019 10:28
Last Modified:31 Jan 2019 16:22

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