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Department of Mathematical Sciences

# Seminars

## Stats4Grads: Odds and free coupon: modelling by desirability axioms and checking avoiding sure loss via the Choquet integral

Presented by Nawapon Nakharutai, Department of Mathematical Sciences

20 June 2018 11:00 in CM105

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 model the odds and free coupon 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.