  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.
