• John HaighEmail author


We point out that the term odds is ambiguous, either relating to the true probability an event occurs, or to the payout price offered by bookmakers. The UK National Lottery changed its format in 2015; comparisons are made between the old and new formats, with well-organised counting central to analyzing both. When examining roulette, we draw parallels between differential equations and difference equations, and show how similar are the methods used in both fields—a link between discrete and continuous mathematics. We discuss how bookmakers may set their payout prices for horse races, and paradoxes that can arise. We look at different formats of poker, both in casinos (video poker, Casino Stud Poker) and at home (e.g. Texas Hold ’Em); again, counting and the idea of average are central. Finally, we describe the operation of UK Premium Bonds. None of this material is taken as an encouragement to students to gamble: on the contrary, by showing how to analyse commercial gambling games, we hope they will become well informed about the widely differing rates of return that are offered.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK

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