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Teaching - course material, including course documents, problem sheets, and revision material.
Applied probability, with especial reference to optimal strategies in diverse games and gambles, and index betting.
"Probability Models", Springer, SUMS. Published January, 2002. Corrections available
As the blurb on the back cover says, "..is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experience of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared, or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion.
No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions."
"Taking Chances: winning with probability", O.U.P. (1999). Paperback version (2000). Corrections available
"Taking Chances: winning with probability", Second Edition. O.U.P. (2003). Corrections available.
(This book is my attempt to make the ideas of probability accessible to "the intelligent layman". Reviewers have said nice things about it: see, for example, pages 574-576 of The American Mathematical Monthly, Vol 107(6) June 2000.)
"Optimal strategy in a dice game" (with M Roters), J. Appl. Probab. 37(4) (2000) 1110-1116.
"The Kelly criterion and bet comparisons in spread betting", The Statistician 49(4) (2000) 531-539
"(Performance) index betting and fixed odds", The Statistician 48(3) (1999) 425-434
"The Statistics of the National Lottery", J. Royal Statist. Soc. A 160(2) (1997) 187-206.