The Theory of Gambling and Statistical Logic, Second Edition

Many readers will find this book to be an entertaining and useful presentation of gambling ideas and lore. However, there are some errors in the "Basic Theorems" beginning on page 51. In particular, Theorem V on page 60 is not correct. The "maximum boldness" strategy is need not be optimal in a subfair game when there is a bound on the size of bets. Likewise "minimum boldness", also known as "timid play" need not be optimal when there is a house minimum. (For counterexamples, see the article by Heath, Pruitt, and Sudderth in The Proceedings of the American Math. Soc. vol 43, pp. 498-507, April 1972 and the article by Ruth in the Journal of Applied Probability, vol 36, pp. 837-851, September 1999.