Dr. Z's racetrack module for 41C

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Book Review by R. J. Henery, University of Strathelyde

Beat the Racetrack. By William T. Ziemba and Donald B. Hausch. San Diego, Calif., Harcourt Brace Jovanovich, 1984. xx, 392p., $22.95.

The book is primarily aimed at the serious gambler and the reason is simple: it describes a betting system that really works -the authors say it works, E. 0. Thorp believes it works, even I believe it works. Mind you, I have my doubts. . .
The system is based on the fact that the odds quoted in horse races reflect very closely the horses' true chances of winning. In Tote pools for example the money laid on each horse to win enables us to estimate the chance of that horse winning. However the public at large, both in England (sic) and the United States, is not so good at judging the proper odds for horses being placed (being 1st or 2nd) or showing (being 1st, 2nd or 3rd). By exploiting this "market inefficiency" the authors can select out a few really promising bets and they have shown their faith in the system by wagering quite large sums of money, for example at one point gambling $294 from a total wealth of $479. Presumably, according to the proportional betting criterion they advocate, the authors would always be willing to risk as much as 60 per cent of their wealth on the appropriate system bet. That shows faith! At any rate they did come out winning.
The early chapters deal with: the origins of the system from a suggestion of Harville; the different types of bet; how to predict the place and show probabilities; analyses of past races; how much you should bet. Although the primary (indeed the necessary) requirement of any system should be to ensure that the chosen bets are likely to be profitable, the authors devote an inordinate amount of space to the question of how much to bet. Later chapters describe, rather repetitously, the operation of the system at the racetrack. Even inveterate gamblers will find the pace of the book very slow here, and there are pages and pages of race-cards which could well have been omitted altogether.
The final chapter is a mathematical appendix which summarises the basis of the system. Here an attempt is made to show that in a particular sequence of 22 bets there is only a very small chance (quoted as 3E-5) that their average profit of 22.9 per cent of stakes could have been surpassed by "random betting", which is later assumed to (i) lose 17 per cent of stakes on average, (ii) always bet the same amount, and (iii) always bet on horses with win probability 0.771. This is surely not random betting!
The point is this: does the system do more than just select a bet at very short odds, i.e. does it give a greater expected return? Since short odds horses are underbet to win, it is not unreasonable to expect that the same holds for short odds bets to show. The serious gambler wants to know the advantage in show bets rather than win bets at odds of 2 to 1 on, these being typical odds for a large system bet. If win bets were made consistently at such odds the average loss would be much less than 17 per cent, indeed Table 3.5 in the book indicates a possible profit of 3.4 per cent, and this makes it very much easier to achieve gains of 22.9 per cent in short sequences of bets. It should be noted also that wide variations in the size of bets make for wide variations in gambling fortune and this also makes a short term gain more likely.
The book, and the theory on which it is based, will be a useful guide to gamblers, but until the method has been more fully tested, preferably in England, the reviewer intends to keep his bawbees in his sporran.

BEST!
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