The Theory of Gambling and Statistical Logic

After publication of the revised edition of this work (1977), I smugly presumed that the fundamentals of Gambling Theory had been fully accounted for — an attitude comparable to that attributed to the U.S. Patent Offi ce at the end of the 19th century: “ Everything worth inventing has already been invented. ” In the more than 30 years since, progress in the fi eld of gambling has not faltered. Improved computational facilities have led to the solution of games hitherto deemed unsolvable — most notably, Checkers. Such solutions have a regenerative effect, creating more problems that demand yet further solutions. Computer simulations have provided numerical answers to problems that remain resistant to closed-form solutions. Abstract branches of mathematics have been awakened and applied to gambling issues. And, of paramount signifi cance, Parrondo’s Paradox has advanced the startling notion that two losing ventures can be combined to form a winning prospect. Reader and author are equally admonished: Never bet against the future . Gambling remains a near universal pastime. Perhaps more people with less knowledge succumb to its lure than to any other sedentary avocation. As Balzac averred, “ the gambling passion lurks at the bottom of every heart. ” It fi nds outlets in business, war, politics; in the formal overtures of the gambling casinos; and in the less ceremonious exchanges among individuals of differing opinions. To some, the nature of gambling appears illusive, only dimly perceivable through a curtain of numbers. To others, it inspires a quasi-religious emotion: true believers are governed by mystical forces such as “l uck,” “f ate,” and
“c hance.” To yet others, gambling is the algorithmic Circe in whose embrace lies the roadmap to El Dorado: the “f oolproof” system. Even mathematicians have fallen prey to the clever casuistry of gambling fallacies. Special wards in lunatic asylums could well be populated with mathematicians who have attempted to predict random events from fi nite data samples. It is, then, the intent of this book to dissipate the mystery, myths, and misconceptions that abound in the realm of gambling and statistical phenomena.