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[Schoolman]

An entertaining preface to the classic book "The Theory of Gambling and Statistical Logic", by Richard A. Epstein (2nd Revised Ed. 2009). I particularly liked the bit about mathematicians in lunatic asylums. Enjoy.

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 sig-
nifi 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 out-
lets 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 emo-
tion: true believers are governed by mystical forces such as " luck, " " fate, " and
" chance. " To yet others, gambling is the algorithmic Circe in whose embrace
lies the roadmap to El Dorado: the " foolproof " 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 mis-
conceptions that abound in the realm of gambling and statistical phenomena.

The mathematical theory of gambling enjoys a distinguished pedigree. For
several centuries, gamblers ' pastimes provided both the impetus and the only
concrete basis for the development of the concepts and methods of probabil-
ity theory. Today, games of chance are used to isolate, in pure form, the logi-
cal structures underlying real-life systems, while games of skill provide testing
grounds for the study of multistage decision processes in practical contexts. We
can readily confi rm A.M. Turing's conviction that games constitute an ideal
model system leading toward the development of machine intelligence.

It is also intended that a unifi ed and complete theory be advanced. Thus,
it is necessary to establish formally the fundamental principles underlying the
phenomena of gambling before citing examples illustrating their behavior. A
majority of the requisite mathematical exposition for this goal has been elabo-
rated and is available in the technical literature. Where defi ciencies remain, we
have attempted to forge the missing links.

The broad mathematical disciplines associated with the theory of gam-
bling are Probability Theory and Statistics, which are usually applied to those
contests involving a statistical opponent ( " nature " ), and Game Theory, which
is pertinent to confl ict among " intelligent " contestants. To comprehend the
operation of these disciplines normally requires only an understanding of the
elementary mathematical tools (e.g., basic calculus). In only a few isolated
instances do rigorous proofs of certain fundamental principles dictate a descent
into the pit of more abstract and esoteric mathematics (such as, Set Theory).

If this book is successful, readers previously susceptible to the extensive
folklore of gambling will view the subject in a more rational light; readers pre-
viously acquainted with the essentials of Gambling Theory will possess a more
secure footing. The profi ts to be reaped from this knowledge strongly depend
on the individual. To any moderately intelligent person, it is self-evident that
the interests controlling the operations of gambling casinos are not engaged
in philanthropy. Furthermore, each of the principal games of chance or skill
has been thoroughly analyzed by competent statisticians. Any inherent weak-
ness, any obvious loophole, would have been uncovered long ago; and any of
the multitude of miraculous " systems " that deserved their supernal reputation
would have long since pauperized every gambling establishment in existence.

The systems that promise something for nothing inevitably produce nothing for
something.

It will also be self-evident that the laws of chance cannot be suspended
despite all earnest supplications to the whim of Tyche or genufl ections before the
deities of the Craps table. Such noumena cast small shadows on the real axis.

In the real world there is no " easy way " to ensure a fi nancial profi t at the
recognized games of chance or skill; if there were, the rules of play would
soon be changed. An effort to understand the mathematics validating each
game, however, can produce a highly gratifying result. At least, it is gratifying
to rationalize that we would rather lose intelligently than win ignorantly.

[Gizmotron]

Let's take Set Theory, Axiom of Choice. If I can discover a sleeping dozen that lasts for more than 20 consecutive spins then I can place bets as if I know the future. On the first bet I have 65% chance of winning the first bet. I have a 40% of winning both bets needed to pay for any later loss. Even though I have a 65% chance of winning the second bet, as a set, I only win 40% of the time. Now that's the risk. The rewards can be anywhere from nothing to as much as 30 wins in a row without a loss. All this from identifying a set. Now, from experience, I know how to live with these risks and rewards. I'm not claiming special powers or trying to sell anything. I just know that the degree of session difficulty can be a known thing. I live on the edges of chance, observing and reacting to its changing features. It's an art form similar to jazz music and improvisation.