What's Luck Got To Do With It? The Pschology and Mathematics Behind the Illusion of Luck in Gambling

PART 1 EXPLORES THE psychology of gambling. Gambling behavior and addiction have been studied since the turn of the twentieth century when psychopathologists began investigating repressed libidinal impulses, the conflicts between the id and superego. Those tensions between the demands of conscience and the performances of the ego led to fascinating theories of gambling addiction. Some of these early theories have been disputed and some still claim that the impulsive gambler may not have a conscious will to win, but rather surprisingly an internal conflict causing an unconscious desire to lose.
Though the pathology of compulsive gambling is still not satisfactorily explained by any one theory, it looks as though, in certain personalities, dormant gambling tendency can be awakened by a variety of environmental factors that play a fundamental role in determining motivation for gambling and other addictions.
Gambling impulses are not easily categorized. Certain gamblers are driven by unrealistic desires to control fortune through some weaving of skill, greed and luck. They have illusions of influence over randomness and are compelled to impose some sort of order or meaning to their future. Selected inherited histories of neurotic tensions stored in the id, possibly guilt, may urge others. Addictions could be genetically determined or subliminally dependent on life’s experiences. They may come from a driving need for stimulation, an antidote to boredom perhaps caused by overactive dopamine nerves.
With the recent wondrous technologies of MRI and PET scans, researchers are able to see increased levels of dopamine activity in pathological gamblers during pleasurable as well as risky behaviors. With increased and prolonged activation neural pathways of dopamine transmission (reward pathways) are strengthened to favor pleasure, reward and punishment as well as other distinguishing behaviors of the individual, thereby reinforcing those behaviors.
However, dopamine production also occurs during many types of high anxiety brain activity such as reward, fear, pleasure, laughter as well as other addictions. The pleasures of eating, sex, alcohol, nicotine and other drugs also trigger increased dopamine activity. Thereby muddling the distinction between the excitement of gambling and the benign pleasures of life.

Part 2 surveys the history of gambling. It begins, more or less, in the gaming houses of Louis XIV’s Paris at a time when the common person on the street believed his or her destiny was predicted by astrology, tarot, or palm reading, when amulets and crosses were worn to ward off the evil eye, and a time when the momentous ideas of probability where just being discovered and formulated by Pascal, Fermat and others.
Mathematical explanations of worldly phenomena generally arrive either long after or long before a great deal of experience and observation. So to get a flavor of that experience we turn to a general history of seventeenth and eighteenth century gambling rooms and coffeehouses of Europe and then pass a focal shift from Europe to America, where nineteenth century life itself is a game of chance, where New Orleans crap games are plentiful, and when Mississippi river boats paddle gambling upstream to Visksburg and Memphis, and then up the Ohio to Louisville, Cincinnati and Cleveland.
The end of Part 2 examines the World economic tailspin of October 2008. Centered on awareness that even the shrewdest investments are still gambles, this part explores the naive reliance on the illusion of luck applied to financial markets along with the complexities of risk behavior under unchecked opportunities.

Part 3 is where the mathematics of gambling is explained. Centering on the general mathematics of gambling, primarily on probability and statistics through a simple—very simple—tutorial on what probability and statistics are about, this book moves on to explain expected value, the law of large numbers, coincidences, distribution functions and the mathematics of roulette, slots, craps, blackjack and poker.
Gambling is not done in theory, but rather in the real world where honest dice are carefully manufactured for fairness, and where balls and wheels machined to supreme tolerances. Mathematics may model the real world, but what gives us that critical, magical connection between the ideal and physical worlds? To predict favorable outcomes our models must closely mimic the ideal. The truly amazing thing is that we can make that connection. Bridges stay up and dams hold because they were built through reliance on mathematical models. Chance seems to be far more mystifying, immeasurable and far more connected to some unfathomable uncertainty; yet, we have truly amazing theorems dealing with likelihood, which tell us that we can cleverly measure nature’s secrets of randomness, confine uncertainty by mathematical means and manage the phenomenology of chance by mathematical theorems such as the weak law of large numbers. Ultimately, we begin to understand greed and luck in gambling as well as why people accept bets with negative expectation and finally answer the central question of the book from both mathematical and psychological positions—what makes us feel lucky in gambling?

Selected Works

What are the chances? This is the question we ask ourselves when we encounter the freakiest and most seemingly impossible coincidences, like the woman who won the lottery four times or the fact that Lincoln’s dreams foreshadowed his own assassination.
Hardly any math symbols were used before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve to what we know of today? Enlightening Symbols explains the fascinating history behind the development of our current mathematical notation system, shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.
Princeton University Press (2010). A book about the nature of gambling, emphasizing the dangers and pitfalls of feeling lucky. It will investigate the hooks of gambling and what makes gamblers feel lucky. Using both mathematics and psychology it will illustrate the misconceptions of luck, explore what it means to have a good chance, and to create an awareness of expected outcomes.
Published by Dutton in April 2007. Now available in bookstores. "THIS is one of the most fascinating science books I have ever read . . . Mazur has succeeded in telling a fresh and untold story with clarity and style." -- The New Scientist
One of Choice's Outstanding Academic Titles of the Year 2005-- “This book is a treasure of human experience and intellectual excitement.”
Editor of the revived classic by Tobias Dantzig, Number: The Language of Science.