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What's Luck Got to Do with It? The History, Mathematics, and Psychology of the Gambler's Illusion

Joseph Mazur
PRINCETON UNIVERSITY PRESS 2010, 296 PAGES
PRICE (HARDBACK) £20.95 ISBN 978-0-691-13890-9

What's Luck Got to Do with It?

Joseph Mazur’s book takes us on a fascinating journey looking at the misconceptions involved in gambling. The
reader learns the history of gambling, the way mathematicians analyse luck and the psychology that affects gamblers.

A wonderful endorsement of the book is given by the coin probability professor, Persi Diaconis from Stanford University, ‘Mazur’s book treats luck in a fresh light. The philosophy and emotional aspects (along with a little mathematics) are all there. The reader who delves in will be lucky indeed.’

The book attempts to answer such questions as:

  • why do so many gamblers risk it all when they knowthe odds of winning are against them?
  • why do we expect heads on a coin toss after several flips have turned up tails?

Each chapter in Mazur’s book is littered with research quotes to help us try to understand these difficult questions. For example with the question of an expected head on the next toss of a coin, Mazur quotes research by Tversky and Kahneman who found in the 1970s that people expect that important characteristics will be represented in each of its specific local parts. Yet as we know this is not how chance works and these local events will merge into insignificance as the number of trials increases.

The research of Giloviich, Vallone and Tversky in the 1980s suggested that this is not how people think and that for the most part people reject randomness in the appearances of long runs in short samples, as they think these seem too purposeful to be random. This is not just a modern day fallacy; Pierre-Simon de Laplace said ‘false sense of probability through errors in judgement over random events, creating wishful biases in favour of the gambler’s fallacy’.

The book devotes a whole chapter to the history and mathematical uses of Bernoulli’s theorem, which is now more commonly called the weak law of large numbers. As well as dealing with the history and mathematics of various games of chance, the book also tries to come to terms with what it means to be feeling lucky, looking into the idea of ‘hot hands’ and how people have the illusion of control over randomness when they are hot after a long winning streak.

With plenty of engaging anecdotes, I found this book a delight to read. As you would expect it does not contain all the answers to why people throwaway their money on theNational Lottery, but it does give a great insight to the psychological and emotional factors that are gambling addiction.
Nick ‘The Greek’ Dandalos who once won half a million dollars in a single game said ‘The next best thing to gambling and winning is gambling and losing.’

Steve Humble FIMA
NCETM
Mathematics Today October 2011

What's Luck Got to Do with It? The History, Mathematics, and Psychology of the Gambler's Illusion can be purchased at Amazon.co.uk