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Chance, Luck and Statistics

Horace C. Levinson
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Charlie Ashbacher
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While it is difficult to completely explain the principles of probability and statistics without the extensive use of mathematical equations, it is not impossible — and this book is an existence proof. Levinson has created what clearly are the best textual descriptions of the basics of probability and statistics that I have ever read. Using the standard games of poker, craps and roulette he steps the reader through the possible results and what can and most likely will occur. It is so well done that no previous experience with the games is necessary, you simply need to follow along with the descriptions of the actions.

The lack of equations clearly differentiates it from most other books on probability and that may be anathema to a mathematician. However, the goal of all technical books is to instruct the reader. On that score, it is impossible to criticize Levinson's book. It is split into two parts: the first covers chance and the second statistics. Like all good writers covering chance, Levinson points out that unexpected events are expected, and what may be expected is most unlikely. For example, I have always found it difficult to convince students that when you flip a well-balanced coin many times, one of the most unlikely events is an equal number of heads and tails. It always seems to baffle them that the probability of equal numbers of heads and tails approaches zero as the number of flips of the coin gets larger. Levinson's treatment of this basic idea of "intuition" versus the reality of probability is very clear. I will incorporate some elements of it into my lectures when I teach basic statistics the next time.

My favorite explanation in the book is why it is essential that all casinos set a house limit on bets. For if they did not, a consortium of people with "unlimited" resources would break the bank. Not could or can, but would. The probability of this event can easily be proven to be certainty. It amazed me to think that after two decades of teaching probability and statistics, I had never really stopped to consider this simple problem in that way.

Unfortunately, the book is not suitable as a textbook. The lack of equations prevents the inclusion of problems or any form of rigorous mathematical reinforcement of the topics. This is really not meant to be a criticism of the book, just a bit of a lament. The inclusion of equations would have altered the charm of the book and I understand why the author chose to leave them out.

Citizens of a modern industrial state with a free media are constantly bombarded with statistical data, not all of which is developed by people whose motives are pure and whose ethics are sound. It is up to all of us to do the best we can to filter out the noise and extract the information needed to make sound social and civic decisions. In fact, I consider knowledge of statistics to be an essential life skill. Anyone possessing basic mathematical knowledge can learn that skill by reading this book.

Charlie Ashbacher ( is the principal of Charles Ashbacher Technologies, a company that offers state of the art computer training. He is also an adjunct instructor at Mount Mercy College in Cedar Rapids, Iowa, and at the end of this academic year, he will be three courses short of having taught every class in the math and computer science majors. A co-editor of the Journal of Recreational Mathematics, he is the author of four books in mathematics and one in computer programming.

Preface to Dover Edition
  Chapter I " Chance, Luck and Statistics"
  Chapter II Gamblers and Scientists
  Chapter III The World of Superstition
  Chapter IV Fallacies
  Chapter V The Grammer of Chance
  "Chapter VI "Heads or Tails"
  Chapter VII Betting and Expectation
  Chapter VIII Who Is Going to Win?
  Chapter IX Chance and Speculation
  Chapter X Poker Chances
  Chapter XI Poker Chances and Strategy
  Chapter XII Roulette
  "Chapter XIII Lotteries, Craps, Bridge"
  Chapter XIV From Chance to Statistics
  Chapter XV Chance and Statistics
  Chapter XVI Fallacies in Statistics
  Chapter XVII Statistics at Work
  Chapter XVIII Advertising and Statistics
  Chapter XIX Business and Statistics
Appendix I
Appendix II