Ten Great Ideas about Chance by PERSI DIACONIS & BRIAN SKYRMS

CRAIG CORMICK is president of Australian Science Communicators.

Princeton University Press ( 2017) RRP $ 27.95 WHAT ARE THE ODDS you knew the idea of chance was, until the 16th and 17th centuries, more mystery and magic than mathematics?

I had thought the Greeks would have been all over mathematical probability, but they put it all down to Tyche, the goddess of luck.

The real foundation work was done by an Italian gambler and mathematician. Gerolamo Cardano (1501-1576) thought chance could be measured. His book Liber de ludo aleae (“Book on Games of Chance”) was the first systematic treatment of probability. It also included a section on cheating.

Cardano’s work was followed by Galileo Galilei, Blaise Pascal, Pierre de Fermat, Jacob Bernoulli and others, all seemingly fixated on better understanding the roll of dice or the toss of coins. Slowly the study of chance moved away from the gaming tables towards the fields of law, politics and medicine. That work was done by philosophers and economists including David Hume, Immanuel Kant and Karl Popper. Thus this book is, as the authors put it, part history, part probability and part philosophy.

The book gets even more interesting when it looks at the work of psychologists Daniel Kahneman and Amos Tversky, who studied how we commonly make mistakes in reasoning about chance and probability, using mental shortcuts, biases and framing to overstate or underrate the likelihood of things occurring. That the physiology and logic of chance are different subjects is one of the 10 great ideas to which the book’s title refers.

Much of the text involves quite complex mathematics, but the authors generally find practical examples to explain the concepts – such as the chapter on inverse inference, which explains the reason so many published research papers are non-replicable is an overemphasis on p-values.

This book will not increase your odds of winning at games of chance, but it will give you some greater understanding of why you lose.