The Unfinished Game by Keith Devlin

Devlin, Keith. The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: Basic Books, 2008.

The Unfinished Game is a book about math, history and how ideas can change the way we live. The title refers what is also called the problem of points. When a game of chance is ended prematurely, what is the fairest way to divide the pot?

The prevailing idea before Blaise Pascal and Pierre de Fermat is that it is impossible to tell the future, and that made it hard rightly to divide the potential winnings. These mathematicians didn’t work out a way to predict the future, but they did figure out how to calculate the likelihood of different potential outcomes. The fair way to split the pot was in proportion to each player’s probability of winning.

Settling a debate amongst gamblers isn’t and especially important, but the concept of probability they created, along with its correct calculation, gave birth to something we do all time: manage risk. By estimating the likelihood of various events, we can make decisions generally increase our successes and reduce our losses. The insurance industry is built on understanding probability and decisions we make every day about what investments to make, what activities to undertake, even what to wear, are informed by our estimates of the probability of some future condition.

This concept of probability is common now. It can be daunting to think of how revolutionary it was at the time.

An interesting revealed in the book is how Pascal and Fermat worked out these ideas. It was through friendly correspondence. While much is made of the contentious debates and battles of ideas, much of our increase in knowledge comes from the cooperation of curious and committed colleagues. Both men were brilliant thinkers, but they weren’t haughty or difficult, though Fermat didn’t get along with everyone as well as he did with Pascal. For all the great math they considered in their letters, the correspondence is characterized by humility and grace.

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