# The Unfinished game – Review

This book is about a set of letters exchanged between Pascal and Fermat in the year 1654 that led to a completely different way of looking at future. The main content of the letters revolved around solving a particular problem, called “**problem of points**”. A simpler version of the problem goes like this:

Suppose two players—call them Blaise and Pierre—place equal bets on who will win the best of five tosses of a fair coin. They start the game, but then have to stop before either player has won. How do they divide the pot? If each has won one toss when the game is abandoned after two throws, then clearly, they split the pot evenly, and if they abandon the game after four tosses when each has won twice, they do likewise. But what if they stop after three tosses, with one player ahead 2 to 1?

It is not known how many letters were exchanged between Pascal and Fermat to solve this problem, but the entire correspondence took place in 1654. By the end of it, Pascal and Fermat had managed to do what was unthinkable till then – “**Predict the future**”, more importantly act based on predicting the future.

Pascal tried to solve the problem using recursion whereas Fermat did it in a simpler way,i.e. by enumerating the future outcomes, had the game continued. The solution gave rise to a new way of thinking and it is said that this correspondence marked the birth of risk management, as we know today.

The book is not so much as an analysis of the solution(as the author believes that today, anyone who has had just a few hours of instruction in probability theory can solve the problem of the points with ease) but more about the developments leading to 1654 and developments after the 1654. In the process, the book recounts all the important personalities who played a role in making probability from a gut based discipline to a rigorous mathematical discipline. The book can be easily read in an hour’s time and could have been a blog post.