Review of "Against the Gods: The Remarkable Story of Risk" by Peter Bernstein

The period before 1200 AD starts with the ancient greeks. Sokrates defined a concept, εικοσ, which meant something like "likeness to truth". Truth to the greeks could only be obtained through rigorous proofs. A truth was, and still is, that the sum of the angles of a triangle is always 180 degrees. What we today call probability had no place and Aristoteles reportedly said that a geometer who argues in terms of probabilities is not worth an ace. The time period until Fibonacci introduced the arabic numerals is very interestingand takes us from ancient Greece, through the Arab empires and to the city states of Italy. Interspersed throughout the text are quotes such as the following from Omar Khayyam:

The Moving Finger writes; and, having writ, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of

Fans of Sheldon Cooper might recognize the first one and a half lines.

Luca Paciolo was a monk and a mathematician as well as a collaborator of Leonardo da Vinci that was born in 1447 in Tuscany. He is also referred to as the father of accounting and bookkepping due to being accredited with the idea of double-entry bookkeeping. In his work Summa de arithmetica, geometria, proportioni et proportionalita he not only introduced double-entry bookkeeping, he also posed the following puzzle:

Anne and Bjørn plays a fair game of balla. They agree to play until one of them has one six rounds. The game stops when Kari has won five rounds and Ola six. How should the stakes be divided?

This problem puzzled mathematicians and gamblers over the years. Chevalier de Mére, a french writer living in the 17th century, posed this problem again to, among others, Pierre de Fermat and Blaise Pascal who subsequently collaborated and solved the puzzle. The key insight they had, that had been missing from previous unsatisfactory solutions, was that the division should mainly depened on what could happen in the remainder of the game; not what has happened. Previous solutions suggested to split the stakes proportionally with respect to rounds won. However, this leads to strange outcomes. For example, if two players play a fair game where the winner is the first to win 4 rounds. If the game then ends after only 1 round the winner of that particular round will have won 100% of the rounds played and get all the stakes, but the actual probability of that player winning gets closer and closer to 50/50 the more rounds agreed upon. In this example the actual change of winning would be only 42/64, a bit less than 66%.

The first cup of coffee ever made in the British Empire was apparently made by a Cretan scholar studying at Oxford from 1637 to 1648. The first coffee house in London was opened by another greek, Pasqua Roseé, in 1652. Another early coffee house was Lloyd's coffeehouse which opened around 1686 which quickly became a popular haunt for sailors, merchants and ship-owners to exchange news and soon after a market place for maritime insurance. I will not go closer into the history of Lloyd's, but it is an interesting story in itself.

The book is a terrific read: well-written with a good balance of facts and anecdotes that transports you to the setting. You can imagine the hustle and bustle of Lloyd's coffee house and Cardano taking the first steps towards a theory of probability by trying to gain an edge when playing dice. It is a great non-fiction book and interesting for anyone with the slighest interest in the market and human behaviour when faced with uncertainty as well as anyone interested in history.