Most of the important things in life come down to chance. The friends you make, the job you get, the spouse you marry, the children you have, and your health are all determined largely by chance. But even the small, everyday events in our lives are in large part determined “at hazard”, as the old expression for randomness goes. Virtually everything from “will I catch the bus this morning?” to “will I get that business deal?” is determined by luck.

So, what can we, rational beings who strive for security and predictability, do about it? Fortunately, while we cannot determine the events of our lives, there is a well-developed theory in mathematics, called the theory of probability, which can help us to at least assess in a quantitative way the chances of occurrence of events.

The theory of probability was developed by 17th-century mathematicians who were enlisted by gamblers to help them to identify casino games with the highest chances of winning. One incorrigible gambler, the French nobleman known as the Chevalier de Méré, asked the mathematician Blaise Pascal (1623-62) to assess the chances of winning at dice games that were then popular in France. As a result, Pascal began a correspondence with another mathematician, Pierre de Fermat (1601-65) — the man who gave us Fermat’s Last Theorem, solved late in the 20th century — and through their correspondence emerged the theory of probability.

This allowed the Chevalier de Méré and subsequent modern gamblers to determine the exact chances of winning any game.

But most things in life are not as simple, conceptually, as the roll of a die, the toss of a coin, or the spin of a roulette wheel. Events that matter to most people are immensely more complex than mechanical gambles. Is there any way to find the probabilities of complicated events, such as: what are the chances that the economy will pick up this year? Or what is the probability that I will be promoted at my job? Or what is the chance that “someone special” I have just met will want to pursue a romantic relationship?

Bruno de Finetti (1906-85) was an Italian mathematician with wide-ranging interests that extended to psychology and economics. While still in his early twenties, he developed a theory that probability is not an absolute quantity, but rather a measure of information. As such, it can be subjective. For example, the probability that a stock will go up, as assessed by an insider of the company, is clearly not the same as the probability of this event as assessed by someone who is not an insider but knows the industry well, and may well be different from the probability of the same event as assessed by the average investor. The probability that any person may assign to the occurrence of an event depends on his or her knowledge, experience, and perhaps even “feel” for what may or may not happen. This is what distinguishes it from the objective probabilities of games of chance. De Finetti’s quest was to try to quantify this idea. While he was teaching courses on probability at the University of Rome, he invented what is called de Finetti’s game. Italians, as everyone knows, are avid football fans, and de Finetti used the weekly event “Which team will win this week’s game?” to test the game on his students.

It works like this: if you want to find out what someone really believes are the chances for the occurrence of a given event, gauge these chances against a lottery with a known probability. By doing so, you will make this person compare his belief about one event with the lottery, which carries a precisely known chance of winning. For example, suppose you want to know what your friend thinks is the probability that Team A will win this week’s football game. Ask your friend the following: “Choose one of two actions. You can either wait for the game to take place, and if Team A wins, I will give you £1 million. Or, you can draw a ball out of a bag with 100 balls, 50 of which are red and 50 black. If you draw a red ball now, I will give you the same £1 million. But you must choose now to either draw or wait.” If your friend elects to wait for the game, you ask the next question: “There are now 70 red balls in the bag and 30 black ones. What do you choose?” Suppose your friend says: “I’ll draw,” then your next question should be: “OK, now there are 60 red balls: wait or draw?” If your friend says: “Wait for the game,” you now suggest that there are 65 red balls, at which point your friend might say: “I am now indifferent — either wait or draw.” Then you know that your friend’s true, subjective belief is that the chances Team A will win the game are 65 per cent.

It turns out that most people have fairly well-defined opinions about the possible occurrence of events in their lives, but they are not in touch with their beliefs on a conscious level. There are many reasons for this, among them overconfidence, bravado, or a lack of clear thinking. What the de Finetti game does is to force individuals to evaluate in an objective manner all the factors in their minds in order to come up with a more precise notion of the chances of a given event. The game works very well, and I have often used it, asking myself these questions comparing an event of interest to me and the hypothetical lottery with changing composition in order to clearly assess the probability. But, perhaps not surprisingly, the game fails when it comes to love. The problem is that for some people winning at love is more important than the £1 million — or any amount, for that matter. And when that happens, the game is useless.

Amir Aczel is a mathematician and author of 12 books. His latest is Chance: A Guide to Gambling, Love, the Stock Market, & Just About Everything Else (High Stakes Publishing, £12; offer £9.60, from Books First on 0870 1608080)