For Cardano, this meant measuring how likely random events were. There were no laws about chance events, no rules about how likely something was. If someone rolled two sixes while playing dice, it was simply good luck. Cardano was one of the first to spot that such games could be analysed mathematically. He realised that navigating the world of chance meant understanding where its boundaries lay. He would therefore look at the collection of all possible outcomes, and then home in on the ones that were of interest.
Although two dice could land in 36 different arrangements, there was only one way to get two sixes. He also carried a long knife, known as a poniard, and was not averse to using it. In , he was playing cards in Venice and realized his opponent was cheating. In the decades that followed, other researchers chipped away at the mysteries of probability, too. At the request of a group of Italian nobles, Galileo investigated why some combinations of dice faces appeared more often than others.
Astronomer Johannes Kepler also took time off from studying planetary motion to write a short piece on the theory of dice and gambling. The science of chance blossomed in as the result of a gambling question posed by a French writer named Antoine Gombaud. He had been puzzled by the following dice problem. Which is more likely: throwing a single six in four rolls of a single die, or throwing double sixes in 24 rolls of two dice?
Gombaud believed the two events would occur equally often but could not prove it. He wrote to his mathematician friend Blaise Pascal, asking if this was indeed the case. To tackle the dice problem, Pascal enlisted the help of Pierre de Fermat, a wealthy lawyer and fellow mathematician. Many of the new concepts would become central to mathematical theory.
Their research showed that Gombaud had been wrong: he was more likely to get a six in four rolls of one die than double sixes in 24 rolls of two dice. As well as helping researchers understand how much a bet is worth in purely mathematical terms, wagers have also revealed how we value decisions in real life. During the 18th century, Daniel Bernoulli wondered why people would often prefer low-risk bets to ones that were, in theory, more profitable.
If expected profit was not driving their financial choices, what was? He suggested that the same amount of money is worth more — or less — depending on how much a person already has. For example, a single coin is more valuable to a poor person than it is to a rich one. Such insights have proved to be very powerful. Indeed, the concept of utility underpins the entire insurance industry. Most people prefer to make regular, predictable payments than to pay nothing and risk getting hit with a massive bill, even if it means paying more on average.
Whether we buy an insurance policy or not depends on its utility. If something is relatively cheap to replace, we are less likely to insure it. In my new book, I investigate how gambling has continued to influence scientific thinking, from game theory and statistics to chaos theory and artificial intelligence. After all, wagers are windows into the world of chance. They show us how to balance risk against reward and why we value things differently as our circumstances change.
They help us to unravel how we make decisions and what we can do to control the influence of luck. Encompassing mathematics, psychology, economics and physics, gambling is a natural focus for researchers interested in random — or seemingly random — events. The relationship between science and betting is not only benefiting researchers. Gamblers are increasingly using scientific ideas to develop successful betting strategies.
In many cases, the concepts are travelling full circle: methods that originally emerged from academic curiosity about wagers are now feeding back into real-life attempts to beat the house. The first time physicist Richard Feynman visited Las Vegas in the late s, he went from game to game, working out how much he could expect to win or, more likely, lose. Of course, that was the expected loss over a large number of attempts.
When Feynman tried the game, he was particularly unlucky, losing five dollars right away. It was enough to put him off casino gambling for good. Nevertheless, Feynman made several trips to Vegas over the years. He was particularly fond of chatting with the showgirls. During one trip, he had lunch with a performer named Marilyn.
As they were eating, she pointed out a man strolling across the grass. Feynman found the notion puzzling. Marilyn called Nick the Greek over to their table, and Feynman asked how it was possible to make a living gambling. Nick the Greek told Feynman the real secret behind his success. Unlike the Parisian gamblers who used the martingale strategy, he understood the games, and understood the people playing them.
He had looked beyond the obvious strategies — which would lose him money — and found a way to tip the odds in his favour. Although brilliance is generally less common than bravado, stories of other successful gambling strategies have emerged over the years. The results have certainly varied over the years and while some swear by certain strategies there are others that will just as quickly write them off.
One of those systems that have received a lot of attention over the years is the Martingale betting system. Here is a look at what it is and whether or not it really works. The strategy behind the Martingale system comes from the world of casino gambling, and in particular the game of roulette.
Roulette is a game where there is a wheel with red and black marks. A ball is placed on the wheel and spun around it, and gamblers have the option of choosing whether the ball will land on black or red, as well as on certain numbers. The idea behind the Martingale system is to double the stake size after each losing wager and return to the starting wager amount after every win.
By doing this, all previous losses can be recovered by eventually winning. For example, if betting odds of 3. The system relies on that the ball is bound to bounce in the gamblers favor eventually, so it would therefore be impossible to lose. However, anything can happen in a chance game and the same can be said for betting on sports. The strategy is a simple one to understand but the risks must still be understood because it is no completely foolproof.
Stuart Holland provided an excellent example of how the Martingale system can make something out of nothing in his book titled Successful Staking Strategies. He was able to show how when it comes to the roulette wheel, the mathematical expectation will always stay the same but the risk can change. The same can be said for betting on sports.
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