“The next best thing to gambling and winning is gambling and losing.” So said legendary gambler Nick “The Greek” Dandalos, and he would know. Over the course of his playing career he’s thought to have won and lost $500 million.
Gamblers and statisticians share a love of odds, though the stakes on the table couldn’t be more different between the two. But us statisticians are allowed to fantasise a little, so here’s a hypothetical challenge. Let’s say you fancied a Maserati costing $100,000, but sadly you only had a dollar, what form of gambling will give you the best chance of getting the sports car? I’ll even make it a little easier for you by giving you three choices – a punt on the lottery, a flutter on the horses or a spin on the roulette wheel.
While you think about this, you might be surprised to discover how far back our urge for gambling stretches. Devices that embody randomness have been used in leisure for at least 5,000 years. The ancient Egyptians, presumably when nothing good was on television, sat around and played board games in which moves were decided by throwing an astragalus, which is a bone in the heel that can land on one of four sides.
Gambling became so popular that the Romans tried to restrict it to Saturdays. Even the Emperor Claudius played obsessively and wrote a book called How to win at dice. People continued for centuries to make bets and quote odds: in Paris in 1588 you could get 5 to 1 against the Spanish Armada sailing to invade England, although this was probably a ruse by the Spanish.
What is remarkable is that in all this time, right up until the Renaissance, nobody analysed gambles mathematically. This could be partly because people thought the outcomes were decided by some external force of fate, but it is now thought that the gap between theory and practice was too great, and therefore no-one had the idea of putting a number on chance - in other words calculate probability.
Not until the Chevalier de Mere, it seems. The Chevalier was a very perceptive gambler in Paris in the 1650s, and he reckoned that odds were slightly in his favour of getting a six in four throws of a single dice, but that the odds were slightly against him of throwing two dice and getting a double 6 in 24 throws. By chance (or fate) he brought the problem to two of the smartest mathematicians at that or any other time, Blaise Pascal and Pierre de Fermat. They confirmed that he had a 52% chance of winning the first bet, and a 49% chance of winning the second, so the Chevalier had got it right from what must have been very extensive and expensive experience.
The Chevalier also presented the mathematicians with the ‘problem of points’ – if a game has to stop before the end, in what proportions should the stake be divided up? A modern counterpart is the Duckworth-Lewis method in cricket, used for allocating runs scored by a team when a match is stopped by the weather – which in England is pretty much all the time. If you thought the game of cricket is difficult to understand, the Duckworth-Lewis method is almost totally incomprehensible to even the most ardent fan. No surprise, then, to hear that statisticians designed it.
After the Chevalier’s time the scientific assessment of odds disappeared for a few centuries, as the 1700s became a golden age of betting on the basis of gut-feelings rather than calculations. It was the time of ‘eccentric wagers’, such as a large sum won by the Count de Buckeburg in 1735 for riding from London to York seated backwards on a horse.