Alex's Adventures in Numberland - Alex Bellos [125]
Levin opened his callipers and started measuring between all the significant points.
‘Ooh, yes,’ he grinned.
CHAPTER NINE
Chance is a Fine Thing
It used to be said that you go to Las Vegas to get married and to Reno to get a divorce. Now you can visit both cities for their slot machines. With 100 slot machines, Reno’s Peppermill Casino isn’t even the largest casino in town. Walking through its main hall, the roulette and blackjack tables were shadowy and subdued in comparison to the flashing, spinning, beeping regiments of slots. Technological evolution has deprived most one-armed bandits of their lever limbs and mechanical insides. Players now bet by pressing lit buttons or touch-screen displays. Occasionally I heard the rousing sound of clattering change, but this came from pre-recorded samples since coins have been replaced by electronic credits.
Slots are the casino industry’s cutting edge; its front line and its bottom line. The machines make $25 billion a year in the United States (after they’ve paid out all their prize money), which is about two and a half times the total value of movie tickets sold in the country annually. In Nevada, the global centre of casino culture, slots now make up almost 70 percent of gambling revenue – and the number nudges higher every year.
Probability is the study of chance. When we flip a coin, or play the slots, we do not know how the coin will land, or where the spinning reels will stop. Probability gives us a language to describe how likely it is that the coin will come up heads, or that we will hit the jackpot. With a mathematical approach, unpredictability becomes very predictable. While we take this idea for granted in our daily lives – it is implicit, for example, whenever we read the weather forecast – the realization that maths can tell us about the future was a very profound and comparatively recent idea in the history of human thought.
I had come to Reno to meet the mathematician who sets the odds for more than half of the world’s slot machines. His job has historical pedigree – probability theory was first conceived in the sixteenth century by the gambler Girolamo Cardano, our Italian friend we met earlier when discussing cubic equations. Rarely, however, has a mathematical breakthrough arisen from such self-loathing. ‘So surely as I was inordinately addicted to the chess board and the dicing table, I know that I must rather be considered deserving of the severest censure,’ he wrote. His habit yielded a short treatise called The Book on Games of Chance, the first scientific analysis of probability. It was so ahead of its time, however, that it was not published until a century after his death.
Cardano’s insight was that if a random event has several equally likely outcomes, the chance of any individual outcome occurring is equal to the proportion of that outcome to all possible outcomes. This means that if there is a one-in-six chance of something happening, then the chance of it happening is one sixth. So, when you roll a die, the chance of getting a six is . The chance of throwing an even number is . The chance of throwing an even number is . which is the same as . Probability can be defined as the likelihood of something happening expressed as a fraction. Impossibility has a probability of 0; certainty, a probability of 1; and the rest is in between.
This seems straightforward, but it isn’t. The Greeks, the Romans and the ancient Indians were all obsessive gamblers. None of them, though, attempted to understand how randomness is governed by mathematical laws. In Rome, for exale, coins were flipped as a way of settling disputes. If the side with the head of Julius Caesar came up, it meant that he agreed with the decision. Randomness was not seen as random, but as an expression of divine will. Throughout history, humans have been remarkably imaginative in finding ways to interpret random events. Rhapsodomancy, for example, was the practice of seeking guidance through chance selection of a passage in a literary work. Similarly, according