Alex's Adventures in Numberland - Alex Bellos [131]
Another way of looking at an expected loss is to consider it in terms of payback percentage. If you bet £10 at craps, you can expect to receive about £9.86 back. In other words, craps has a payback percentage of 98.6 percent. European roulette has a payback percentage of 97.3 percent; and US roulette, 94.7 percent. While this might seem a bad deal to gamblers, it is better value than the slots.
In 1893 the San Francisco Chronicle notified its readers that the city was home to one and a half thousand ‘Nickel-in-the-Slot Machines That Make Enormous Profits…They are of mushroom growth, having appeared in the space of only a few months.’ The machines came in many styles, but it was only at the turn of the century, when Charles Feya German immigrant, came up with the idea of three spinning reels, that the modern-day slot machine was born. The reels of his Liberty Bell machine were marked with a horseshoe, a star, a heart, a diamond, a spade, and an image of Philadelphia’s cracked Liberty Bell. Different combinations of symbols gave different payouts, with the jackpot set to three bells. The slot machine added an element of suspense its competitors did not have because, when spun, the wheels came to rest one by one. Other companies copied, the machines spread beyond San Francisco, and by the 1930s three-reel slots were part of the fabric of American society. One early machine paid out fruit-flavoured chewing gum as a way to get round gaming laws. This introduced the classic melon and cherry symbols and is why slots are known in the UK as fruit machines.
The Liberty Bell had a payback average of 75 percent, but these days slots are more generous than they used to be. ‘The rule of thumb is, if it’s a dollar denomination [machine], most people would put [the payback percentage] at 95 percent,’ said Anthony Baerlocher, the director of game design at International Game Technology (IGT), a slot-machine company that accounts for 60 percent of the world’s million or so active machines, referring to slots where the bets are made in dollars. ‘If it’s a nickel it’s more like 90 percent, 92 percent for a quarter, and if they do pennies it might go down to 88 percent.’ Computer technology allows machines to accept bets of multiple denominations, so the same machine can have different payback percentages according to the size of the bet. I asked him if there was a cut-off percentage below which players will stop using the machine because they are losing too much. ‘My personal belief is that once we start getting down around 85 percent it’s extremely difficult to design a game that’s fun to play. You have to get really lucky. There’s just not enough money to give back to the player to make it exciting. We can do a pretty good job at 87.5 percent, 88 percent. And when we start doing 95, 97 percent games they can get pretty exciting.’
The size of a cash register, Charles Fey’s Liberty Bell was an immediate success when it was first manufactured at the very end of the nineteenth century.
Baerlocher and I met at IGT’s head office in a Reno business park, a 20-minute drive from the Peppermill Casino. He walked me through the production line, where tens of thousands of slot machines are built every year, and past a storage hall where hundreds were neatly stacked in rows. Baerlocher was clean-shaven and preppy, with short dark hair and a dimple in his chin. Originally from Carson City, half an hour’s drive away, he joined IGT after completing a maths degree at Notre Dame University, Indiana. For someone who loved inventing games as a child, and discovered a talent for probability at college, the job was a perfect fit.
When I wrote earlier that the core concept of gambling was the notion of expected value, I was giving only half the story. The other half is what mathematicians call the law