Alex's Adventures in Numberland - Alex Bellos [134]
It follows, however, that insuring against losing a non-catastrophic amount of money is pointless. One example is insuring against loss of a mobile phone. Mobile phones are relatively cheap (say, £100), but phone insurance is expensive (say, £7 per month). On average you will be better off if you don’t take out insurance, and instead buy yourself a new phone on the occasions that you lose it. In this way, you are ‘self-insuring’ and keeping the insurance company’s profit margins for yourself.
One reason for recent growth in the slots market is the introduction of ‘progressive’ machines, which have little to do with enlightened social policy and lots to do with the dream of instant wealth. Progressive slots have higher jackpots than other machines because they are joined in a network, with each machine contributing a percentage to a communal jackpot, the value of which gets progressively larger. In the Peppermill I had been struck by rows of linked machines offering prizes in the tens of thousands of dollars.
Progressive machines have high volatility, which means that in the short term casinos can lose significant sums. ‘If we put out a game with a progressive jackpot, about one in every twenty [casino owners] will write us a letter telling us our game is broken. Because this thing hit two or three jackpots in the first week and the machines are $10,000 in the hole,’ Baerlocher said, finding it ironic that people who are trying to profit from probability still have trouble understanding it on a basic level. ‘We’ll do an analysis and see the probability of it happening is, say, 200 to 1. They had [results] that should only happen half of a percent of the time – it had to happen to someone. We tell them, ride it out, it’s normal.’
IGT’s most popular progressive slot, Megabucks, links together hundreds of machines across Nevada. When the company introduced it a decade ago, the minimum jackpot was $1 million. Initially, casinos didn’t want the liability of having to pay out so much, so IGT underwrote the entire network by taking a percentage from all of its machines, and paid the jackpot itself. Despite paying out hundreds of millions of dollars in prize money, IGT has never suffered a loss on Megabucks. The law of large numbers is remarkably reliable: the bigger you get, the better it all works out.
The Megabucks jackpot now starts at $10 million. If it hasn’t been won by the time the jackpot reaches around $20 million, casinos see queues forming at their Megabucks slots and IGT gets requests to distribute more machines. ‘People think it’s past that point where i normally hits so it’s going to hit soon,’ explained Baerlocher.
This reasoning, however, is erroneous. Every game played on a slot machine is a random event. You are just as likely to win when the jackpot is at $10, $20 or even $100 million, but it is very instinctive to feel that after a long period of holding money back, the machines are more likely to pay out. The belief that a jackpot is ‘due’ is known as the gambler’s fallacy.
The gambler’s fallacy is an incredibly strong human urge. Slot machines tap into it with particular virulence, which makes them, perhaps, the most addictive of all casino games. If you are playing many games in quick succession, it is only natural to think after a long run of losses: ‘I’m bound to win next time.’ Gamblers often talk of a machine being ‘hot’ or ‘cold’ – meaning that it is paying out lots or paying out little. Again, this is nonsense, since the odds are always the same. Still, one can see why one might attribute personality to a human-sized piece of plastic and metal often referred to as a one-armed bandit. Playing a slot machine is an intense, intimate experience – you get right up close, tap it with your fingertips, and cut out the rest of the world.
Because our brains are bad at understanding randomness, probability is the branch of