I used to think I had the perfect system for winning at roulette. Many people believe they have perfect systems and they are all delusions, because, unless there is something wrong with the table, in the long run everybody loses except the management.
On standard tables, the house plays 35-1 odds if your number comes up. That means that if you bet £1 you get £35 plus your stake back. You would end up all square in the long run if it weren't for the fact that, apart from the 36 numbers - half of which are red, half black - there is also a zero. This gives the house an advantage of 2.7 per cent.
I knew all this, but it didn't affect my own system. It was so straightforward and obvious that many people had thought of it before me. It even has a name: a martingale. You decide the amount you want to win, say, £100, and you bet that amount on the red (the bank pays "even money" for a winning bet on red or black, even or odd). If you win, you collect your winnings and leave. If you lose, you bet £200. If you lose again, you bet £400 and so on until you get your £100. Even if you have a run of bad luck, red will have to come up eventually and when it does you will win your £100 and leave.
I've just been reading a book by a mathematician called John Haigh, which I knew I had to get hold of as soon as I heard the title: Taking Chances: winning with probability (published by Oxford University Press). It deals with issues of probability in all sorts of sports and games, from the Lottery to tennis, and it is so thorough that it even includes a discussion of my personal theory.
Haigh observes that my system would work perfectly if casinos allowed unlimited stakes and gave credit (or you had an unlimited amount of stake money). Otherwise, it doesn't. He gives the example of a house limit of 100 units and you want to win just one unit. If you employ the Sean French system, you will win 99 per cent of the time.
But look at it from the house's point of view. When you win, you just win one unit. In the 1 per cent of times you lose, you lose a whopping 127 units. If everybody played my system, most people would win, but the house would come out comfortably ahead.
As Haigh puts it: "The combination of a house edge on any bet, whether on one spin or on many, is to ensure that every collection of bets, whether on one spin or on many, is at a disadvantage to the punter."
And yet roulette tables around the world are still crowded.
My favourite books contain little nuggets of information that I'm able to store and then produce in order to amaze friends. (While I'm amazing them, these friends all display a characteristic glazed expression.) Taking Chances is full of them. For example, imagine you play roulette by putting £1 on a number. If it wins, you leave your winnings on the number. Imagine winning four times in a row. That doesn't sound ludicrously difficult. There are only 37 numbers. You would win £1.7 million. And although the chances of your achieving this are a slightly daunting - one in 1.9 million - as Haigh points out, this is seven times better than the odds of winning a similar amount in the National Lottery.
And yet, I have discovered from this book, I am one of only 10 per cent of people in the UK who have never bought a Lottery ticket.
As about 90 per cent of you know (or maybe fewer, because you are an educated lot), you can choose any six numbers between 1 and 49. A machine then selects six. If you have got all six right, you win the jackpot, or a share of the jackpot.
Charles De Gaulle once said of France: "How can you govern a country that makes 300 different kinds of cheese?" (Actually I made that figure up. When anybody quotes this, they always give a different figure.) My adaptation of this to Britain is gloomier. What can you do with a country in which more than ten thousand people a week choose as their six numbers 1, 2, 3, 4, 5 and 6, while even more choose 7, 14, 21, 28, 35 and 42? Even if they win (with odds of 14 million to one against), they'll get nothing more than a few hundred pounds each.
Haigh is good on the various choices you can make to optimise your chances. He doesn't mention that it is best to buy your ticket on the day the numbers are picked. If you buy your ticket any earlier, the chances of your dying before the draw are vastly greater than winning the jackpot.