Counting cards

New Scientist discusses money-making from probability theory.

The simplest way is to start at zero and add or subtract according to the dealt cards. Add 1 when low cards (two to six) appear, subtract 1 when high cards (10 or above) appear, and stay put on seven, eight and nine. Then place your bets accordingly - bet small when your running total is low, and when your total is high, bet big. This method can earn you a positive return of up to 5 per cent on your investment, says Thorp.

Seems a reasonable return.

There is also a good explanation of arbitrage.

Each bookie has looked after his own back, ensuring that it is impossible for you to bet on both Oxford and Cambridge with him and make a profit regardless of the result. However, if you spread your bets between the two bookies, it is possible to guarantee success (see diagram, for details). Having done the calculations, you place £37.50 on Cambridge with bookie 1 and £100 on Oxford with bookie 2. Whatever the result you make a profit of £12.50.

Simple enough in theory, but is it a realistic situation? Yes, says Barrow. "It's very possible. Bookies don't always agree with each other."

Guaranteeing a win this way is known as "arbitrage", but opportunities to do it are rare and fleeting. "You are more likely to be able to place this kind of bet when there are the fewest possible runners in a race, therefore it is easier to do it at the dogs, where there are six in each race, than at the horses where there are many more," says Barrow.

Even so, the mathematics is relatively simple, so I decided to try it out online. The beauty of online betting is that you can easily find a range of bookies all offering slightly different odds on the same race. "There are certainly opportunities on a daily basis," says Tony Calvin of online bookie Betfair. "It's not necessarily risk-free because you might not be able to get the bet you want exactly when you need it, but there are certainly people who make a living out of arbitrage."

Arbitrage is not risk free because you might not be able to get the bet you want exactly when you need it. But there are certainly people who make a living out of it
After persuading a few friends to help me try an online bet, we followed a race, each keeping track of a horse and the odds offered by various online bookies. Keeping track of the odds to spot arbitrage opportunities was hard enough. Working out what to bet and when was, unsurprisingly, even harder. Arbitrage is not for the uninitiated.