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Getting an even chance with the odds, by Belinda Levez

The ancient Greeks, experts in many branches of mathematics, failed to recognise the connection between gambling and maths. Instead they relied on Hermes ­ the god of gambling for luck. When a pair of dice was thrown they thought all numbers had an equal chance. Thanks to the calculations of Blaise Pascal in 1654, today’s craps players know that a seven is the most likely score. Unfortunately so too do gambling operators. They use computers to calculate odds ensuring they give themselves huge profits. However even with modern technology, the gambling operators can be as clueless as the ancient Greeks.

In 1991, British bookmakers found themselves in the rough with the odds they offered on golf betting. It was two industry insiders, a pair of bookmakers, who discovered that the odds offered for a hole-in-one were ridiculously high. They studied the statistics for European golf tournaments and found that holes-in-one were becoming increasingly common due to more skilful players. They expected to get odds of around 2/1 for a hole-in-one. However, when they checked the prices offered, they found that odds of around 20/1 and as high as 100/1 were quoted. Realising they were on to a winner, the pair gave up work and travelled the country placing bets. They staked around $40,000 and won over $700,000 before their coup was discovered and the bookmakers drastically reduced the odds. Golf is unlikely to provide punters with such a bonanza again but it could happen with another sport.

Casino operators thought they had the advantage on blackjack. A trio of Americans proved them wrong. In 1956, Roger Baldwin developed the Optimum Strategy, which, Julian Braun further adapted. By 1962, Edward Thorp had invented the first card counting techniques. A combination of basic strategy and card counting gives players the edge. Although casinos knew that their profits were in danger, instead of adjusting the odds, they tried to make it harder for these winning techniques to be used. They even blundered by introducing more decks of cards. Thorpe proved that this made card counting more profitable. Nowadays casinos bar suspected card counters.

Special offers are often worthy of attention. When Blackjack was first introduced to American casinos it wasn’t a very popular game. To attract business casinos were offering 10/1 for blackjack made with either the jack of clubs or jack of spades. Nowadays they pay a mere 2/1.

Horse racing also provided punters with an unexpected bonus. Tricast bets, where punters must predict the first, second and third past the post weren’t particularly popular. To encourage punters to make this bet, British bookmakers offered a 33 per cent bonus for a correct tricast. Some shrewd gamblers realised that this was a great opportunity to make money. British racecourses are all different. On some courses there can be an advantage to a low draw and on others to a high draw. The punters used this knowledge and made full cover bets with whatever draw was favoured. The bonus gave them the edge to make it worthwhile. The bookmakers retaliated by reducing the maximum bet but punters simply spread their bets around different shops. Still losing heavily the bookmakers withdrew the special offer.

Having the insight to spot something that no one else has thought of can pay dividends. Joseph Hobson Jaggers worked in a textile mill where wooden spindles were used to wind the wool. He noticed that the spindles got worn. He realised that the spindles of roulette wheels may also become worn resulting in an imbalance of the wheel. In 1873, he took a trip to Monte Carlo. He and six assistants recorded the numbers spun on roulette for six days.

Analysis of the results showed that a set of nine numbers on one of the wheels kept on winning. Jaggers bet on this wheel and won $300,000 in four days play. The following day he started to lose heavily. Then he realised that a scratch, which he’d noticed on the ‘winning wheel’, was missing. The casino operators had switched the wheel. He checked round the other tables and found ‘his wheel’ back. A further gambling session won him $450,000. The casino operators reacted by changing the wheel’s design. A removable metal fret was fitted to separate the numbers. At the end of a day’s business the fret could be moved to a different position. Jaggers decided to quit while he was ahead and netted a profit of $325,000 ­ equivalent to around $3 million today. Unfortunately casinos operators now ensure that roulette wheels are regularly serviced and balanced.

Finding these great gambling opportunities can be like looking for a four-leafed-clover. As Blaise Pascal showed sometimes it’s a simple case of doing the maths. However if maths is all Greek to you, you can still pray to Hermes for luck.

(C) © Belinda Levez 2001 All rights reserved.

Belinda Levez is a former croupier with London’s top clubs and author of the Teach Yourself How to Win series of books.

[Article submitted June 2004]

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