Theory of roulettivityRobert Blincoe meets a man whose ‘no-lose’ roulette system works sufficiently well to earn a book deal and a ban from a major casino group
Casinos love system players. When Edward O Thorp, the US mathematician who developed the blackjack card-counting system, first came on the scene in 1961, one casino manager said with scorn, “We send taxis for system players.”
And apart from good card-counters, which casinos are super-vigilant about stopping, they still send taxis for system players. They think they're money in the bank, because systems don't work in the long term. But Thorp's methods worked, and the lasting importance of his research, and the thing he's most proud about, is that it “showed many intelligent people that the conventional wisdom was false, for example, 'You can’t beat the game because if you could, someone would have tried it and they would have changed the rules.'”
This keeps gambling system players and system developers going. They think they've seen something no one else has.
Balvinder Sambhi is a professional roulette player, and he plays systems. His latest book, out for Christmas, is called Breaking the Roulette Wheel and should retail at £100. On a rainy November night, cosy and warm in Birmingham's Gala casino, he takes me through his latest model, a ‘no-lose system’. He knows I'm a sceptic with a maths degree, but he's happy to put his system on the line.
The background is that he's been testing and playing his latest system over the last six months. He's had publicity in The Daily Mail, The Daily Express, and The Birmingham Sunday Mercury over being barred from the Grosvenor Casino group. The group declines to comment, but Sambhi says it’s because he was winning, and had been on a £28,000 streak with a best day of £4,000. Learning his trade, over 10 years, he says he had lost plenty of money to them in the past.
He says that during this playing and testing phase he has not lost money on any day. “It's not been broken, and it will not break,” he says.
The system Sambhi shows me is based on a 40-spin cycle. It's not the only system in his book, but it's a simple one to watch and learn. He has eight specific numbers he looks out for, two groups of four numbers that are adjacent, in the form of a square, on the betting table. To make a bet on each group of four, you place your chip where they intersect, and this is known as a corner bet. I promised Sambhi not to say what the eight numbers are, you have to buy the £100 book for that, but any student of probability will tell you any eight will do.
First of all, you wait until these eight numbers have not come up in 12 consecutive spins, and then you place the minimum 10p corner bet on each four. If you lose you increase your stake. Sambhi's progressive system doesn't double stakes every loss, but makes sure a win covers all previous losses (corner bets pay 8-1). If you win you start again waiting for the numbers not to come up in 12 consecutive spins.
The system requires a bankroll of £2,500. Sambhi says one of his numbers will come up in 40 spins, so if they haven't come up in the 12 spins you've waited, they'll appear in the next 28. “They will come in. It's impossible for them not to come in,” he says. “It won't go past 40 spins.”
He actually thinks 40 spins is very conservative limit, and he set that as the number to ensure his system was no-lose. “In my experience it's not going to go past 30 spins. But I'd rather have a no-lose system and that's why there's the safety guard of the extra 10 spins.”
In fact, the gaming statistician, The Wizard of Odds (wizardofodds.com), has made three 10,000 spin simulations available on his website. Sambhi has examined the 30,000 randomly generated numbers (I have not) and concedes there is an example of a break of 36 virtual spins between any of his special numbers appearing. But still less than his 40 limit.
It's convenient to point out here that Sambhi differentiates between the straightforward mathematical probabilities of roulette wheel situations, computer generated simulations of scenarios, and his real world experience. “Saying it can break, and it breaking are two different things,” he says. “With all my data and experience it has never broken. Mathematics and probability have nothing to do with it.”
Opinions differ on that. At the least, myself, the Wizard of Odds and Stephen Hawking if you asked him, would be on one side - Balvinder on the other. His system combines elements of two classic betting approaches. One is the gambler's fallacy, which is about the belief that past events can influence future events. The other is the Martingale betting system, which involves keep doubling your stake if you lose, with the idea you come out ahead eventually.
Both these ideas are very seductive. Linked to roulette, the gambler's fallacy suggests that if you've had a run of reds, for example, it is more likely that a black is due. Or in Sambhi's case, if you wait for 12 consecutive spins for your eight numbers not to come up, then they are more likely to hit when you start betting on them.
Sambhi thinks his specific eight numbers come up more often than any others. In his experience. Unless the wheel is biased, it's not true, though in the short term it might appear some numbers hit more than others.
The probability that one of eight specific numbers won't come up in 40 spins, on a single zero wheel, is (37-8)**40 / 37**40 = 5.86 x 10**5 = 0.0000586. It's about 0.006%. It's very unlikely, which Sambhi intuitively knows. But just because they haven't come up in 12 spins doesn't make them more likely to come up – the wheel doesn't remember what's come up before. On each spin, the probability that one of the eight numbers comes up is 8/37 = 0.216. A 21.6 percent chance. And that stays the same from the first spin to the last – if none of the eight have come up in the first 12 spins, and still not come up in the next 27 during the betting window, then with Sambhi's system you will be betting £2,465.80 to clear your losses and win £234.20 on a 21.6% chance. It hasn't become a 100 percent certainty because Balvinder has never seen the situation come up. (And never forget that on a single zero roulette wheel, the house edge is always 2.70 percent.)
His method of slowly raising his stake, at 8/1 odds, slightly sidesteps the major Martingale problem. The Martingale is usually applied to doubling up on even odds, and leads to quickly having to bet an astronomical sum to recover a series of losses, and the sum needed outstrips the table limit. Using the terminal betting system in Gala, and being able to follow every open roulette table, Balvinder could start at 10p and stay within table limits over 28 consecutive bets.
And though mathematically it's pointless, there is an inbuilt advantage to Sambhi's method of waiting 12 spins to start. It means you bet less. There are fewer opportunities to win or to lose. He believes his method is a way for low earners to improve on their regular income, and if they put in five-to-eight-hour days they can make £100-£250 a day. The least he says he's won in a day is £50. “You've got to put the hours in. You can't expect £500 an hour.”
So how did Sambhi do in the four hours we were together? His favourable betting conditions only came up three times, and then his numbers came up on the first spin, the fifth spin, and the sixth spin respectively. Though he'd loaded the betting terminal up with £800, with more cash ready to go if necessary, he won just £3.40. But at least he won.
He was happy he hadn't faked anything, and had shown me his system and not lost. Anyone who buys his book can come to Birmingham and sit with him as well for a master-class. He says he won more than £50 after I'd gone, and £250 in five hours in a later session.
All I can say is he didn't lose, he's charming company, and the Gala manager was very unhappy he had two men sitting round a terminal, with sheets of paper, making notes and abusing the free drinks. Good luck to him and you. |
