REVERSE LABOUCHERE

Although there is a tendency to belittle reverse versions of roulette betting systems, in 1966, an Englishman and his team of twelve players broke the bank at one of the French casinos in Nice with the reverse Labouchere system. The Englishman’s name is Norman Leigh and some people have called him a con artist and accused him of exaggeration. That may or may not be true, but he did write a very interesting book about the experience.

As in the regular Labouchere system, a line of numbers is written down, and the first bet is the sum of the first and last numbers in the line. At this point the rules are reversed: Whenever a win occurs, the amount of the bet is added to the end of the line, and whenever a loss occurs, the first and last numbers in the line are canceled. When the line ultimately clears, there is a net loss instead of a net gain.

When Mr. Leigh and his team were playing, they used the aggressive starting line of 1-2-3-4, and every time the line played out it cost them ten units. Winning streaks were allowed to run to the table limit, if possible. The theory was that the small losses are eventually paid back when a long winning streak occurs. In the case of Norman Leigh and his companions it worked out as planned, but that does not mean it always will.

INSIDE BETTING SYSTEMS

Inside bets are any bets placed directly on the main field of numbers. This includes single-number bets that pay 35:1 through six-number bets that pay 5:1, and everything in-between. It does not include dozens, column bets, or any even-money bets.

Most inside bet systems are based on the notion that a sleeper will eventually have to awaken. Although the term sleeper is the common vernacular, a more descriptive term is overdue number. It is commonly believed that if a particular number has not won in a long time, it is “due” or “overdue.”

On the surface, the idea seems to have some merit. Since the probability of a given number winning is 1/38, or 1 chance out of 38, the expectation is that each number on the wheel will win an average of once every thirty-eight spins of the ball. If a particular number has not appeared in, say, seventy or eighty spins, it is overdue and should show up very soon, if only to comply with the law of averages. What isn’t always understood is that the so-called “law of averages” can only be relied on over the very long term. In roulette, the long term could mean thousands or tens of thousands of spins.

Actually, if a particular number comes up very seldom or not at all, it is probably because the wheel is not random. It is not at all difficult to cause a wheel, either accidentally or deliberately, to favor or disfavor certain numbers. If, for instance, the number 29 has not won in a long time, it may be because the pad at the bottom of the pocket had at one time been replaced during routine maintenance. If the replacement material had a different resilience, the ball may now bounce out of that pocket more readily than the other pockets. This would be enough to cause a substantial reduction in the probability of occurrence for number 29. Thus, any bet placed on that number is a losing proposition, even though the number always seems overdue.

Another point to remember is that a roulette wheel has no memory. Every spin of the ball is an independent event that has no bearing on what happened in the past. If the wheel is truly random, then the probability of a given number coming up continues to be 1 out of 38, no matter how long it has been since the last time that number won. Let us say the number 29 came up five times in the last 38 spins five times the expectation. What is the probability of 29 winning on the 39th spin? If the wheel is unbiased: Exactly one chance out of thirty-eight.

Well, what happened to the law of averages? Was it repealed? Of course not. Three weeks later, on that same hypothetical wheel, number 29 may not show up for 200 spins of the ball. After the first 100 spins, some players will notice the “sleeper” and start betting on 29. One-hundred spins later, after they all lost their bankrolls, 29 finally appears. They do not believe it, but the law of averages is intact.