THE MARTINGALES

The Martingale and its variations are the most popular and best-known betting systems in the world. Also known as doubling-up or progression systems, they are praised by those who have won big and damned by those who have lost their shirts. There is no question that they can produce either result. The basic Martingale principle, which can be applied to any repetitive even-money wager, was devised at least 300 years ago and its popularity has never waned.

As with almost all roulette betting systems, this one is applied to the even-money outside bets, as defined above. In its most fundamental form, the amount of the initial bet is doubled after each successive loss. After each win, the bet is reduced to its initial value and remains there until the next loss occurs. In this way, all losses are eventually recovered with a net gain in the amount of the initial bet.

For instance, if an initial bet of 5 units is lost, the next bet would be doubled to 10 units. If the second bet also lost, the third bet would be 20 units; if the third bet lost, the fourth bet would be 40 units, and so forth. If the 40-unit bet won, the amount of the first three bets (5 + 10+ 20=35) would be recovered with a net gain of 5 units. Whenever any bet is won, the next bet is reduced to the initial value of 5 units.

The danger in this system is that eventually a long string of successive losses will keep increasing the amount of the bet until it reaches the table limit. At many roulette wheels, the table limit for outside bets is set to 200 times the minimum bet. This ratio will allow seven consecutive bet doublings before the table limit is encountered.

Eight losses in a row for an even-money bet is not as rare an occurrence as one might think. Statistically, it will happen an average of once for every 170 spins of the ball. In most U.S. casinos, a roulette ball is typically spun sixty to eighty times every hour. Consequently, for a particular even-money bet one can expect such a losing streak to occur on an average of about once every two hours on any given  wheel. Even more worrisome is the fact that it could happen in the next ten minutes.

The classical Martingale is obviously not for everyone, especially if you think in terms of dollars instead of the innocuous “units.” After seven straight losses, the idea of risking an additional 640 dollars in an attempt to recoup the 635 dollars already lost, and ending up with a five-dollar profit seems ludicrous to most people.

SYSTEM TABLE LIMITS

For many years, gambling industry experts and consultants such as John Scarne have advised casinos to “protect” themselves from systems players by maintaining tight table limits. As a result, most casinos have kept the minimum-to-maximum bet ratio at their roulette tables to no greater than 100 to 1, or, at most,