The so-called Martingale Roulette Betting system had been around for nearly half a century before it got its name. The Venetian adventurer Giacomo Girolamo Casanova de Seingalt (1725~1798), who is better known simply as Casanova, wrote in his memoirs that he used a simple betting progression at the Ridotto Casino in 1754. His system was to keep doubling the size of his bet following each loss until his wager eventually won.

No one is quite sure why the practice of “doubling up on a loss” became associated with Henry Martingale, the proprietor of a British gambling house in the latter part of the 18^th century. Whatever the reason, the name stuck, and today this very basic betting strategy is recognized the world over as the Martingale progression.

The Math of Martingale

When playing Roulette, the Martingale system of wagering is best applied to even money bets, such as Black or Red, Even or Odd, and Low (1~18) or High (19~36). Each of these betting areas represents exactly 18 numbers, so at the European Roulette table, the odds of winning any of these bets is the same, namely 18:37 or 48.65%—a bit less than half. At the American table, the ratio is 18:38 or 47.37%.

If the first bet of one unit loses, the player doubles it to two units. The total outlay at this point is three units. A winner will return four units for a profit of one unit and the progression can begin again. If the second bet loses, the players will double it again to four units, making the total risk at this point 1+2+4 = 7 units. A win will return eight units, for a net profit of one unit.

Martingale betting continues in this manner until a winner is obtained, so the player must be prepared to keep doubling up for a potentially long series of losses. Exactly how many losses depends on what the player is willing to risk. Someone of great wealth might have no problem backing the bet dozens of times, but for most players the limit is realistically capped by the size of their bankrolls. A string of eight losses, for example, would require bets of 1+2+4+8+16+32+64+128 = 255 units.

As detailed in the section on Roulette Odds, it is possible to calculate the probability (P) of a winner for any numbers of spins (N) by using the equation P = 1 – {(37-B)/37}^N, where B is the number of potential winning numbers. For even money bets, B=18, so the odds of winning once in any series of eight spins is P = 1 – {(37-18)/37}⁸ = 99.52%. That is about as close to certainty as one can get when gambling, which easily explains Martingale’s great appeal as well as its longevity as a gambling system.

Martingale in Practice

Unfortunately, there are no guarantees that nine losses will not come up in a row, no matter what the statistics imply. On the eighth wager after seven losses, the player must risk 128 units to back all that has been lost and gain a profit of just one unit. However, the odds of winning on the eighth spin are still less than 50%, as explained above. There are certainly better uses of 128 units than to risk it all to win just one.

For this reason, most Martingale players prefer to set a much lower limit on the number of losses they are willing to sustain before calling the progression quits. Backing a series of six spins could cost 1+2+4+8+16+32 = 61 units, but it yields a probability of winning of P = 1 – {(37-18)/37}⁸ = 98.17%. And some players will not wager on an even money area of the table unless it has already lost twice, believing that another six losses in a row is highly unlikely, even though the true odds are always the same no matter what results have come up in the past. The Roulette wheel has no memory.

In fact, when backing a bet for a maximum of six losses, the Martingale progression can be expected to fail about once every 55 times (1.83%). Winning one unit 54 times and losing 63 units once is a sure way to lose everything in the long run. One way to avoid this downward spiral is to set a low profit objective, such as 20 units, and either quit or change betting systems as soon as it has been reached.