Roulette - Martingale System

The Martingale system is an old one dating back many many years and originally referred to a class of betting strategies popular in 18th century France.

The numerous even-money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a Martingale betting strategy, wherein the gamer doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet

The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake.

Since a gambler with infinite wealth will with probability 1 eventually flip heads, the Martingale betting strategy was seen as a sure thing by those who practised it. Unfortunately, none of these practitioners in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt those foolish enough to use the Martingale.

Moreover, it has become impossible to implement in modern casinos, due to the betting limit at the tables. Because the betting limits reduce the casino's short term variance, the martingale system itself does not pose a threat to the casino, and many will encourage its use, knowing that they have the house advantage no matter when or how much is wagered.

Example
Suppose that someone applies the martingale betting system at an American roulette table, with 0 and 00 values; on average, a bet on either red or black will win 18 times out of 38.

If the player's initial bankroll is $150 and the betting unit is $10, he can afford 4 losing bets in a row (of $10, $20, $40, and $80) before he runs out of money. If any of these 4 bets wins he wins $10 and wins back any past losses. The chance of losing 4 bets in a row (and therefore losing the complete $150) is (20/38)4 = 7.67%.

The remaining 92.3% of the time, the player will win $10. We will call this one round (playing until you have lost 4 times or until you win, whichever comes first). If you play repeated rounds with this strategy then your average earnings will be (0.923·$10) − (0.0767·$150) = −$2.275 per round.

Therefore, you lose an average of $2.275 each round. However, if the gambler possesses an infinite amount of money, the expected return is (18/38)*b per roll (where b is the initial bet). With an initial bet of $10, the expected return is thus $4.736 per roll.

Source: Wikipedia.org

Note:
We offer this article as a reference to the game roulette and accept no responsibility for any losses you may incur if you choose to use it whilst gambling for real money. Remember that like many other gambling games roulette is a game of chance. We do however wish you every success.

More about Roulette
We have more information about the game of roulette and if you're just learning to play the game you'll find the following sections especially helpful.

The History of Roulette
The Roulette Table Explained and Basic Game Guide
Standard Roulette Bets Illustrated & How To 'Place Your Bets'
Types of Online Roulette
Roulette Betting Systems