Basics: Martingale

Many believe that when playing roulette, not everything should be left to chance. Otherwise, a player could lose their money very quickly. Although roulette is a game of chance, a player can try to use strategies and systems to improve their chances of winning. Or at the very least decrease the chance of losing all too much…

As we use systems and strategies to try to beat the odds, it is important to realize the difference between these two things:

  • A strategy is a sort of "betting plan" which describes how long to play, at what table (which makes a difference regarding minimum and maximum bets and bankroll), how many chips to bring to the game, and most importantly, when to quit when faced with big losses!
  • A system is a set of rules that govern when to bet what amount of chips. It is based on mathematical calculations of chance, and designed in a specific way so that when the system is finished, the player has a net profit. The most famous roulette betting system is the Martingale.

The History of the Martingale System

In 1654 the mathematicians Blaise Pascal en Pierre de Fermat began exchanging letters discussing the mathematics of "double or nothing" bets. In this correspondence, for the first time in history, they raised the question of what the likelihood is of a specific event, and not simply looking at how many points were scored in the game. Today they are credited with laying the foundations of the theory of probability and introducing the concept of expected values.

This led to a betting system for roulette (and other games of chance) that was popular in 18th-century France. Its popularity hailed from the (unjust) belief that it would always result in a win for the player. Later, in the early 1900s, the French mathematician Pierre Lévy introduced the mathematical concept of a martingale, and it was used to prove that in real life situations even the Martingale system could not guarantee profits.

How does the Martingale System work?

The Martingale system is the most basic system based on betting outside even money bets. It makes a player double his bet after every loss. Once the player wins, the system resets. This means that one win will recover all built up losses and result in a net profit of the initial stake. This also makes it one of the most aggressive systems, since its progression is geometrical. (Generally, the fewer wins you need to recover your losses, the more aggressive and dangerous a system is.)

As an example of how this system works, let’s imagine we constantly bet on Red, and start with betting 1 chip. If the sequence of results were to be Black, Black, Black, Black, Red, the following would happen:

  1. The first bet is 1 chip on Red. But the outcome is Black, so we lose.
    Net profit: -1
  2. We have lost, and so must double our bet. We bet 2 chips (on Red again). But we lose.
    Net profit: -1-2 = -3
  3. Another loss means doubling the bet again: 4 chips. We lose.
    Net profit: -1-2-4 = -7
  4. We have lost again, so must double again. We bet 8 chips. And lose again…
    Net profit: -1-2-4-8 = -15
  5. After this loss, we double again and bet 16 chips. This time, we win!
    Net profit: -1-2-4-8+16 = +1
  6. After this single win, we have suddenly turned our major loss (fifteen times the original stake) into a win, albeit a very small one. Of course, we could have accomplished a similar result by using a different initial bet (and thus risking more to win more) or by betting any other outside even money bet.

    If you look back at the example above, you will see that doubling our bet simply means betting 1 chip more than our current net loss. This is exactly the reason why the system works: the sum of all the previous losses will always be one less than our next bet, meaning we always stand to make a profit on every spin. But as you can see above, even a short losing streak increases the required bankroll significantly. We needed 31 chips to win just one! This is the danger a system as aggressive as the Martingale. And the fact that it takes only one win to recover from even the biggest loss, makes the system all the more attractive, adding to its danger.

    Advantages and Drawbacks

    The major disadvantage to a system such as this, with a required bankroll that increases geometrically, is that it is relatively easy for a player to end up in a situation where he is faced with unrecoverable losses: the required bet exceeds the table limit, or he runs out of chips. And, mathematically, even if both of these were never to happen, the player would still need infinite time (something no person has) to ensure that he always recovers what he lost.

    Since every roulette table at every casino has a betting maximum, and there is a limit to every player’s bankroll, it is a mathematical certainty that at some point the Martingale system will result in the player either losing all of his chips or hitting the table limit. Other betting systems attempt to decrease the odds of this happening by decreasing the speed at which losses have to be recovered, sometimes dramatically (such as Oscar’s Grind).