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The illusion of Martingale in gambling

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A martingale is a technique giving the illusion of increasing the chances of winning in gambling while respecting the rules. The principle depends completely on the type of game that is the target and, in many cases, the rules are intended to prevent the possibility of a martingale. Nevertheless, the term is accompanied by an aura of mystery that some players would know the secret techniques to cheat the chance and, for example, beat the bank in casinos. To do this, a martingale must change the expectation is such that, in the long term, the chances of winning are lower than those of losing. It is therefore to increase the chances of winning and, ideally, they are superior to those of losing.

Different martingale

Many martingale are only a dream of the author, some are in fact inapplicable, some do allow to cheat a little. Gambling are unfair in general regardless of the strategy adopted, the expected gain from the casino (or state in the case of a lottery) is greater than that of the player. In this type of game, it is not possible to reverse the odds, only to minimize the probability of ruining the player.

The classic martingale

The classic martingale is to play a simple luck at roulette (red or black, odd or even, etc.) to win, for example, a unit in a series of moves by doubling the bet when losing, until the player wins. Example: the player bets 1 unit on red, if red comes out, it stops playing and he won 1 unit, if black comes out he doubles up betting 2 units on red and so on until he wins.

Having an even chance of winning, he may think he will eventually win; when he wins, he is necessarily reimbursed for everything he has done, once more his initial bet.

This martingale seems to be safe in practice. Theoretically, to be sure of winning, you should have the opportunity to play an unlimited number of times. This has major drawbacks:

  • This martingale is limited by bets that the player can do, because you have to double down on every shot as you lose 2 times the initial bet, then 4, 8, 16 …. if you lose 10 times, it must be able to advance 1,024 times the ante for the 11th game. So you have lots of money for little gain.


Initial bet of 1 euro.

  • Down 1 euro or 2 euros you earn less your previous bet 2-1 = 1 euro, or you lose.
  • Down 2 euros or 4 euros unless you win your previous bet: 4-2-1 = 1 euro, or you lose.
  • Down 4 euros, or 8 euros unless you win your previous bet 8-4-2-1 = 1 euro, or you lose.
  • Down 8 euros, 16 euros less than you earn your previous bet 16-8-4-2-1 = 1 euro, or you lose.
  • Down 16 euros, 32 euros less than you earn your previous bet 32-16-8-4-2-1 = 1 euro, or you lose.
  • Down 32 euros, 64 euros less than you earn your previous bet 64-32-16-8-4-2-1 = 1 euro, or you lose.
  • Down 64 euros, 128 euros less than you earn your previous bet 128-64-32- 16-8-4-2-1 = 1 euro, or you lose.
  • Getting 128 euros, 256 euros less than we earn our previous bet 256-128-64-32-16-8-4-2-1 = 1 euro, or you lose.

In short, the more the player bets, the more he must bet to win only 1 euro.

  • The roulette has a “0” that is neither red nor black. The elementary probability Ep of winning in every draw is 18/37 (0.48648) and not 1/2. The probability of winning by having an infinite sum is 1.
  • In addition, to avoid this strategy, the casinos offer table games for every setting: from 1 to 100 euros, 2 to 200, 5-500, etc. So it is impossible to use this method on a large number of shots, which increases the risk of losing everything.

Example: set of 5 with casino limit 500. So you can bet, due to losses, 7 times only (up to 320), this requires an initial sum of 635 and the number of possible victorious in series in this case is 17. If you are “cautious” and there is a series of seven outcomes of the same color, one can expect a gain relatively assured, in 8 victorious series, 40 for a initial capital of 635 or 6.3% gain.

If the probability of losing decreases, the loss increases with the number of consecutive played rows and earnings expectancy remains negative (loss), the risk being run on all of the sums invested.

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