Martingale (betting system)

As Martingale Martingale or short is called since the 18th century a strategy in gambling, especially when Pharo and later at roulette, in which the insert is increased in case of loss.

Classical Martingale

Description

The classical and simplest form of Martingale, Martingale classique, is the doubling or doubling and is illustrated by the roulette game.

The player starts with a bet of one unit ( one piece) to a simple chance, such as rouge or noir.

The Martingale player bets mostly on the Perdante (see Marche ), which is the one opportunity that has recently lost: the last ball dropped to Rouge, so he relies on Noir.

If he loses, it shall in the next coup two pieces, he loses again, he is four pieces, etc. Once he wins, all previously incurred losses have been settled, and the player can look forward to a total profit of one piece. Following a profit he sets his attack on the casino away again with a piece.

However, this seemingly secure system does not work - what countless players not to be in defiance of their own experience to convince: Many players overlook the fact that a continued doubling the latest when reaching the preset of the casino maximum ( ie the maximum bet) is no longer possible, However, in most cases much earlier fails due to the limitations of their own capital.

Who plays consistently Martingale eg with a bankroll of 1000, which is indeed conclude with a relatively high probability of a certain game systems (eg 50 coups ) with a modest gain of about 25 pieces, but he bears the generally completely underestimated risk of losing the entire assets: a total profit expectation is negative; that is, in the long run wins the casino.

Especially in the fact that a Martingale players quite often achieved small gains and has to wait for the (in the mathematical sense) surely, from a total loss for a considerable time, the explanation lies in the phenomenon of the proverbial beginners luck: He who does not constantly in the course of a game evening with equal playing high stakes, but the stakes in whatsoever increases, has - as a Martingale player - relatively good chances to recover any losses and yet complete at last with a positive balance.

Example

A player may play the Martingale on impairment at roulette. To illustrate, first a few simplifying assumptions were made:

  • Zéro as any other pair numbers mean loss (that is, give it no Prison )
  • The launch used a "piece ", amounts to 10 €, after loss are successively 20, 40, 80 €, etc. set.
  • Laid down by the casino maximum amounts to just € 20,480, so the Martingale may include a maximum of 12 games.

The probability of losing a single game is 19/37 ≈ 51%.

The probability of losing 12 games in a row:

Accordingly, the probability to end a martingale with profit:

That really seems to be an excellent opportunity, but: In the case of the happy conclusion of the player wins just 10 €, while he loses in the event of a loss € 40,950 (namely ).

For the casino is not so much the winning probability, rather than the profit expectation of meaning. The expected value for the player, however, is negative:

That is, approximately 37.7 % of the initial rate at a game series.

Apart from this is hard to believe that a player who the casino enters with a capital of € 40,950, starts to play with a bet of 10 €, so that already means to him a much shorter series of losses for the loss of the entire bankroll ( ie. ruin in the mathematical sense ).

The fact that a player in case of occurrence of Zéro loses only half used, can be mapped so that a player with probability 18.75 on 37 loses the bet and with probability 18,25 to 37 wins one unit - the house edge in a single game then just corresponds to 0.5 / 37 ≈ 1.35%, as it is also in the actual game with Prison the case.

Then the following values ​​are obtained:

  • With probability ≈ 0.0287 % ( ie 1: 3487 ), the Martingale is lost,
  • With probability ≈ 99.9713 % the Martingale is obtained.

The expected loss is thus about 1.75 €, or about 17.5 % of the initial rate per game series.

Variants of Martingalespiels

Apart from doubling a myriad of other Martingale strategies has been developed, the most important examples - both because of historical interest and on the other hand widespread - are

  • The Montante Americaine or Labouchère, Labby, Annulation Americaine,
  • The Montante Hollandaise Hollandaise or cancelation,
  • The progression d' Alembert, named after the mathematician Jean Baptiste le Rond d' Alembert,
  • The Fitzroy system.

All these game strategies, it is that the use in case of loss is increased is, or whether that is increased in the event of a win (see Parolispiel ) or that consistently ( égale mass ) with the same insert is played are actually not promising: the mathematical proof of the nonexistence sure win strategies can be performed using the martingale theory.

Etymology

The word " martingale " comes from the Provencal and is derived from the French town of Martigues in the Bouches -du -Rhône on the edge of the Camargue from whose inhabitants were once considered somewhat naive. The Provencal expression jouga a la martegalo means something like " to play very reckless ."

Since the Martingale was the most famous game system and is, the term was also used as a synonym for " game the system " and so gave this game system of martingale theory, a branch of probability theory its name.

The likewise " Martingale " said auxiliary reins in horse riding should also be named after the town of Martigues, but has this meaning of the word " martingale " has nothing to do with the game system.

Giacomo Casanova

One of the many players of the Martingale was Giacomo Casanova, he noted in the story of my life:

After initial player lucky Casanova noted admittedly a little later:

Because of this literary testimony doubling also Martingale de Casanova is called.

House advantage Martingale (probability theory) Gambler's fallacy
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