## Funktioniert Martingale an der Börse/Forex?

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### Wer sich an gar keine **Martin Gale** binden *Martin Gale,* sind regelmГГige. - Was ist die Martingale Strategie?

Dies bedeutet, dass die Wahrscheinlichkeit, alle Spiele in Folge zu verlieren, mit der Anzahl der Spiele immer geringer wird. Originally, martingale referred to a class of betting strategies that was popular in 18th-century France. The strategy had the gambler double their bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake.

As the gambler's wealth and available time jointly approach infinity, their probability of eventually flipping heads approaches 1, which makes the martingale betting strategy seem like a sure thing.

However, the exponential growth of the bets eventually bankrupts its users due to finite bankrolls. Stopped Brownian motion , which is a martingale process, can be used to model the trajectory of such games.

The term "martingale" was introduced later by Ville , who also extended the definition to continuous martingales. Much of the original development of the theory was done by Joseph Leo Doob among others.

Part of the motivation for that work was to show the impossibility of successful betting strategies in games of chance. A basic definition of a discrete-time martingale is a discrete-time stochastic process i.

That is, the conditional expected value of the next observation, given all the past observations, is equal to the most recent observation.

Similarly, a continuous-time martingale with respect to the stochastic process X t is a stochastic process Y t such that for all t.

It is important to note that the property of being a martingale involves both the filtration and the probability measure with respect to which the expectations are taken.

These definitions reflect a relationship between martingale theory and potential theory , which is the study of harmonic functions.

Given a Brownian motion process W t and a harmonic function f , the resulting process f W t is also a martingale.

The intuition behind the definition is that at any particular time t , you can look at the sequence so far and tell if it is time to stop.

An example in real life might be the time at which a gambler leaves the gambling table, which might be a function of their previous winnings for example, he might leave only when he goes broke , but he can't choose to go or stay based on the outcome of games that haven't been played yet.

That is a weaker condition than the one appearing in the paragraph above, but is strong enough to serve in some of the proofs in which stopping times are used.

The concept of a stopped martingale leads to a series of important theorems, including, for example, the optional stopping theorem which states that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial value.

From Wikipedia, the free encyclopedia. The likelihood of catastrophic loss may not even be very small. The bet size rises exponentially.

This, combined with the fact that strings of consecutive losses actually occur more often than common intuition suggests, can bankrupt a gambler quickly.

The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance.

In mathematical terminology, this corresponds to the assumption that the win-loss outcomes of each bet are independent and identically distributed random variables , an assumption which is valid in many realistic situations.

It follows from this assumption that the expected value of a series of bets is equal to the sum, over all bets that could potentially occur in the series, of the expected value of a potential bet times the probability that the player will make that bet.

In most casino games, the expected value of any individual bet is negative, so the sum of many negative numbers will also always be negative.

The martingale strategy fails even with unbounded stopping time, as long as there is a limit on earnings or on the bets which is also true in practice.

The impossibility of winning over the long run, given a limit of the size of bets or a limit in the size of one's bankroll or line of credit, is proven by the optional stopping theorem.

Let one round be defined as a sequence of consecutive losses followed by either a win, or bankruptcy of the gambler.

After a win, the gambler "resets" and is considered to have started a new round. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds.

Following is an analysis of the expected value of one round. Let q be the probability of losing e. Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose.

The probability that the gambler will lose all n bets is q n. When all bets lose, the total loss is. In all other cases, the gambler wins the initial bet B.

Thus, the expected profit per round is. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round.

Increasing the size of wager for each round per the martingale system only serves to increase the average loss.

Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled.

Thus, taking k as the number of preceding consecutive losses, the player will always bet 2 k units. With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point.

Once this win is achieved, the gambler restarts the system with a 1 unit bet. With losses on all of the first six spins, the gambler loses a total of 63 units.

This exhausts the bankroll and the martingale cannot be continued. Thus, the total expected value for each application of the betting system is 0.

In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of Eventually he either goes bust or reaches his target.

This strategy gives him a probability of The previous analysis calculates expected value , but we can ask another question: what is the chance that one can play a casino game using the martingale strategy, and avoid the losing streak long enough to double one's bankroll.

Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll.

In reality, the odds of a streak of 6 losses in a row are much higher than many people intuitively believe.

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