Table of contents:
- 1 An example based on Roulette
Originally, the Martingale Strategy, also known as Martingale, comes from the 18th century and refers to a strategy in gambling in which you increase your stake in case of a loss. To be exact, the stake is doubled if you lose.
In other words, you bet on the occurrence of a certain event. If this does not happen, the stake is doubled and the bet is placed again on the occurrence of this event. This continues until the desired event occurs.
An example based on Roulette
As an example, let’s take the gambling game Roulette. You can bet on the colours (red or black) for example. In this example you bet on the occurrence of a certain event. Let us assume that the last colour in Roulette was red. You bet on the opposite colour black.
For example, you start with one Euro. Now the ball falls on the colour red again. You now double the bet of one euro and bet two euros again on black. So you double the bet until the desired color is reached.
In this table you can see how this strategy seems to work and how easy it is to use. But this strategy does not work in reality.
Why does the Martingale strategy not work in Roulette?
There are not only the colors red or black, but also green (the zero). This means that as soon as the ball lands on the zero, you have lost half the bet and you are blocked for the next round.
In addition, there is a fixed maximum bet in Roulette, also known as the table limit.
A few mathematical facts
In roulette there are 37 numbers. The numbers 1 to 36 plus the green zero (zero). So there are 18 black and 18 red numbers.
The chance to win is therefore 18/37=48.6%. This implies a 51.4% chance of losing.
This means that the chance of winning my bet on the next spin is always only 48.6%, while the probability of me losing my amount and having to double my bet again is 51.4%.
The probability that if you bet on red and lose 7 games in a row is (19/37)7 = 0.94%.
Despite this relatively small chance, you will never win enough in the long run to make up for such a series of losses. Since the win is always only the initial stake of 1 Euro, you would have to win 127 times to make up for the loss.
It must be noted that the chances of winning do not increase with increasing losses. The ball has no memory and will always land randomly on a certain field. The assumption that the probability of winning increases with an increasing number of losses is therefore not correct.
Therefore, the application of the strategy in Roulette is not necessary for practical and mathematical reasons.
Application of the Martingale Strategy in Forex Trading
Many will now certainly say that may apply in the casino, but in Forex trading there is no zero, but only long or short. In addition, there is also no maximum bet as in the casino. So the strategy in forex trading should be successfully applicable or not?
It is important that the probability of winning is not increased by this strategy. The long-term profit is still the same. All that the strategy achieves is a time shift of the losses. Under the right conditions, the losses can thus be shifted to such an extent that it looks like a more certain chance of winning.
In trading, the Martingale Strategy is a “cost-averaging” strategy, which reduces the entry price with every doubling of the position size, or increases it in the case of a short fall. The strategy doubles the position size until a winner occurs.
In the example we buy 1 lot (100k) of the EUR/USD currency pair at a price of 1.18. Profit Target and Stop Loss are 20 pips. So the strategy is 1R, as typical for the Martingale strategy. For this reason alone, the strategy is not recommended, as the CRV is always 1R. If you also assume that the trader’s hit rate is 50%, which is exactly what Eugene Fama said in 1965 in a famous article “Random Walks in Stock Market Prices”, it is a zero-sum game in the long run. On top of this, however, there is a high probability that the entire trading account will be destroyed at some point.
EUR/USD is running against us and has reached our theoretical stop loss. However, instead of closing the position, as one should always do under the aspects of a reasonable risk and money management, we buy back. And this time 2 lots, so our break-even is not 20 pips, but only 10 pips. “Averaging down” by doubling the size of the position reduces the break-even to recover the losses. After the fifth trade, the break-even point is 17.388 (rounded up from 1.173875). This means that when the price returns to this point, we are back to +/- zero. When this level is reached, one can exit and thus cover all losses from previous trades.
By doubling the size of each position, when the price is reset to 1.1740, the profit target of 20 pips is reached. This is because the average price was 1.17388 and 1.173875, respectively, and the exit was at 1.1740. A profit target of 1.25 pips was achieved with 16 lots, making a total of 20 pips.
Martingale strategy not recommended for stock market trading
With the Martingale strategy, a winner can cover all losses and reach the initial profit target. This is also evident from the following formula:
- 2n = ∑ 2n-1 +1
This may sound tempting, but from the perspective of risk and money management, which are the essential foundations for long-term stock market success, it is absolutely not recommendable. In this example, you risk 15 R for a trade of 1 R (corresponds to 100% in relation to the risk). This corresponds to a ratio of -15:1, which is absolutely insane!
From a mathematical and theoretical point of view, the Martingale Strategy should work, as it is well known that markets move in drive and correction shafts and that every trend usually corrects at some point, but the timing is uncertain.
Furthermore, forex markets in particular tend to have very long trends. Moreover, to experience this point in time, one would need an infinite amount of capital, as a loss series of 10 or more trades over time is very likely. In the above example, after only 4 loss trades, we already had a position of 31 lots. This corresponds to 3.1 million dollars. If we had 10 losing trades in a series, we would need 2047 lots. That’s $204,700,000.
Even if one trades the smallest size, which would be a nano lot ($100), it would still be $204,700. Although Forex trading uses leverage, so that theoretically not the entire capital sum must be available in the broker account to be able to trade the entire position, but this is where the greatest danger lies with the Martingale strategy, especially in Forex trading.
With a leverage of 1:100, an account balance of $2047 would be enough to trade 31 nano lots. However, if the position continues to run into loss, which is not unlikely, one has a loss that is 100 times the account balance. This once again illustrates the disrupted extent of this “strategy”. Fortunately, with many brokers the losses may not exceed the account deposit, so that the stake is limited and therefore the strategy would not even be realizable (as in roulette). But even if brokers offer that the losses can exceed the account deposit, applying the strategy would sooner or later ruin every trader.
Assuming that the trader trades with a leverage of 1:10 and his account deposit is $15,000, he could survive a maximum series of losses of 8 losers. Because then the capital investment would already be $10,230 (1023 Nano-Lot x 100 / 10 Leverage).
Mathematical facts when trading the Martingale Strategy
The more trades that are made with this strategy, the more likely it is that a long series of losses will be caught.
The statistical profile of this strategy corresponds to the Taleb distribution. This means that the strategy has a payout profile with a small positive return, but with a “low” but significant risk of total loss. You have a high probability of a small profit, but a low probability of a significant loss. The payout profile of the strategy therefore behaves differently than most strategies should. In fact, the expected value of this strategy is less than zero.
The risk increases exponentially with this strategy, while the payout profile of the profit is only linear.
With a number of n losses, the trader’s risk increases by 2n-1
If one assumes, as mentioned, that the hit rate is 50%, then the following profit expectation of the trades results:
Profit ≈ (1/2 n) x p
- n: Total number of trades
- p: Profit per trade
Using the above example as a guide, the trader sets himself a loss limit of 8 loss trades. Thus the largest traded lot size would be 256 lots. This maximum amount would only be lost if a loss series of 9 losses occurs.
The probability that this would occur is (1/2)9.
This means that one must assume that the maximum loss is reached every 512 trades.
After 512 trades:
- Expected gains: (1/2) * 29 x 1 = 256
- Expected highest loss -256
- Expected net profit is therefore 0
The Martingale Strategy may sound very appealing at first glance, but the strategy is not to be recommended under any circumstances. Not even if the Forex markets trade in a range!
The strategy makes it clear that one should never expand loss positions in discretionary trading. Because this is often the beginning of the end. But what you can do is to use an anti-martingale strategy and increase your position when you are already ahead. This is also called pyramidizing. But it is important that the risk does not increase under any circumstances. Also, the pyramidization strategy is only recommended to very experienced traders.
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