|
/ | Articles |
Articles 
Trading What is Martingale and Is It Reasonable to Use It?
To post a new articles, please log in or register
|
What is Martingale and Is It Reasonable to Use It? [ ru ] What Is Martingale?If you write "martingale" in a search engine box, it will return a large
number of pages with the description of this system. It is interesting that among
others you will meet web-sites of online casinos, which assure that this system
works, all you need is entering your credit card number to start scooping up money.
What is strange - are the casinos ready to give their money such easily? If the
Martingale really works so good, then why have not all the casinos turned bankrupt
yet? So, what is Martingale? Here is the definition from Wikipedia: The Martingale is a betting system in gambling. The meaning is the following: More information is here: http://en.wikipedia.org/wiki/Martingale_system
Where Is Martingale Used?The simplest gamble for analyzing the Martingale is chuck-farthing. The chances
to win and to lose are equal - the gambler wins if a coin comes up heads and loses
if the coin comes up tails. The Martingale system for this game works in such a
way:
The Martingale can also be used in playing the roulette, betting on red or black.
The chances are less than 50/50, because there is also Zero, still very close to
it. Mathematical PartLet us conduct a mathematical calculation of the dependence of the loss probability on the possible profit at the game with a coin using the Martingale system. Let us introduce the following symbols:
As we double the bet after each losing toss, we can derive the following equation:  Each set with the amount of tosses less than k-1 returns the profit q. As the probability of winning at a toss
= ½, the average set length is 2*. Let us label by P(N) – the probability that we will not turn bankrupt within
N tosses. As N tosses constitute approximately N/2 sets (the average set length is 2), and the probability to
win in the set is (1/2)^k-1 , then
 We get the function of the win dependence on N. But the total number of tosses (N)
is not informative enough, so let us try to bind N with an expected profit. Suppose,
in the result we want to double our capital. As in set each we win q=Q/(2^k-1),
the total profit is calculated according to the rule of the compound interest (more
information about compound interest is here):
 After simple transformations we get the following formula for N:
 After calculating the probability of the profit P(N) using the equities (1)-(2)
we get the following results:
If we consider N a noninteger (do not round off the results of the equity (2) to a whole number), then P(N) does not depend on k and is equal to 1/2 (you can easily verify it, inserting (2) into (1) and using the simplest properties of logarithms). I.e. using the Martingale does not provide any advantages; we could as well bet all our capital Q and the winning probability would be the same (1/2). Conclusions of the Mathematical PartFrankly speaking, at the beginning of preparing calculations for this article I expected that the Martingale would increase the probability of loss. It appeared to be wrong and the risk of loss is not increased. Still this article very vividly describes the meaninglessness of using the Martingale.
Expert AdvisorAfter getting the above formulas, the first thing I did was writing a small program, emulating the process of playing chuck-farthing and composing the statistics of the losing probability (P) dependence on the coefficient k. After the check I found that the program results (it can be called "an experiment") coincide with mathematical calculations.Of course, the ideal variant would be writing an Expert Advisor, trading by the same rules as in chuck-farthing and making sure that theoretical and experimental data are identical. But it is impossible because the starting bet is calculated using the formula:  And in the Forex we can "bet" only a sum multiple of 1/10 of a lot. That
is why it is impossible to write an Expert Advisor, vividly proving the above formulas.
Nevertheless, for completeness of analysis, we still can write an Expert Advisor,
using the Martingale. But here the starting bet will be fixed - 0.1 of a lot. Analogous,
the bet will be doubled at a loss and return to the starting one at profit. As
described in the beginning of the article, a trade will be opened in the following
way: a trade is opened in a random direction with the probability 50%, stoploss
and takeprofit are fixed and equally distant.  The above screenshot displays the results of testing this Expert Advisor. You see,
though the general direction of the curve is upwards, from time to time it suffers
large dips. As a result of the last dip the Expert Advisor stops trading, because
the balance is not enough for the next bet with a doubled lot. And at the moment
of stop the balance is positive - here is the difference from the theoretical calculation
in "the mathematical part". P.S. The files attached contain the screenshot of all necessary mathematical calculations
and the Expert Advisor. Translated from Russian by MetaQuotes Software Corp.
Original article: http://articles.mql4.com/ru/392 Warning:
All rights to these materials are reserved by MetaQuotes Software Corp.
Copying or reprinting of these materials in whole or in part is prohibited.
Firstly, sooner or later, though the probability be small, you will have enough consecutive losses to bankrupt you. Remember that the probability of any sequence of profits and losses is equal to that of any other sequence. So, for example, you are just as likely to get seven consecutive losses as you are to get six consecutive losses then a win.
Secondly, I'm no mathematician, but it seems to me that you will lose in the long run if for no other reason than that you are paying a spread for each trade. To make the probablility of loss equal to that of gain, you will have to use a single price to calculate the positions of your s/l and t/p, so that the s/l and t/p will be equidistant. You will either have to pay more for the stoploss than you would take in profit, or for equal loss and gain you will be more likely to hit the stoploss than the takeprofit. If I am wrong here, tell me! I have seen Martingale system advertised for sale, but having written a simple EA to test the idea, decided not to involve myself in it. However, Paroli's system, the opposite of Martingale, is attractive, even though it, too, suffers from similar problems. There is no way you can make something unpredictable into something with a probability greater than 0.5. Trading MUST involve making judgements and using skill to predict; those unwilling to develop the skill will, I believe, fail. You simply have to make winning more probable than losing. If you can do than, perhaps Martingale may enhance your trading. I have to say I am a complete beginner at EA programming and only have a little experience trading and that was mostly in options. Automated trading is a fascinating idea and I think I shall enjoy pursuing it.
2008.03.09 15:47 clam0391
1 comment
|
