Does the martingale system really work?

Martingale is working but you must have the "BIGmonies" I making the joke, you see. I not use it but it can work, but must have unlimited money or be prepared to lose the big. Choice up to you, no.

In addition to the links I posted in post #155 (examples of martingales that have blown accounts), here are some definitive answers about martingale — and other staking systems — by math experts:

Mike Shackleford (The Wizard of Odds); also here
Michael Bluejay (VegasClick.com)
Eliot Jacobson, PhD

Here is an ingenious proof as to why martingale offers no advantage over flat betting. Read the second post on that page, by MathExtremist.

To anybody who asks "but what does casino gambling have to do with forex?", MM is universally applicable.
Mathematically, forex is nothing more than a win/loss generator, just like any other game of chance.

thanks for the info, hanover! I've often wondered if martingale inline with fundamentals would be the way to go, but.. The market can remain irrational longer than you can remain solvent. and it reminds me when I start to think that way. lol

I have tried it on blackjack. It used to work sometimes, but at the end, it's always an account killer.
To recover from loss faster, martingale is good but not a permanent solution.

The quotes you used, none of the authors ever said that martingale did not work. And they can't do so honestly; it's like saying that combustion 'doesn't work'. What the mathematicians have all concluded is that WITHOUT AN EDGE, martingale will not work over many repetitions. No betting strategy would work over many repetitions without an edge. Apparently some people read this to mean: martingale can never work under any circumstances.

Allow me to quote from an upcoming manual from Maat of AwarenessForex.com that deals with this very problem of not using martingale:
[begin quote]
......Casino owners MUST remove the edge from a game before they allow players to play (against the dealer). Some games like slot machines are obvious losers. But more 'fair' games like blackjack where you could actually card count are carefully manipulated so that you cannot win consistently enough; or they ask you to leave. Games where the dealer takes a flat rake, and you play against other players, the dealer has no incentive to intervene. Forex/futures brokers are all "supposed to" work this way: having clear rules of engagement and then properly hedging their risk. Some forex brokers got a bad name by using these casino type of tactics to manipulate winning traders in order to profit themselves instead. Both players of the rigged casinos and shady forex brokers have easy fixes; leave or find a new venue.

Forex, like any derivative contract, must have buyers and sellers in order for price to fluctuate. This means that the price will constantly move up and down in waves; sometimes small....sometimes big but as long as there is sufficient movement there is an opportunity to profit. Instead of the futile attempt to guess the future market direction, why not speculate on the current direction with a scaled position approach? I've demonstrated when using tradecycles how martingale is mostly required in order to ride a larger, steep trend (by riding the smaller [counter]trends in between).

Many traders who are "drawdown-adverse" attempt to use single lot sizes so that it decreases the drawdown and/or increases the range from the first order position. The market pulls back [counter-trend], but only about 25-30% from the peak of the mini-trend before continuing in the original trend direction [and again repeating more pullbacks later]. With those pullbacks, you could profit, breakeven, or cut your losses shorter with the top-heavy, increased position sizes of martingale; the worst case scenario is hitting your stop loss. But with single lot sizes, you'd either need a larger pullback now or allow the market to trend further away from the starting position (with a larger drawdown) until you either run out of margin or you get your pullback. The smaller ranges (30-150 pips); the pullback have a near 100% chance of occurring, with only the rare surge or even rarer tsunami that can usually be detected and avoided. The larger range pullbacks do also occur [sometimes!].....but can go several hundred pips first. This results in having worst drawdowns with smaller returns if you were to attempt to ride the entire larger trend. So the very drawdown you were trying to avoid catches up with you anyway.

Another money management pitfall that single lot size/single position traders make the mistake of trying to win every trade, instead of focusing on net profits. From the same starting point, 2x and many times 3x martingale will give you a >90% opportunity to exit the entire series of trades with a net profit (or smaller loss), regardless of whether the overall trend goes up or down. You can then re-enter when the next opportunity comes. Single position traders will either get stopped out or will hit their profit target. How many times you hit the profit target....who knows? But even with $0 commissions, 0 spread, and a free VPS / internet connection, you must have a very high % winning strategy, betting large amounts to win big over many repetitions in order to be profitable.

The market never goes in a single direction forever; it fluctuates up and down like the tides of a beach. This in itself already gives you a high positive expectancy of the price movement itself. Likewise, you never need use martingale with infinite levels; 1-8 levels is sufficient in my experience. You need the courage and consistency to apply a mechanical strategy properly. I'm very surprised over the [professional??] traders who claim that using martingale as part of a risk/money management strategy does not work; yet I have not seen them ever offer any transparent alternative. Trying to gain risk-free profits with lucky single entry positions very often ends up attracting the very losses you are trying to avoid.......
[/end quote][emphasis added]

@ybfjax: With respect, the guy you're quoting seems to be contradicting himself.

On the one hand, he's saying that it's possible to gain an edge from price behavior ("The market never goes in a single direction forever; it fluctuates up and down like the tides of a beach. This in itself already gives you a high positive expectancy of the price movement itself"). Sure, FWIW I agree.

But then he suggests that professional traders offer no workable (profitable?) alternative to martingale ("....I have not seen them ever offer any transparent alternative. Trying to gain risk-free profits with lucky single entry positions very often ends up attracting the very losses you are trying to avoid.").

Hence, if I understand him correctly, he's saying that an edge in itself can't deliver profit, unless martingale is added to it.

If so, that's clearly false. Reasons:

1. There are profitable traders who don't use martingale.

2. It's a mathematical fact that staking systems can't alter expectancy (PipMeUp has posted a neat mathematical proof here). Progressive staking systems increase the average bet size, and consequently increase risk of ruin exponentially. In other words: no long term benefit, but significantly increased risk.

3. An 'edge' is not necessarily the result of trying to avoid losses. It's simply an outcome where profits exceed losses, over time, and irrespective of staking.


Bottom line: his entries and exits either give him an edge, or they don't:

1. If he does have an edge, there's no need to employ progressive staking (that's analogous to the winning formula used by casinos).
2. If he doesn't have an edge, progressive staking is merely trading off guaranteed recovery in the short term, for possible disaster in the long term.

He says that 1-8 levels is sufficient. It's my view that, given enough time, every price pattern that can possibly occur, will eventually do so.
Will he ever encounter 8 consecutive losses during his trading lifetime?

1. If not, then martingale will "work" for him, exactly as he says.
2. If so, then how easily can the (consequential) loss be shrugged off? That's a personal question that I believe every trader must consider.

[EDIT]
He seems typical of what I would call the "martingale mentality". Despite his comment about price behavior being predictable, he apparently can't find an edge that allows him to overcome his losses. Hence he assumes that (1) nobody else can, either; and (2) that if he can eliminate the losses, he has solved his problem. Hence he turns to martingale, and justifies his use of it by saying that 8 consecutive losses is an impossibility.

If you use a system with RR=10 you need a win rate greater than 9.1%
If you use a system with RR=5 you need a win rate greater than 17%
If you use a system with RR=2 you need a win rate greater than 33%
If you use a system with RR=1 you need a win rate greater than 50%
If you use a system with RR=0.5 you need a win rate greater than 67%
If you use a system with RR=0.1 you need a win rate greater than 91%

What win/loss do you need for a system with RR=0???

Martingale tries to get 1 unit of profit risking 2^n units of risk, the RR decreases exponentially towards 0.

Whenever you reach step 5 your RR is now 0.03, you need a winner with 97% chance for a martingale based system keeps an expectancy of... break even!
At step 6 your RR is 0.0156, you need your next trade be a winner with 98.5% chance.

Martingale doesn't win after N tries. IT DIFFERS THE PAYMENT OF THE ACCUMULATED LOSS.

a/ Martingale always improve any losing system into a slighly less but yet another loser system. Simply because the system "lives on credit".

b/ Martingale always degrades any winning system because the maximal bet size in % of your account for a given system is 100((RR+1)winrate-1)/RR, beyond it turns a loser. Martingale will always go beyond unless you under-bet so much at the 1st step that it makes no sense trading this variant.

a/ and b/ imply that if your system is improved by a Martingale, your system is a loser.

You understood most of it. One misunderstanding is coming from the use of the term edge. You would have to define the term edge as it relates to trading a complete system. I define it as a positive expectancy over the total series of trades in a walk-forward, live[preferred] or simulated trading environment. How many exact repetitions you want to test or see before you accept that the system has a positive expectancy is somewhat subjective; but the trading conditions and rules must be consistently applied. Any adjustments also must be consistently applied. So you would need to see how the detection, entries, and exits work together to [re]produce the profits and losses.

I take it by your wording that the edge can ONLY refer to entry OR exit. If this is true, how would you confirm the edge exist with only one component of a full trade?

Maat has said that he has not seen a professional trader offer a transparent alternative. To clarify, he has not seen a mechanical system that did not use some kind of multiple positions spread out in series (aka cost averaging, martingale, etc) in order to [re]produce profits and manage losses consistently. Nether have I, but it would be interesting if someone could do so. What has been seen are large marketing campaigns, fake statements and/or testimonials, respected media press, etc. "proving" that a so-called system works or doesn't work. It is based on popularity and consensus, almost like a religion (#1); rarely is any honest investigation done to validate the underlying strategy.

In addition, many traders have misused "marty", mainly due to a misunderstanding of the elusive term: price action. This has contributed to most of the negative bias; usually by over-gearing the equity vs available margin.



Could you please provide an example of a mechanical trading system that only uses single position per [trade]cycle to achieve positive expectancy? I say mechanical because a system that has a hidden or discretionary component cannot be forward-tested transparently or independently verified (a historical trading statement, by itself, can be faked). Then we are back to square one in terms of trying to "prove" whether the system is valid or not.


Unfortunately, the "proof" here does not provide an example of how it applies to a complete trading system (entries and exits) or assumes only a single position is possible per instrument simultaneously. Multiple positions sizing options are readily available and are only limited by the broker/exchange position limits, and the available margin.

There is a risk of loss of capital in forex and derivatives trading, leveraged or not and it is not suitable for all investors. If we are unwilling to put capital at risk strategically, how could we ever hope to profit from the venture in our own accounts and/or trade other people's funds? Forex would not be the best place to leverage capital for someone risk-adverse.


Perhaps the definition of an edge was not clear earlier. You mention that [for trading derivatives] that in your definition, there is no need to employ progressive staking. I interpret progressive staking to mean multiple positions (averaging) as opposed to a single entry position. Since price is linear, there are only two ways to enter the market: long (buy) or short (sell); and the same is true to offset or exit the positions. The only way to prove whether an edge exists would be to have BOTH entry and exits for ALL positions opened over a series of trades: a system, tradecycle, etc; the positions much be closed to fully analyze them.

If you are using a single entry position for each tradecycle (entry + exit offset), then the only way I see to have a positive expectancy would be to have a high percentage of winning trades (nearly 100%). That requires that your entry AND exits be very accurate direction-ally. Imagine a mechanical system that could give you exact entry and exit price points in advance. If you could cover commissions + spread + slippage + drawdown so that you are in net profit: risk free profits, if you could sustain it.

The tradecycles that Maat implements is about not knowing in advance exactly what direction the price may go after you enter the first trade; you can get an immediate pullback or the market can go further first before it pulls back. You instead prepare to enter and exit positions over the entire range based on net profit targets. You give ALL of your positions room and hold onto the risk strategically until the pullback occurs. You do not know when the retracement is going to occur. So the aggressive position sizing is needed so that even with a small retracement, a net profit/ breakeven/smaller loss is >50% than hitting the stop loss. It's been >95% in practice, mainly because the pullbacks always happen; it is the "when" (the full range from the first entry) that is unknown until it happens. a couple of pips may not seem like a lot, but with position sizing, 2 pips of 0.01 lot and 2 pips of 1.00 lots Perhaps a screenshot would help demonstrate this concept.

On rare occasion, he has hit the stop loss in heavy trends where pullback took longer to occur than the range was setup for or when using too much aggression. But he has made back losses in every instance i have seen on larger accounts. It was actually good to know that martingale does not have to be implemented in an all-or-nothing approach.

All successful systems that I am aware of have limits or boundaries. The biggest problem with traders who experiment with martingale or multiple positions in a basket is that it is usually based on random entries and exits; there was no real strategy being how the profits or losses are to be taken for all possible combinations of price movement (range limits). Price is linear, so maat shows that the boundaries are easy to set.
To clarify a previous misconception, he never said that 8 consecutive losses is an impossibility. As eluded to earlier, an edge for a trading system is realized with a combination of entry, position sizing, and exit to produce a synergistic effect of net profit; no one component can survive or be put in a valid prospective to determine the positive expectancy without the other 2.

After seeing how tradecycles work (link) and the importance of using mechanical systems (link) in a live trading environment (demo or development phase also), it is very interesting to see that aggression in the form of 2x or even 3x martingale is quite safe. There's no need for "all-or-nothing" approach if used correctly.

I think I've covered all that I can remember. Anyone who would like to investigate for themselves more about using tradecycles to implement aggressive position sizing for profit can look more closely at the following free tools:

APAMI - to measure price action clearly in real time.
Forex cost averaging spreadsheet - to determine precisely how to lay out your trades within a designated range, and the pullback required for breakeven, etc. Takes into account commissions, spreads, pip value, etc. but you have to manually adjust each scenario (grid).
Tradecycles part 1 - how to begin laying out a mechanical trading system.
Tradecycles part 2 - using automation to be even more objective with trading decisions.
Trading as a religion (#2) - Not specific to tradecycles, but essential to understanding how fear can rationalize itself in seeking profitable trading strategies.

Here is the error I see in your analysis (and it is a common error): The whole presumption you state above and in a previous thread with RR and how it applies to martingale appears to be based on either the underlying price movement, the entries, and/or the exits being completely random. But as stated earlier, observation has shown that linear price movement never goes straight up or straight down; it trends in small ranges at a time. Could be 10 pips or 50 pips at a time...who knows each individual wave without hindsight. We can objectively measure the likely range on a market-by-market basis and then take the risk on the pullback. You use multiple positions as necessary to spread out the risk to cover the most likely ranges. You use increased position sizes (often double or triple down) to decrease the distance pullback required to profit.

I respect that you insist that one particular method cannot work long term. Can you please provide an example of a mechanical system for derivatives with RR > 1 that does NOT use some form of martingale or multiple simultaneous open positions to achieve consistent profits? When you or anyone makes statements like "Martingale always degrades any winning system because...." [emphasis added], I am presuming that you:

a) already fully familiar with the ins and outs of one or more of these winning trading systems to which you refer (how the entry is spotted, when to enter, when to offset, how often this occurs, etc).
b) can clearly demonstrate in a walk-forward fashion how the winning system works to produce profits. You already have this in "a)", so I guess this is more about putting it in a form that other forum members can follow (preferably with at least 1 screenshot or diagram illustration).
c) show how martingale (1x, 2x, or 3x preferably) makes the system unprofitable vs single position size.

Interestingly enough, the only way I've seen to measure RR objectively in a trading environment is to test it in a demo, replay, or live environment. And I do look forward to seeing your implementation or demonstration of such a system. I'll leave you with one more quote from the book:

[begin quote]....As far as I can tell, you must actually take the risk by taking the trades....that's how you see for yourself if a system works or not beyond the theory. A lot of investors and traders looking to avoid taking risk get hung up on this part; they 'feel' safer with a smooth looking equity curve and single position and the hope that the market will always go "their" way.

Why reinvent the wheel of chasing the market direction (incorrectly), trying to beat the market with exotic-sounding tactics, or trying to scam your supplier with some latency arbitrage or other technological trick? The only way I know to be profitable consistently is with a mechanical trading system.....The tools I offer help greatly in visualizing this process honestly from a speculative trader's perspective....[end quote]
[Some of the tools are listed in the previous post at the bottom.]

I will always be amazed to see how clueless about mathematics the "traders" are. Especially thoses who are also clueless about trading...

@ybfjax:
You talk as if Maat's approach (grids, averaging, martingale, ....) is the only possible way to trade. Just because he apparently can't find directional or behavioral biases in the market doesn't necessarily mean that a more knowledgeable trader can't.

You ask: Could you please provide an example of a mechanical trading system that only uses single position per [trade]cycle to achieve positive expectancy? I say mechanical because a system that has a hidden or discretionary component cannot be forward-tested transparently or independently verified (a historical trading statement, by itself, can be faked). Then we are back to square one in terms of trying to "prove" whether the system is valid or not.

Attached is an example of a trend-following EA (written by my programmer friend) that was tested over 6 years of high quality tick data and more than 800 trades on EURUSD, assuming a spread of 1.8 pips per trade. It uses a combo of directional bias and key price levels for its entries, cuts losses quickly, and lets profits ride — frequently on multiple entries — while trends exist. There is absolutely no curve fitting; varying the parameters has little effect on the overall result. As you can see, it has around a 40% win rate (due largely to the tight initial stoplosses), but each losing sequence is followed by a new equity high, whenever EURUSD enters a 'trend'. And it uses completely flat staking: every position is sized at 0.5% risk of equity. That is what I mean by an edge from entries and exits. This is one of 4 different EAs we have that have backtested profitably, and are currently being tested further on live data.

Unlike your friend Maat, the EA makes no special attempt to avoid, or recover from, losses. Around 60% of the trades are losses. It wins overall because, like all good trend following systems, the winning trades harvest many more pips than the losses forfeit.

[Note to everybody: we will not be discussing the method more fully, nor sharing/selling the EA. It is for our own use only].

If a 'dumb' EA (it takes no cognizance of news, session considerations, correlation with other markets/instruments, orderflow, macroeconomics, heavyweight bank agendas, supply & demand, weekend gaps, etc etc) can locate and exploit directional biases profitably, how much more so an knowledgeable trader, who can consider many 'intangible' factors, and weigh them sensibly?

Amongst my forex buddies, there are two who are very profitable. One (Andrew) sizes consistently at 0.25% to 0.5% equity per trade, and is the most disciplined trader I've ever seen. He has very few losing months. Coincidentally, when I first met him about 6 years ago, he was running a martingale system developed by Don Steinitz, which subsequently blew two accounts; by reverting to consistent sizing, and employing sound entries and good risk management, Andrew has been consistently profitable for more than 4 years, trading mainly price action on H1, H4 and D1 charts.

Increasing stake size when the probabilities are more favorable is smart (that's how card counters beat blackjack), but increasing stake size merely to recover recent losses has no mathematical basis. The problem with martingale is that probabilities in the market are unlikely to double (favorably) with each loss, hence the staking rapidly gets out-of-whack with any increase in probability (example: the further price moves away from a mean, the greater the probability of some kind of pullback) that's being offered. Moreover, the trader must somehow find a starting stake size that's both small enough to allow the account to survive several consecutive doubles, and large enough to return a satisfactory level of income.

That highlights the core balance that must be addressed with any trading system: maximizing return while also keeping drawdown within personally acceptable levels. The problem with position sizing algorithms is that they merely increase or decrease both return and drawdown in like proportion. The 'dumb' EA results that I posted can be used to exemplify this: the results show a ~12% p.a. return and ~5% worst case drawdown, by sizing at 0.5% of equity. We can scale both return and drawdown proportionally, up or down to any levels we wish, by adjusting our sizing accordingly.

Math is math; it is inviolable. Hence I stand by the statements that I made in my earlier posts (and also in myths #2 and #12 here). Due to its inherent recovery mechanism, martingale will always deliver continuous profit, provided that the number of allowable doubles is never exceeded, causing immediate ruin.

martingale trading is caused by a defective gene.not all of us were meant to survive.

Dear Hanover,

In your previous post you say that your EA sometimes opens multiple entries. As you may know I try to show (here) that any fiddling with the open position doesn't improve the expectancy of any winning system. So far I could show that all the commonly used "tricks", like trailing SL to BE quickly, taking partial profits and so on are all bad practice. I could show a grid (aka anti-martingale) is wrong too. But I'm still struggling at showing that a pyramid is wrong as well. The difference between forward grid and pyramid being that the subsequent entries have themselves an positive expectancy and take profit at the same time as the first position (I'm not talking about inner, shorter term, trades).

If this AE closes the additional positions at the same time as the first one is closed (really a pyramid), and if you happen to have the code of this AE in reach of hands and be kind enough to modify it quickly I'd be really grateful to see how it performs without adding to a winner, preferably with fixed lot size MM.

I know I'm asking a lot for a Sunday :°)

@PipMeUp:
It's almost midnight here in NZ, hence I'm going to bed soon. I have to make an early start tomorrow.

But just quickly, IMO there are two ways of looking at pyramiding:

1. Each position should be taken on its own merit, i.e. needs to meet valid entry criteria. In that sense, I'm treating each position as being independent, although I realize that (because they overlap time-wise, and are being impacted by the same price move), that's not strictly true. The EA doesn't 'intentionally' pyramid for the sake of it; it simply makes an additional entry every time it finds valid criteria.

2. It's justifiable to stack up our bets, the more heavily conditions are in our favor (e.g. when the count is highly positive, when playing blackjack). If markets are trending strongly, and there is good underlying reason for it (e.g. macroeconomic factors), then it makes sense to let positions run longer, and even stack positions to multiply profits. IMO it's the market condition that should determine the strategy; I don't think it's necessarily valid to have one math principle that's designed to fit all conditions: if (and I stress IF), for example, the probability of a move continuing — under certain conditions — increases, the longer the move continues, then pyramiding makes perfect sense; if not, it doesn't. I discuss some of the math ideas involved in pyramiding here, and strategies suitable for different market conditions here.

I'll talk to my friend tomorrow and ask him if he is willing to modify his EA. It would be interesting to see how much less(?) profitable it would be if it were only allowed one open trade at any given point.

[quote=hanover;6932418I'll talk to my friend tomorrow and ask him if he is willing to modify his EA. It would be interesting to see how much less(?) profitable it would be if it were only allowed one open trade at any given point.[/quote]Thanks a lot. The experiment is only interesting if the exit criteria of both the positions is the same. Otherwise, if the second entry has its own exit criteria, the results will degrade. That's because the expectancies sum up.

Regarding your schema (the 1st link) you write
Here comes all of my problem. "upon reaching level B, the probability of outcome "1" is significantly greater than outcome "2", than it was at A" is TRUE. It is easy to show that the probability of "reaching 1 from A given that we are now at B" is strictly greater than the probability of "reaching 1 from A" alone (1). But the conclusion is problematic because they all use the point 2 as a SL, the R:R of Mr Z is worse than the one of Mr X. His expectancy has no reason to be greater even with (or just because of) the increase of probability. Pushing the example to the absurd Mr Omega should open a position spread+0.1 pip below point 1 with a near infinite position size! We perfectly know what this kind of method (huge SL + microscopic TP) result in!

I try to prove that actually Mr X (very big RR, small win/loss) will outperform both Mr Y (pyramid) and Mr Z ("always" right because very small R:R), perhaps not in this trade, but in the long run.

X will achieve this by using methods like trailing the SL to BE quickly. Your conclusion is only true for this particular trade. But it is wrong statistically. Suffocating the trade kills your edge. Assuming a positive expectancy, the few losers you save would have been more than covered by the winners you kill, even if they are less in number. --Assuming a zero or negative expectancy, nothing you can try will work anyway.--

Have a good night.
---------------
(1) That's because p(A AND B) < p(A) for any events A and B.

@PipMeUp:

Let's look at an example, given the diagram/scenario in my linked post:
Suppose every trade has a common TP that is 50 pips higher than point B, and a SL of 10 pips below its entry.
And suppose that, having reached point A, the probability of price reaching the TP is 60%; and if price reaches point B, the probability of its continuing to the TP is now 90%.

Then, expectancy = (lots x win pips x winning probability) – (lots x loss pips x losing probability)
Expectancy for trader "X" = (2x70x0.6) – (2x10x0.4) = 76
Expectancy for trader "Y" = (1x70x0.6 + 1x50x0.9) – (1x10x0.4 + 1x10x0.1) = 82
Expectancy for trader "Z" = (2x50x0.9) – (2x10x0.1) = 88

OK, so logical extrapolation suggests that no matter what the TP, SL and probabilities, trader "Y", by diversifying will never outperform either "X" or "Z". The trader who stakes highest while probabilities are at their greatest, will always outperform the others. In that sense, you are absolutely correct.

However, probabilities ultimately come down to order volumes and flow, which are continuously changing. Hence when price reaches point A, we might (assuming that the probabilities can be calculated) have a +EV trade, thus justifying an entry. But the order volumes between A and B could subsequently change before price reaches point B, reducing the probability of reaching the TP from (say) 90% to 70%. If so, trader "X" will win overall, thus:
Expectancy for trader "X" = (2x70x0.6) – (2x10x0.4) = 76
Expectancy for trader "Y" = (1x70x0.6 + 1x50x0.7) – (1x10x0.4 + 1x10x0.3) = 70
Expectancy for trader "Z" = (2x50x0.7) – (2x10x0.3) = 64

Again we see that "Y", by diversifying, ends with a result that's somewhere between the results of "X" and "Z". Diversification has a smoothing effect, rather than delivering an optimal result.

Of course the probabilities are, at best, fuzzy, as the order book is constantly changing. Some would go so far as to say that trading is more of an "art" than a precise "science". Hence it might be best to enter some of the position at point A, and then manage the trade dynamically as the action unfolds; if price reaches point B, and the probabilities still look good, then add another position, for the same reason that the blackjack player increases his bet because the count is now higher than it was at the time of the original bet. If (whether rightly or wrongly) we view the second setup as being independent of the first, and it is a +EV trade in its own right, then we are justified in taking it anyway, on that basis.

I guess a lot depends whether one sees trading as a dynamic (and hence largely discretionary) process, or a totally mechanical process where one derives his probabilities purely from the results of prior testing (in which case we "know" the probability of price's continuing to the TP from point B, within the bounds of statistical error, before price reaches that point). Whereas the dynamic approach allows us the possibility — for whatever it's worth — of assimilating and processing new data as the trade(s) unfold.

Not sure that I've completely answered your points. Your knowledge of statistical math is much better than mine.

Oh la la no no no!!!! Wait up!

There is a major flaw here! The probability I'm taking about is the probability of the event "the price reaches the TP of the first entry (point B) before the SL of the first entry (point 2)". If it is true that the probability of this event is improved by the addition of the piece of information "price reached B", this DOESN'T imply price will now on go to B in straight line. It can perfectly have 90% chance going to B but can re-test the entry level before! The second entry gets absolutely "no premium" because I'm already in the market. Market is agnostic to that. Actually Z is buying so late that he cannot set a SL that small. His probability is only increased if he keeps the point 2 as his SL. Killing his R:R.



"Of course the probabilities are, at best, fuzzy, as the order book is constantly changing."
Indeed you can never know the values of the probabilities. But you can work with them nonetheless. You can sometimes compute the likelihood of a probability (the probability of "my probability is X"). That's exactly what a Kalman filter does for instance.

"Diversification has a smoothing effect, rather than delivering an optimal result."
A very smooth equity curve means your DD is very small. This allows pushing the leverage a bit, which now outperform the 2 others who cannot do the same without a very high risk of ruin. (This is why managing my expectancy is so important.)

Great posts guys and the best read on the subject I found on the internet - Thanks once again

In plain terms (unlike the avenues you guys have explored) and keeping things simple this infographic is spot on (hope it's of interest) - http://forexuseful.com/authors/forex...le-infographic

Martingale is basically a double or nothing game.If your system is a winner it will make you quicker money if it is a loser then it will blow your account quicker.I calculated that if you have a constant 1:1 RR then you need at least 51% win rate to be always winner with a martingale,ofc you would be a winner without it, just that martingale will win you money quicker.Lower any value there and it will be a loser for example 1:1 RR and 50% win rate it neutral, it depends on your luck, but 1:1 RR and 49% WR will surely blow your account up, same for 0.9:1 RR with 51% win rate.But if you have a constant, 1.2:1 RR with 51% win rate then you have a Holy Grail.

Of course in forex you really dont have a mechanical edge so big like 51%, the biggest i've got with a martingale system designed by myself was 1:1 RR with 46% WR which was of course a loser but i just find impossible to make 5% percent for the holy grail in so much changing enviroments like forex market,no matter how hard I tried, so that EA was a loser unfortunately.

Agree - 50% or more in martingale is tough. I think part of it is there are very few systems that can make it within a 1 hour chart. You need directional bias at some point that has an edge. Otherwise, you just kind of grow your account and then destroy it.