Vasily, great article. Thanks.

Everyone should agree with every point you made, and be aware of the pitfalls of using a betting martingales. It's like: you can always do it, it might even be fun for a time, but, don't expect to win the game in the long run.

@Guy R. Guy R. Fleury, I agree with you, I would like to add that the "modified martingale" is the most used in sports betting. Technically it works good, although I don't use it, I have made and tested the model which was successful.

The model was developed for a soccer, and I started from the empirical evidence / indicators that each team has a draw results where the odds is/are 3.00 or more.

This model can be used only on betting exchange service because there are no limits, the traditional bookmaker (a classical bookmaker) will never allow the martingale as betting system.

The pitfall can be summarised by a half-phrase: limited starting capital hence non-zero chance of a ruin. The rest is redundant really...

Nice graphical illustration of why the "doubling down" prop trading strategy would fail.

Often times people who talk about martingale failing, do not discuss the context in which it will be used in a live market. They talk about what does NOT "work", but cannot detail what DOES work.

Cost averaging is used at all levels of the market, from individual traders, to brokers, to dealers and banks. You must know what your net exposure is at all times, which requires a weighted average of all open positions.

When you 'make markets' as a value trader or with arbitrage, I can't imagine NOT using some form of cost averaging. Especially as a value trader, single lot sizes is not aggressive enough to keep up with a trending market. Trending = short term intraday volatility or larger macro trends.

@Jon, yes. In a game with an upside bias, meaning with odds > 0.50, an anti-martingale would be the way to go. A cost averaging formula would do that. And the cost averager would win as if by default since in a game with an upside bias, the best bet is to always bet the same side as the bias which in such a case would be for prices to go up.

Jon Grah, I explicitly mention in my article that I assume 50/50 chances of profit and loss (which is not implausible since in reality the ratio is often even worse: in roulette there is a zero, in (most times unpredictable) market there are broker fees and bid/ask spread).

But I never said that I reject any kind of cost averaging. Moreover, I, for one, always buy an asset in 2 - 4 tranches when I believe that it reached it minimum and will reverse (e.g. I did so for Tom&Gerry: https://www.linkedin.com/today/post/article/tom-gerry-turnaround-two-german-fashion-smallcaps-vasily-nekrasov). But my tranches are usually equal, in either case I never double the stake.

Martingale model is proven verified deep destruction in very very short time when market behaves against, only immatures apply it. Even if successful, still its risk is far higher than the reward like comparing one drop of profit with the whole sea of risk

Does it work with financial assets that have autocorrelation?

Again Zubair Badar and others, do you present an alternative model that can help make markets as a profit-motivated trader (e.g. arbitrage, value trading, dealers, etc) that is proven to work over time?

Mark Yeun, it might (depending on the strength of autocorrelation) but generally, a martingale-like system is always suboptimal.

A (fractional) Kelly is much better. I have written somewhat technical paper on it (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2259133) but I am also going to discuss it in more simple words in my blog.

And anyway, asset returns are usually have very little autocorrelation.

Jon Grah one should exclusively rely on genuine & original accuracy of strategy itself without manipulating lot size. If strategy is sufficiently good then no need to change lot size. It gives 100% peace of mind and it works

but but... your system should itself be accurate and reliable to practice this.

money management is something very very sensitive until you know its exact balanced quantified measurement of all aspects. Better to avoid.

Zubair Badar, I have another opinion about money management. Of course it is useless if one have no positive edge but converse is not true: i.e. one can lose even with a positive edge if one bets too aggressive. In my paper I discuss the case with a stock which can go either +170% or -70%.

On average you have a good positive edge: (1.70 - 0.7) / = 0.5 but in the long term ((1 + 1.7)(1 - 0.7))^n = (0.81)^n -> 0 as n gets large.

@Vasily, very true. However, note that it takes time to have 1.70 as well as 0.70. If you look at the portfolio level, you are usually talking in years to reach those levels.

Also, (1.70*0.70)^n = 1.19^n which gives the strategy a positive edge and makes it a long term winner.

The numbers you must have looked at are: 1.70*0.50 = 0.85 which is a doomsday scenario.

But, still, your intended equation is right. As n increases, on a negative edge, you get an almost assured zero as final output for such a trading strategy. Even if such a strategy in itself is improbable.

Good money management systems can make you win 9 times out of 10 but in 1 time it hits like ironsmith as compared with the goldsmith. that 1 time can happen once in a year, 2, 3 or 5 years but it happens unusually. this is tested

Even if money management makes profit still its risk/reward ratio is worse than the risk reward of the strategy itself when you compare on yearly basis. in short time things could be favorable.

Balanced money management can be applied to maintain best risk/reward ratio but thats a different topic to discuss to know its howness and modeling

Zubair Badar, as i've said many times, markets must be 'made' aggressively and in real time, which either requires large lot sizes up front, or increased position sizing. You have not demonstrated a strategy where avg is NOT used and can be consistently profitable.... And automated without some sort of averaging.

But i digress. Too many people talk about MM without showing how the strategy plays out in practical terms. They imagine some 'riskless' trades of picking tops and bottoms, always AFTER the fact :(