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You are talking about a winning and a losing system. If the both the winning system and the losing system persists over a longer period of time, this simply means
- that you have streaks of bets with a higher expectancy, and streaks of bets with a lower expectancy
- or otherwise put that the trades a positively correlated
Now assuming that the bets of the winning and the losing system taken my themselves do not show any correlation, the overall system will show positively correlated bets. This can be exploited by adapting position sizing via progressive betting.
I have not checked them, but I think that @Nickemp's results are genuine. So what he clearly showed is that his progressive betting approach increased the returns relative to the win rates.
The point is not the (correct) result, but the explanation.
By using the progressive betting system, he also doubled position size. For any system with a positive expectancy, if you double your position size, you will double your returns. If you trade 1 contract over a year and get a return of $ 30,000, you will possibly earn $ 60,000 when trading 2 contracts. This also implies higher risk.
When you apply a progressive betting system to uncorrelated bets (which makes no sense), you may still benefit from the side effect of increased position size. But then you do not need the system, you can simply double your position size and leave it that way, which would even reduce the dispersion of the cloud shown on the graph presented by Nickemp.
I thought the strings would equal out because they are based on a 50% chance. It doesn't intuitively make sense to me either and you explained the reasons why much better than I could have. Most of my "thanks" have been to you btw for taking the time to be helpful so often.
Here's where I am now.. If the expectancy of extended strings to occur regularly is valid and the loser at the end doesn't wipe out the profit margin - increasing the position size accordingly is no longer an uncorrelated bet.
I bet others will eventually tinker with and replicate Nickemp's work and that might be more convincing.
Maybe it's just over my head - I can't calculate what the results would be for a larger fixed position size on all trades in my head - but it doesn't make sense to me.
If raising the wager 50% at the start of a string is the optimal betting size; the success of isn't because you have any better chance on that next flip. Rather the combination of strings occurring naturally, compounded with the continual increase in leverage, would make the average return greater on whatever the likely hood of having long enough strings or/and enough of them.
If you look at nickemp's chart in post # 75, the red dots represent the expected return using a fixed bet of $500.
For instance, the chart shows that the expected return is about $75,000 if you have a 55% success rate and bet $500 each time. If you were to double that bet to $1000 rather than $500, the expected return would double to $150,000. The distribution of blue dots suggests that the string betting system with a $500 starting bet might give you a $150,000 return, or it might not, depending on how the strings play out.
So here's the question: assuming you want to target that $150,000 return, what's the best way to do it:
1. Use a default $500 bet size, and increase it after each win, so that some bets are $500 and others are $4000 or more depending on the outcome of the preceding bets; or
2. Use a default $1000 bet size and don't alter it based on the outcome of the preceding bets.
I would expect choice 2 to give you a more predictable and stable equity curve, without those gut-wrenching large losses that occur at the end of each string of wins under the progressive system. So if you can afford to make your default bet $1000, in most cases I'd see this as preferable to the string system. Unless, that is, the results of your trades are correlated, which is a question I'm personally still grappling with.
We have now discussed it over and over. Let me just state again the essential point to understand progressive betting.
Essentials
(1) A progressive betting system uses the outcome of the prior trade to establish the position size of the following trade. This is the definition of progressive betting.
(2) If the outcome of the following trade does not depend on the prior trade(s), this does not make sense.
(3) If there is a dependency, progressive betting can have a positive or negative impact.
Side Effect
A progressive betting system always has an impact on position size. If you increase position size, you increase the returns for profitable bets, but increase the losses for non-profitable bets. Your returns will be better but your risk of ruin will be higher as well. The side effect can also be observed for non-correlated bets.
Martingale and Anti-Martingale systems
A Martingale system increases the bet size after a loss. It can be used when the outcomes of consecutive bets are negatively correlated. Example: Black Jack.
An Anti-Martingale system increases the bet size after a win. It can be used when the outcome of consecutive bets are positively correlated. Example: Pyramiding Trades
This is a crucial point. It really depends on your trading system and whether it is the type of trading system where the result of one trade is influenced by the previous trade or not.
For example, a few types of systems that usually will have dependencies include: always-in systems, trend-following systems that take every trade without skipping any (winners are more likely after a series of losers and vice versa), and mean reversion systems that take repeated entries on the same MR setup even if the previous entries have failed (each consecutive attempt to catch the same falling knife will have higher probability of success, and if you keep trying, eventually you will catch that falling knife)
If, however, your trading system is the type that is not usually in the market and waits for a certain setup to occur, then the chances are smaller that there will be a dependency between the trades.
So far, a few brokers have offered CL in their portfolio.
It is expensive. About $30 USD per lot transacted.
I have been using a Mini-Lot broker, 10,000 units = 1 lot for my automated GBPUSD trading. So far it is good because I have a Grid/Martingale …
This sounds very impressive, but is the simplest of all progressive betting systems. You will know this from Roulette:
You start wit $ 1 and put it on black. If you win you get another $1. If you lose, you double up and bet $2. You continue doubling up until you win. This way you will always win. For example if you experience 10 consecutive losses (probability is around 1:784) and then win, your profit is Profit = $ - 1 - 2 - 4 - 8 - 16 - 32 -64 - 128 - 256 - 512 + 1024 = $ 1.
The problem of such bets is the asymmetric risk profile. Every casino has a limit, and let us assume that the limit of the casino is $ 50,000. With 16 consecutive losses (probability around 1: 42,777) you cannot continue to play. Statistically you will have 42,776 winning strings with a profit of 1$ and one losing string, which comes at a combined cost of $ 65.535. The difference is the edge of the casino.
Now, if you want to apply that wonderful system to trading, you can get yourself a Grid Martingale Expert Advisor. It has different levels for averaging down, so you can play it in the way you can play Roulette. Now, if the bets are uncorrelated, your account will prosper for some time, before experiencing a sudden death.
The only way to make money with a Martingale System would be to find a system that produces bets, which are negatively correlated. Does anybody have some evidence that such a negative correlation can be exploited?
I spent weeks studying Vince 8 years ago and setting up excell files of a 35+ year trading history to calculate optimum f on my personal trading history.
Well worth the effort, and it uncovered that my bet sizes were often way too big. It also reduced my overall market exposure, and confirmed a kind of anti-Martingale approach of the type Vince discusses in his "Leveraged Trading Space"
But even @ optimum f, I still didn't like the drawdowns, and the potential drawdowns, especially when trading in highly correlated assets in leveraged positions, although the run ups were exciting.
Then I found that adjusting optimum f for the biggest drawdown /size of loss I'm willing to suffer helped both my trading and my disposition.
Thus, I now use Optimum f % x total equity bet size/largest loss % =bet size/1% of equity. Such sizing also permitted more reliance on trading signals for exits rather than stops.
Then I increased the number of systems I traded and expanded the asset classes involved in an effort to reduce the overall correlation of the different bets in the portfolio.
Seems to work OK and add consistency, but there is more effort to time and monitor many more asset classes/positions, plus be worried about how everything seems to be correlated these days. A lot of work for a lone trader.
Indeed, a resource on correlation coefficients would be most helpful.