In this chapter we will explain what probability is, how it relates to trading and most importantly, let you simulate 'trading an edge' and see how the probability model works out when you are actually trading it. The outcome of these exercises will engrave a deep understanding of what you can expect in the market once you have completed your training, and have set your first steps into a live trading environment.

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Knowing exactly what the probability model is that you are trading, and how probability models behave is CRUCIAL to you trading success as it defies 'normal' human instinct. Without properly understanding its behaviour and doing the exercises that we will ask you to do, it will be nearly impossible to become a successful trader. So please and I cannot stress this enough, don't think you understand what is being taught and skip the exercises. They are incredibly important and when performed correctly are there to reprogram your subconscious brain.
 

TRADING AN EDGE

As traders we are looking for an "edge" to trade. An edge is comprised of two things; probability and Risk/Reward. For now we will discard the Risk/Reward part of the formula and solely focus on the probability side of things.

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Trading an "edge" in this case means that giving a set of conditions that when present, the probability for our trade to work out in our favor is greater than for it to not work out. In other words: "Probability is a measure quantifying the likelihood that events will occur. Probability quantifies as a number between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty."

Without getting all math crazy let's dig a little deeper into it: Probability = number of wanted outcomes / number of possible outcomes.

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As an example let's use the flip of a coin as an example. There are two possible outcomes when flipping the coin: heads or tails. When we flip the coin it can only land on either side. So what the is the probability of flipping a coin?

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Let's calculate: Probability = number of wanted outcome (head =1) / number of possible outcomes (head or tail = 2). The above equals to 1/2 = 0,5 or 50%. So far not that hard right? Let's play a game.  You win $100 when flipping a coin and it lands on head and lose $100 when it lands on tail. After playing 10 games, what would you have made in total?

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I bet your answer would be $0, right? However you might also have a feeling that when played 10 times the odds of it landing 5 times on heads and 5 times on tails might be slightly off, am I right? So by increasing the number of throws the probability model has now changed somehow. But how?

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Before we dig any deeper into this, first let us do an exercise. I want you to pick a coin and toss it 200 times. When flipping the coin, use the "Coin Toss" excel sheet, that is attached to this chapter on the right side of this page. Whenever the coin lands on heads, select head and whenever the coin lands on tails, select tail in the excel sheet. Preferably perform this exercise 4 times over and saving all four versions.

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So now that you're back and you have completed the coin flip exercise, what did you find out? I bet you expected the probability model to work out straight away, or certainly after 20 or 30 flips, right? Maybe the 50% split between heads and tails already played after 20-30 flips. However in most cases this will not be the case.

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The 50% change plays out perfectly when only flipping the coin once, however when we add more flips, the math appears not to work any more until we flip the coin at least 100 times. Flipping it a 1000 times will reveal its true probability being the 50%. So why is this? The answer is "the law of large numbers" and "random distribution". By understanding and embracing these two universal laws you have taken the first step towards becoming a consistency profitable trader. Let me explain both of these laws in detail.
 

THE LAW OF LARGE NUMBERS

In statistics and probability, the law of large numbers states, that as a sample size grows it gets closer to the average of possible outcomes. As you have seen for yourself while flipping a coin hundreds of times, it will take on average 100 flips before the 50% split between heads and tails is mostly realized. With every flip after that increasing the  average probability of 50%. Flip the coin 1000 times and you will get a perfect 50%. Every time!

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This is how casinos make money. They have an edge on every game they offer, ranging from a 0,5% edge on card games (if you are really good) to 35% on slot machines. It is estimated that on average most casino's have an edge of 3% over all the bets they take. Casinos don't care about the outcome of any specific bet, they know that with a large enough sample size, their built-in edge of 3% will play out.That's not much you think. However if you consider that 1000's of bets are placed every day that 3% quickly adds up. 
 

RANDOM DISTRIBUTION

By now you have grasped and understood that in order for your probability model to play out, you need a large sample set. But why is this? Why is the outcome of each individual trade completely disconnected and unimportant to the probability model it is part of?

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Statistically this phenomenon is called "standard deviation". During our coin flip exercise you will have discovered that is takes quite a few flips before we go from a "high standard deviation" - meaning results are left and right from from the true probability - to a '"low standard deviation" meaning results are close to the true probability In our case 50%.

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And this is reason #1 why new traders fail in the market. They don't understand a) the law of large numbers and b) the random distribution of winners and losers. They learned that their strategies yields a 80% strike rate (probability) and expect that strike rate to translate into money within the first 10 trades they take. Not taking into consideration the emotions a trader must cope with when trading real money, and learning how to enter and manage position correctly while experiencing these emotions, the reality is that when taking 10 trades with a 80% strike rate will probably not yield 8 wins and 2 losses. You need a large number of trades for you probability model to work out, AND the results of each individual trade is complete disconnected from past or future trades and therefore unimportant.

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Just like with the coin toss where you may have tossed heads 5 times in a row, statistically one could lose 12 times in a row with an 80% strike rate! Certainly new traders, when breaking even on the first 10 trades,  will wonder why their strategy isn't working. Most of them will either quit trading before the edge has a change to play out or search and try a new strategy that promises even greater results. Thus resetting the law of large numbers of that probability model once again. 
 

PROFITABILITY MODELS

Now let's talk about the two types of strategies that define an edge. The two ways a strategy can be profitable are:

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High Strike Rate - this is a strategy where you win more than you lose. Normally your risk is equal to your reward for these type of setups. For instance, you risk $100 to make $100. Our type-A setups, that you will learn about later in this masterclass, have an 80%+ historical strike rate with a 1-to-1 Risks-to-Reward (RR). Meaning if you were to risk $100 on such a trade, the minimum reward would also be $100 and the trade would play out at least 80% of the time (considering the law of large numbers and the law of random distribution).

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I emphasize this as just a strike rate percentage on its own without RR means nothing. For instance our very same strategy might also yield a historic 90% strike rate when risking $100 to make $20 - which is only 1/5th of the move. Price only has to move up slightly for our profit target to be hit, which is of course an easier target than price having to travel the additional 4/5th as per our earlier example.

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Of course risking $100 to make $20 is absurd, and no strategy will ever be profitable this way. In stead we would like our RR to be the other way around. Risk 1 to make 2, or 3 or 4 even way more. Step into the world of High Risk/Reward trading.

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High Reward/Risk - with these type of setups you would not win often, but when you do, you win big. Some traders are very successful with only a 30% strike rate with these kind of strategies. They lose 70% of the time but when they win, they win at least 3 times their risk. Let's see how that works:

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• 10 trades in total risking $100 per trade

• 7 losses for $700

• 3 winners for $300 each (1:3 RR => $300 per trade) = $900

• Net profit = $900 - $700 = $200

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Unfortunately losing more often than winning is against human nature and presents a psychological barrier. It requires tremendous amounts of experience and confidence in the edge of the strategy that is traded. Generally new traders like to get their feet wet with high strike rate type of entries whilst building their confidence and slowly moving towards a higher risk/reward style of trading.

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At FXCLUSIVE™ we came up with a brilliant way of encompassing both styles of trading into one simple but extremely powerful trade management style that is part of all four strategies that we teach. It is stress free and takes care of the psychological part of trading where we'd like to win more than we lose but also let's us ride the trend stress and risk free.
 

TRADING AN EDGE

Ok, so by now you have learnt quite a bit. Let me summarize what we have reached so far:

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1. A probability model on works when taking into account the law of large numbers

2. Any individual trade outcome is irrelevant due to random distribution of winners & losers

3. High strike rate strategies win more often than they lose

4. High Risk/Reward strategies don't win often but they do win big

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When putting all this together we can finally explain what trading an "Edge" means in terms of the math behind hit.

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You determine the total number of trades, the probability of profit and loss, then factor in the average size of the profit versus the average size of the loss.

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So for example, say you make 100 trades, win 50 and lose 50. Say the average profit is $10, and the average loss is $5. So on 100 trades, you win 50*$10=$500 and lose 50*$5=$250, for a net profit of $250. You risked $500. The edge is $250/$500, or 50%. That means that you would expect to make 50% of the risk on an average trade.

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For my style of trading, if I make 100 trades, I generally win 80 and lose 20. My average profit is 4 units, and my average loss is 2 units. So on 100 trades, I win 80*4=320 units, and lose 20*2=40 units, for a net profit of 280 units. I risked 200 units, so my edge is 280/200, or 140%. That means that I expect to make 140% of my risk on an average trade.

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As to how difficult this edge is to find, you need a very strong trade identification methodology, and most importantly, an extremely robust risk management methodology.

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What is Trading Expectancy?
Simply put, your trading expectancy is the average amount you can expect to win (or lose) per trade with your system, when a large number of trades are taken (at least thirty to be statistically significant). To calculate your trading expectancy, you need to know three things - your win percentage, your average win, and your average loss.

 

The calculation is as follows:

Expectancy = (Probability of Win * Average Win) - (Probability of Loss * Average Loss)

It's a simple equation, but knowing the size of your trading edge as shown by a large positive expectancy can be quite powerful. The impact this knowledge can have on a trader's confidence, patience, and discipline shouldn't be understated.

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It's easy to understand the power of expectancy by thinking of a casino. The casino has many games which have a small positive expectancy in their favour. The edge for the casino is small enough that the players can go on long winning streaks and make good profits in the short term (thus inspiring false confidence), but if they continue to play over the long term the numbers will be in the casino's favour as, on average, they will make a few pennies for each dollar the player risks. The casino always beats the masses in the long run.

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As traders, we can effectively be the casino while sustaining a much larger positive expectancy at the same time. "At the heart of all trading is the simplest of all concepts - that the bottom-line results must show a positive mathematical expectation in order for the trading method to be profitable." Chuck Branscomb

 

Calculating Trading Expectancy
Profitable trading systems can come in many permutations, so we will look at cases with different win rates, average wins, and average losses. We will also consider a system which has an extremely high win rate, but still fails to be profitable over the long term due to a negative expectancy.

For the sake of simplicity in these examples, let's assume we have a trader who is taking $100,000 positions and risking 1% of the position on each trade, or $1,000.

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High Win Rate, Moderate Reward to Risk Trading System
In this example, we see the kind of trading system results that many novice traders aim for but struggle to achieve. This system produces wins 80% of the time and the average profit (reward) is only slightly less than the average loss (risk). This leads to a strong positive expectancy as we can see. For each trade we take with a risk of $1,000, we can expect to make an average profit of $360.

(0.80 * $700) - (0.20 * $1,000) = $360

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The downside of this scenario is that it's often extremely difficult to replicate. Even armed with a system that should win a high percentage of trades if properly followed, a novice trader will have trouble achieving such a high win rate. Impatience, emotional fear, and a host of other issues are likely to interfere with a new trader following their trading plan, and even slight deviations from the high win rate can cause the positive expectancy of a system to disappear.

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Moderate Win Rate, High Reward to Risk Trading System
In this example we have a trader with a very healthy reward to risk ratio where the average win is just over twice as large as the average loss. The average loss has also been reduced as this trader is actively managing their overall risk and stop levels as trades develop (the last example had either wins or full losses), so while some losses still hit the maximum initial stop of $1,000, many of the losses are considerably less and reduce the overall average. While the win rate has been reduced to 55% due to aiming for larger average wins, we can see that the trading expectancy actually improves overall. For each trade we make with $1,000 risk, we can expect to see an average return of $565 in profit.

(0.55 * $1,600) - (0.45 * $700) = $565

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Unlike the previous example, a trading system such as this one is much easier for the novice trader to find consistency with. The pressure of maintaining a high win rate is reduced, a few rookie mistakes won't kill the trading edge, and the excellent reward to risk will quickly cover a small string of losing trades.

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Low Win Rate, Very High Reward to Risk Trading System
In this example we look at a trader who focuses on keeping their average wins as large as possible compared to their average loss. Although the system wins less than 1 out of 3 trades, the impact of an excellent reward to risk ratio allows for a substantial positive expectancy on their trades.

(0.3 * $1,800) - (0.7 * $400) = $260

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These lower win rate systems can be extremely powerful with a large positive trading expectancy, but they can also suffer from long periods of drawdown with strings of losses. Again, this is a difficult scenario for a new trader, as they will often find themselves changing their approach rather than giving the system time and allowing the trading edge to come through over a larger number of trades.

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Many professional traders have built their careers off systems with a low win percentage, but with wins that are many times larger than their average loss. Most trend following strategies are be in this group. They may take a lot of losses when the market moves sideways, but once they hit a trend they take large profits that cover the losses and then some. As legendary trend following trader Ed Seykota says, "one good trend pays for them all".

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Very High Win Rate, Very Low Reward to Risk Trading System
As you can see, even with an extremely high win rate (in this case 95%), success is not guaranteed. While it might seem a bit crazy to take wins that are only an average of $40 with average losses of $1,000, strategies similar to this are actually quite common.

(0.95 * $40) - (0.05 * $1,000) = -$12

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Even when systems like this have a small positive expectancy, they can still run into major problems. In this example we only lose trades 5% of the time, but as unlikely as it is we will eventually have multiple losses in a brief period.

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This kind of massive draw-down means a huge dent in your equity which is extremely difficult to pull yourself out of, especially if adjusting position sizing to a lower amount to compensate for the loss.
 

Summary

A trading system should have a positive expectancy and you as a trader should understand what that means. The natural bias that most people have, is to go for high probability systems with high reliability. We all are given this bias that you need to be right. We’re taught at school that 94 percent or better is an A and 70 or below is failure. Nothing below 70 is acceptable. Everyone is looking for high reliability entry systems, but it's expectancy that is the key. And the real key to expectancy is how you get out of the markets not how you get in. How you take profits and how you get out of a bad position to protect your assets. The expectancy is really the amount you’ll make on the average per dollar risked. If you have a methodology that makes you 50 cents or better per dollar risked, that’s superb. Most people don’t. That means if you risk $1,000, that you’ll make on average $500 for every trade – that’s averaging winners and losers together.

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Even with a 50% chance of success, a large enough sample will reveal that the gambler can and will eventually take at least 15 losses in a row. Winning streaks and losing streaks are simply a part of the business. As traders, we need to understand that no matter how good our strategies are, we will always encounter a string of losses. How you deal with them emotionally and financially will determine how successful you are as a trader.

 
THE DICE ROLLING EXERCISE

In order for you to fully grasp the law of large numbers and random distribution and to see it play out for yourself, we have created three exercises for you to complete. Also, have one dice ready to complete this exercise.

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Please don't read over this chapter and think to yourself; I know that what is being said is true and have already accepted these probability laws. I guarantee you that you have not when you start trading real capital! You absolutely NEED to do this exercise at least once, I can not urge this enough!

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Please download and open the "FXCLUSIVE™ Dice Rollling Experiment" excel file that can be found at the right side bar on the top of this page. This excel files contains three dice rolling experiments that will perfectly simulate:

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1. the results of trading a strategy that has a 67% strike rate with a 1:1 risk/reward;

2. the results of trading a strategy that has a 50% strike rate with a 1:2 risk/reward;

3. the results of trading a strategy that has a 33% strike rate with a 1:3 risk/reward.
    

EXERCISE 1 - STRIKE RATE

The first exercise (blue tab) simulates a 67% strike rate by letting dice numbers 1-2-3-4 win, and dice numbers 5-6 lose. This simulates a 4/6= 66,67% win rate (or strike rate). The risk to reward (RR) for this first exercise is 1:1, which means that if we lose, we deduct $100 and if we win, we gain $100.

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The first tab is an exercise we have already completed, so please use the two blank tabs to the right (Exercise 1 - Blank-1 & Exercise 1 - Blank-2). 

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For every winning trade a "w" or "W" is entered in column B
For every losing trade a "l" or "L" is entered in column B

Please note, that if for some reason you type in any other letter or number and the cell becomes white, to press CTR-z or from the menu select "Edit - Undo". As this will mess with the formulas in the cell.

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Please complete 100 dice rolls and take a close look at the results. As you'll probably noticed, it doesn't matter wether you have a winning or losing streak. After 100 throws the odds of a 67% strike rate play out no matter what the first 10 throws seem to indicate. 

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You might even have noticed that at mostly takes a while for the probability to play out. This a very common phenomenon. After the first 10-20 throws you might have been in the red and just at break even, but after the 20th throw the law of large numbers kicks in, always. Have you noticed?

Once you completed one test, redo the test on the Exercise 1 - Blank-2 tab. You will be amazed by how different the random distribution of winners and losers will be, but the results quite similar.
 

EXERCISE 2 - RISK REWARD

The second exercise (green tab) simulates a 50% strike rate by letting dice numbers 1-2-3 win, and dice numbers 4-5-6 lose. This simulates a 3/6= 50% win rate (or strike rate). The risk to reward (RR) for this first exercise is 1:2, which means that if we lose, we deduct $100 and if we win, we gain $200.

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The first green tab is an exercise we have already completed, so please use the two blank tabs to the right (Exercise 2 - Blank-1 & Exercise 2 - Blank-2). 

For every winning trade a "w" or "W" is entered in column B
For every losing trade a "l" or "L" is entered in column B

Please note, that if for some reason you type in any other letter or number and the cell becomes white, to press CTR-z or from the menu select "Edit - Undo". As this will mess with the formulas in the cell.

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Please complete 100 dice rolls and take a close look at the results. As with the first exercise, you might have encountered a winning or losing streak right from the get-go. Probably a losing streak. But when we win, we double our loss. Even with a 50% strike rate, we win big. 

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Once you completed one test, redo the test on the Exercise 2 - Blank-2 tab. You will be amazed by how different the random distribution of winners and losers will be, but the results quite similar.

Can you see how Risk/Reward is just as important as a sound Strike Rate? Perhaps even more important.. let's further discuss after you've completed exercise 3.

 

EXERCISE 3 - RISK REWARD + STRIKE RATE

The third exercise (yellow tab) simulates a 33% strike rate by letting dice numbers 1-2 win, and dice numbers 3-4-5-6 lose. This simulates a 2/6= 33% win rate (or strike rate). The risk to reward (RR) for this first exercise is 1:3, which means that if we lose, we deduct $100 and if we win, we gain $300.

The first yellow tab is an exercise we have already completed, so please use the two blank tabs to the right (Exercise 3 - Blank-1 & Exercise 3 - Blank-2). Once you completed one test, redo the test on the Exercise 3 - Blank-2 tab. 

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For every winning trade a "w" or "W" is entered in column B
For every losing trade a "l" or "L" is entered in column B

Please note, that if for some reason you type in any other letter or number and the cell becomes white, to press CTR-z or from the menu select "Edit - Undo". As this will mess with the formulas in the cell.

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Please complete 100 dice rolls and take a close look at the results. When you were doing the exercise, you probably thought to yourself; I am only losing trades, this can't be profitable. However when you completed the test and looked at the results, you were probably shocked that it still payed dividends. 

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This is a perfectly normal reaction to have for most. Because you are losing most of the time, your gut tells tells you that this can't be good. Being wrong - or losing - feels uncomfortable. And this is why new traders place way more focus on being right, than on winning big. They cut their profits short because they don't want to lose what they have. And even worse, they let their losses run because they don't want to be wrong. The combination of both is deadly to your P&L. 

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New traders don't think in terms of probability and risk to reward. They seek an easy "fix" to prove their ego's right. A quick in-and-out of a trade, for a quick win and a good feeling about themselves and their ability to trade. Please let this sink in, because I guarantee you that you will go through this process yourself. Trust me.

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Therefore I recommend doing this exercise every single month for about 6-12 months. It will really help to train your subconscious mind to find peace having with a probability mindset. You will be able to better zoom out of your performance and not let the outcome of the last 4-5 trades determine your future actions or your mindset. You will know and trust your probability model and the law of large numbers to do the heavy lifting.

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You will have accepted that the  random distribution of winners and losers can't be affected, and that the outcome of a single trade is to no importance to the probability model and your results when taking into account a large number of trades.