### To bet or to trade that is the question?

Do you trade or really you are simply gambling? That is a good question. The fact is that more than 75% of forex traders lose money and just 5% of them earn enough money to live from trading.

Traders around the world lose a huge amount of money everyday trading in stock exchanges and forex brokers; therefore, the question we proposed here need to be at least investigated.

### The Fair Coin Toss Game as our Neutral Reference

We all know what a fair coin toss game is. It is called fair when the coin is not loaded because the odds of the outcome are fair, 50% chance for both heads and tails.

Let us suppose that you bet one dollar on a fair coin toss game 300 times. What will be its financial result?. How much money will you earn at the end of the game? Since the chance is fifty-fifty on every bet, after 300 bets your best answer may be “close to zero”.
Yes, that can be the case. But not always will be that. Luck plays a role in a game of chances. Let’s find out!

### Ten games

Let’s suppose that ten gamblers are playing against the house in ten different coin-flip games, and record the fate of their wallet, each having an initial \$100 capital.

The beauty of technology is that it facilitates the simulation of real games. Using a short Python code we created and played these experiment. The resulting path of the possible fate of ten players is displayed in Fig. 1.

Fig 1 - 10 Different Games of 300 Fair Coin-toss Games ( click to maximise)

Wow! This is surprising! There are about five traders who ended withing ± 10 dollars from its starting balance. We see that a couple of lucky ones ended with \$12 and \$15 gain. Also, a couple losing \$12 and \$18. And a very unlucky guy who lost close to \$25.

### What is the meaning of these curves?

These curves are what is called random walks. They represent alternative histories of the account balance during the game. Drawing equity paths on games of chance such as these, we can detect easily segments with winning and losing streaks, such as marked in Fig 1 at 1, 2 (winners), and 3,(losers).

We know the rules of this game and, consequently, we also know the gamblers don’t have here any edge. But what if these gamblers didn’t know it? For sure, the lucky ones would be driven to think they had a good trading system, while the unlucky ones would discard it as a losing system.

If we had recorded ten thousand different coin toss games, this would be the shape produced by all  the paths:

Fig 2 -   10,000 Random Paths produced by Fair Coin Tosses

We can see this kind of horizontal smoke cloud spread looks symmetrically from its centre line, the initial \$100 account.

If we plot the final balance on all traders we would get a nice Bell-shaped curve, which corresponds with the Normal Distribution.

Fig 3 - Distribution of Final Results

If we compute the mean and the standard deviation we get:

```Mean: -0.08
STD: 17.6%```

We can deduct from all this that 50% of people would have lost money while the other 50% won.

We can, also, apply what we know about the Normal Distributions and conclude that 68% of all gamblers will fall within one standard deviation from the mean. Therefore 68% of  people will have profits within -17.6% and +17.6%

• 16% of people will lose more than 17.6%. While another 16% will gain more than 17.6%

And, since 95%  of all data in a Normal Distribution falls within two STD from its mean, we can see that

• close to 2.5% of the people will lose more than 35% of the initial capital.
• Close to 2.5% will gain more than 35% of their initial capital.

So

• This game produces close to 19% net losers, and only 19% real winners.

These figures are valid only if we assume that all players will stick to the end. No early exits allowed. The figure increases if we allow people to stop betting because no one leaves when winning.

In reality, trading is worse than this, and I’ll show you why.

Let’s do the smoke cloud of a trading system. Let’s assume we have a fairly good System. 56% winners with a reward-to-risk ratio of 1.  This is a net winning system bettering most trading systems even good traders use, and below its smoke cloud.

Fig 4 - System with 60% Winners and a Reward-to-risk Ratio of 1

Here we can observe 100% net winners after 300 trades. But will all traders respect the rules?

Let’s zoom in on the first 50 trades:

Fig 5 - Zoom in on the first 50 trades

What is visible by looking at Fig 5 is that about 1/3 of traders lose money after 50 trades. But we see that close to 40% of the people lose money past 10 trades.

The distribution of profits after 50 is:

Fig 6 - Distribution after 50 trades

``` Mean: 9.887
Standard Deviation: 6.95```

Looking at these graphs, we could ask ourselves the following questions:

How many people will hold this system 10, 20, 30, 50 trades? My guess is that

• More than 50% of the people abandon the system before having the opportunity to verify its true value because they travel an initially losing path.

Now, how many traders really have an edge? Most traders have rules that work against them.

The majority of people prefer systems with high per cent gainers. To achieve it their reward-to-risk factor is very poor. Usually below 0.5.

Let’s see the cloud of a system with 65% gainers and 0.5 R/r.

Fig 7 - A system with 65% Winners and R/r = 0.5

```Mean: -15.84
Standard Deviation: 23.62```

These two graphs are the result of the psychology of the average rookie trader. The end result of letting losses run and cutting gainers short.

• The system + trader is a net losing system, with a mean of -15.85% loss after 300 trades.

Traders will not wait for 300 trades to default, not even, 50 or 30, before 20 trades they leave the system and start trading another one. The systems might even be good, but the way it is traded makes it a loser.

On this case, we see that 66% of people have lost money after 300 trades.

If we add some percentage of the previous group (who have defaulted a good or bad system), and then people whose trade size is excessive,  we easily reach the same figures that the regulatory authorities claim.

### To Conclude

• We see that most of the people can be fooled by random paths.
• A net winning system can become a loser when you mix the psychology of a trader
• Even when the system is good there are paths, short term, that are losers due to losing streaks and random causes.
• To the majority of traders, trading can be even worse than gambling.
• The house and the broker has an edge, because traders have a discrete amount of money to lose, and the combination of randomness, bet size, and trader’s psychology makes this game a net loser for uninformed traders.

Trading Systems Analyst using robust statistical methods including Monte Carlo resampling. I've been trading my own account for the last 18 years and became a full-time trader in 2013. I hold a degree in Telecommunications Engineering by Univ. Autónoma de Madrid, and a Master in Business Administration and Marketing by Univ. de A Coruña. Skills: System Analysis, Money management, risk, and position sizing.