# Is Trading Gambling?

Variations on this question have been sparking arguments in my comments sporadically since I joined Crypto Twitter. As with many arguments, this one is characterized by plenty of opinions, a few personal attacks and very little real information. This article is aimed at clearing up an all-too-common misconception.

First, allow me to state that no, trading is not gambling if done properly.

As we will see, there is a difference between proper trading and gambling, and even historically profitable traders can be gamblers without realizing it. While most of this article will be in plain, easy-to-understand English, I will recourse to a few mathematical equations and graphs to prove my point.

First, let’s clarify the definition of gambling. Dictionary.com defines gambling as follows:

The activity or practice of playing at a game of chance for money or other stakes.

or

The act or practice of risking the loss of something important by taking a chance or acting recklessly.

The key element in either definition is the presence of chance in the equation, or randomness, upon which the participant stands to either gain or lose. At first glance, this seems exactly like trading; a speculator places a trade with an uncertain outcome, either a gain or loss to himself or his investors. So how can I argue that trading is not gambling?

The answer lies in our expectancy of the outcome, or what we stand to gain or lose through repetitive exposure to the game. While I would agree that taking one trade is a gamble (as there is a chance of both gain and loss), the art of trading well lies not in winning a particular trade, but in performance over an extended sample of trades and removing the element of chance from the equation over a long enough time horizon, while maintaining our ability to continue placing trades (longevity in the game).

Allow me to demonstrate using some math. First, let’s take a look at some probability. Our probability formula is as follows.

Let p=the probability of our event, in this case a positive or negative outcome (we either win or lose money).

Our equation looks like this: P=(number of favorable outcomes)/(number of possible outcomes).

With some simplification, we can see that we have a 1/2 chance of earning money, and 1/2 chance of losing money, expressed as P=1/2

Now, consider that (for example), we have a tested strike rate of 40% and always use a risk/reward ratio of 1 part risk to two parts reward. Our calculation looks significantly different at this point, with our probability value now being P= 2/5, but this does not take into account how much we make vs. lose on a given trade. For that we need another formula. Let X be our expected profitability, with P_1 being our probability of a win (2/5) and P_2 our probability of a loss (3/5).

X = P_1 x (win result) - P_2 x (loss result)

or

X = ([2/5] x 2) - ([3/5] x 1)

If we simplify this down we see that X = 1/5. In plain English, this means that we have a 20% edge over the randomness of the market over a long enough sample size (a negative fraction would be a negative expected edge). This is similar to the operation of a casino, in that they are gambling on the individual results of a hand of blackjack, but because of the number of hands played, *they are guaranteed to be profitable in the long run!*

Now, I must admit that this guarantee is not quite accurate in our situation or that of the casino. After all, what happens when a billionaire walks in, plays a hand for 100 million and wins? Just as a casino has rules in place to prevent that from happening, a skilled speculator will also have rules in place to prevent a large loss or a string of losses from depleting his bankroll. Let’s take a look at a graph of randomly generated motion. This will represent our trader’s portfolio at a 50% strike rate, and 1/1 risk to reward ratio, truly even.

Now, with the starting value set at 25 and standard deviation set to 1(to represent the binary value of a win or a loss), we can see that the value fluctuates quite a bit. Now imagine that each point represents $1,000 and our investor started with $25,000. This graph would match his performance perfectly. Now, using the same starting point and rules, consider this chart, randomly generated from the same source:

Obviously, in this scenario the trader is now bankrupt. We call this an absorption barrier, as once the trader’s portfolio has hit 0, he is no longer able to continue trading. Now, by limiting his downside and maintaining his 20% edge over the market as calculated earlier, he has a much better outlook than the above chart. However, we are curious; what are the odds that our trader has an exceedingly bad string of luck, and manages to go bankrupt anyways? Let’s calculate the odds of a 25-streak loss. Our formula for this is (let Y = probability):

Y= (P_2)^f where f = the streak

or

Y = (3/5)²⁵

Y = 0.000002843.

That’s a ~2.8 in a million chance. Not too likely, but still possible right? Now consider that instead of risking an entire $1,000 each trade, our trader chooses only to risk a dynamic 4% of his account ($1,000 on the first loss, $960 on the second, $936 on his third, etc.) and this trader can never run out of money, and while the odds are in his favor, if he continues to trade for long enough, he will gain from it. Note that since these equations are non-linear, a decrease in risk-per-trade decreases the risk of bankruptcy by an equivalent order of magnitude before factoring in dynamic risk adjustment. In the same way a casino does not worry about strings of losses, neither does a competent trader. Neither are at risk if they are behaving properly according to their system.

Without the element of risk within the system, there can be no gamble. Trading within a well-defined and tracked system removes the aggregate risk from the equation, and much of the confusion comes from the traders going broke who lack such a system. An individual trade may be a gamble, but within a proper system, the risk is removed.

*In a future article, I will cover various methods for discovering, tracking and maintaining a trading edge over the market. If you enjoyed this article, please leave it a few claps and give me a follow here on medium and on twitter! @IDrawCharts*

Please note that the mathematical equations used in this article are basic, and do not account for all possibilities, such as combinations of wins and losses leading to bankruptcy. These are rarer singularly due to path dependency, though not in aggregate. For the sake of brevity and reader comprehension, Brownian equations dealing with randomness and stochastic barriers (portfolio performance expectations / risk of bankruptcy) have been “abbreviated” into less rigorous though more easily understandable mathematical functions which are functionally similar. The effect remains functionally identical, so as to to model risk as having been effectively eliminated within a proper trading and risk management system.