# Chapter 15. Comparison of Forex and Casinos

There are many articles on the Internet, where working in Forex is identified with playing Casino, in particular roulette. The authors of the articles express various arguments, cite mathematical calculations from the probability theory, often without understanding them at all. In this chapter we will try to dispel the myth that Forex belongs to gambling.

The game of roulette is as old as the world. It can safely be called one of the ingenious inventions of mankind. The device roulette and the rules of the game is very simple. But behind the apparent simplicity of winning hidden mathematical laws that bring billions of dollars a year of profit gambling establishments and ruin every year millions of hunters for luck. Let’s try to understand the structure of roulette and understand why playing it is impossible to get a stable income.

In probability theory, two concepts are fundamental: an event and the probability of an event occurring. An event can be defined as anything. A sunny day after a series of cloudy days, a strike of workers at a factory, a chance meeting with an old friend on the street, an accident on the road, a flight delay due to a technical malfunction of the airplane – all these are events that occur with a certain probability.

Among the countless events, there are those that can occur simultaneously (then we are talking about a complex event), and there are those that are mutually exclusive and can never occur simultaneously. For example, you may go outside and meet your old friend near a factory where there is a workers’ strike on a warm, sunny day. In this example, the three events happened at the same time. And such events as, for example, a sunny day and a rainy day are mutually exclusive and will never occur at the same time. It is easy to understand that the probability of occurrence of a complex event is much less than a single simple event included in a complex event, because for the occurrence of a complex event several factors must coincide at once.

Let’s consider another, classical example – a dice. A dice has six faces, each of which has a number (from 1 to 6) printed on it with dots. One of the numbers falling out when throwing the die is an event. Only one number can fall out at a time during one throw. Thus, there are only 6 variants of events when throwing a die, and all of them are mutually exclusive.

It is clear that when we roll a die we will always get a number. That is, the probability of a number falling out can be taken as one or 100%. What is the probability of a single number falling out, for example 1 or 5? Are these probabilities the same? Let’s try to understand this.

In probability theory there is a concept of probability distribution. It is a function of the probability of occurrence of an event from the event itself. We will not go into details, and we will tell only that falling out of numbers on a dice has a uniform probability distribution, i.e. probability of falling out of different numbers is the same. It occurs because the dice has the correct form and uniform density. As there are only 6 numbers on the cube, the probability of falling out of each number separately is 100 / 6 = 16.6666…%.

The next important stage in mastering probability theory is the theory of large numbers. In our example with a dice, its meaning is that if we toss our dice very many times, then each individual number will fall out in proportion to the probability of occurrence of its event. And since all six numbers have the same probability of falling out, each number will fall out the same number of times. And the more times you roll the die, the smaller the error of this statement. The error approaches zero at the number of throws approaching infinity. Thus, if we toss the die 1,000,000 times, each number will come up about 166,667 times with a certain margin of error.

What if the probability distribution is not uniform? Suppose we covered one of the faces of the dice with lead, thus changing its density distribution. The probability of falling out the number 1 became equal to 50%, and the probability of falling out the remaining 5 numbers remained the same, 12.5% each. Now, if we toss the die 1 000 000 times, number 1 will fall out approximately 500 000 times, and other numbers approximately on 125 000 times each.

Let’s return to roulette. There are 37 cells on the field: numbers from 1 to 36 and one zero (0). The distribution of probabilities of numbers falling out in roulette as well as in the die is uniform. So, the probability of falling out each individual number on the roulette is the same and is equal to 1/37. Payable casino winnings in the case of guessing (falling out) separately taken number is equal to 1:36. It turns out that for every ruble we bet with a probability of 1/37 we will get 36 rubles. According to the law of large numbers, if we play roulette X times, betting each time a ruble on one number, our winnings will be:

36/37 * X – X =

X * (36/37 – 1) =

-1/37 * X

You have understood everything correctly – the minus sign in the resulting formula just means your loss and the casino’s winnings. It does not matter what numbers you will bet on. Constantly on the same or all the time on different – the formula from this does not change. Again, the larger X is, the smaller the error of the formula. With a small value of X the margin of error can be large, so if you came to the casino, made a few bets, won, left and never went back again – the casino has made a loss on you. But once won, few people can stop – playing roulette becomes a lifestyle. In the hope of winning again, a person returns, begins to play constantly and often. The number of games played increases, the error of the formula decreases, and eventually the person loses. Even if a particular person after a big win in the casino will never return, there will still come others, new hunters for luck, and the gambling business will flourish.

One note should be made. Judging by the formula it turns out that playing a thousand games on the ruble, the player loses only 1/37 part, ie about 27 rubles. At this rate, you can stay afloat for a long time enjoying the game. In fact, few people play roulette on the ruble, a person is ruined by his own excitement. Making risky big bets man comes to the fact that his capital is not enough to win back. This is what leads to ruin – lack of funds for further play (wagering). If all players were billionaires, they could play for a long time losing only 1/37th of their bets.

1/37 is about 2.73%. This is exactly the casino’s advantage over the player. In the American version of roulette (unlike European roulette) there are two zeros (0 and 00) on the field. In this roulette casino advantage to the player 2/38 – this is about 5.26%, which further tightens the conditions of the game.

Of course in roulette you can bet not only on one number, but also simultaneously on 2, 4 or a whole series of numbers. But with such bets proportionally reduced and payout winnings, ie, the formula does not change. The casino always wins, and its expected profit can be calculated mathematically. On European roulette it is 2.73% of all bets of all players, in American roulette it is 5.26%. For other games also have their own formulas for calculating the probabilities, and accordingly the expected profit of the gambling house. The real profit of the casino differs from the expected profit due to the fact that people simply do not have enough money for wagering – they lose everything.

That is why you can not get a stable income in the casino. With Forex, however, things are completely different. Here we also have events (decrease or increase of currency rates against each other) and probabilities of their occurrence. But the distribution of these probabilities is uneven – it is impossible to derive a clear mathematical formula. Moreover, these probabilities are predictable, and if you properly use forecasting (analysis) tools, such as technical analysis and fundamental analysis, you can get a stable income on Forex.

Why the seemingly chaotic behavior of currency rates can be predicted, we will discuss in detail in the following sections of the site. Now let us just say that the movement of currency rates is created by people themselves (brokers, dealers, Internet traders). If the majority of them buy currency (bullish mood prevails), its rate goes up. If the majority of them sell the currency (bearish mood prevails), its rate goes down. If you can determine the market mood in time and get on the side of the majority, you will get stable profits. Since the majority of Forex traders use similar analysis tools to determine the market mood, all you have to do is to follow the majority, to do like everyone else.

One important caveat needs to be made here. The majority in Forex in this formulation is defined not by the number of traders, but by the volume of transactions they make. Only experienced traders – dealers of large investment companies, investment funds, banks – make large deals on the currency market. These are people with special education, many years of work experience and a huge luggage of knowledge. To trade successfully on Forex you need to copy the model of behavior of such people on the currency market, and this is impossible without appropriate training.

Therefore, before you start working on Forex, you should properly study this market, as well as the tools that professionals use to predict its behavior. This is the only possible way to success!

So, as you can see, working on Forex has little in common with playing roulette. Continue studying the material of the site, and you will learn a lot, which means that in time you will receive a stable income on Forex. The size of this income will depend solely on you. Your success is only in your hands!