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# What is the theory of probability in betting

The theory of probability in bets is the study of the influence on them of random events, patterns and operations. The theory of probability (TV) itself is based on the belief that all random events are not random and are subject to a pattern that can be explained mathematically.

For the first time, scientists became interested in this direction back in the XX century, and for the first calculations they used gambling: roulette and dice. This was done for a reason, but with the aim of explaining the phenomenon of a casino, which always wins in any case. It was then that the first calculations were carried out and formulas appeared that make it possible to calculate the theory of probability.

To make it clearer, let’s look at a specific example. Probably the easiest of these is to flip a coin. As you know, any coin has two sides: heads and tails. If you throw it in the air, it will fall either on one side or on the other, that is, the probability of falling heads and tails will be 50%, 1/2 or 0.5. But in reality this will not happen, and why, we will tell later.

## Basic terms

Before talking about what the theory of probability in sports betting means, let’s look at the basic terms, which we will need to understand in the future.

**Probability** – the degree of possibility of a certain event occurring, which is expressed in whole and fractional numbers from 0 to 1.

**Event** – the resulting outcome as a result of performing certain actions. It is of 3 types:

- Reliable (the coin will definitely fall);
- Impossible (a coin cannot hang in the air);
- Random (randomly heads or tails).

**Expected value** – addition of possible outcomes and multiplication by the probability of their obtaining.

**Dispersion** – deviation from the mathematical expectation by a certain amount. If, again, consider the example with a coin, you can remember that the probability of getting heads and tails is the same: 50% each. But in fact, one of the sides can fall 5, 10, or even 20 times in a row. This is the deviation from probability. But over a long distance, the situation will level out.

## Probability theory in betting

So, we have considered the basic concepts, and now it remains to figure out how TV is connected with sports betting. And it is directly related, since any game in sports is an event with certain outcomes, the probability of which can be calculated.

Let’s return, again, to our example with a coin: there were only two possible outcomes with a probability of 50%. In sports betting, everything is much more complicated, because in most matches the opponents are not equal in strength, plus you need to determine not only the victory of one of the parties, but also other outcomes, such as handicaps, totals, and so on. This is exactly what bookmaker analysts do, determining the probability of each of the outcomes and converting this value into odds.

The bookmaker coefficient shows the probability of passing the event. It can have different forms (decimal, fractional, American and others), but in the countries of the former Soviet Union, it is the decimal ones that are most popular. If you divide the unit by the coefficient, you can find out its percentage. This is a simple formula for defining the theory of probability in betting.

**For example:**

- a coefficient of 1.5 will have the following probability: 1 / 1.5 = 0.66 or 66%;
- coefficient 2.3 will have the following probability: 1 / 2.3 = 0.43 or 43%;
- a factor of 4.7 will have the following probability: 1 / 4.7 = 0.21 or 21%.

This is how the odds are formed in bookmakers, and the probability of a particular outcome is determined by analysts using special programs that take into account hundreds of different factors. But, speaking of the odds, it is important to consider one more point: the bookmaker’s margin.

## Why does a bookmaker need margin

The bookmaker’s margin is his insurance against losses, his guaranteed winnings. Analysts in the bookmaker calculate the probability of the passage of events and convert it into coefficients. To make it clearer, let’s look at a specific example in the match between Atletico Madrid and Liverpool.

We see that the bookmaker gives the odds of 3.36 for the home win, 3.36 for the draw, and 2.32 for the away win. Let’s convert this to percentages:

- 1 / 3.36 = 0.297 or 29.7%;
- 1 / 3.36 = 0.297 or 29.7%;
- 1 / 2.32 = 0.431 or 43.1%.

And now it adds up and we get the following: 29.7 + 29.7 + 43.1 = 102.5. But the probability cannot be more than 100%, so where did the extra 2.5% come from? This is the bookmaker’s margin, his percentage that he takes for his services. And that particular margin is still very low, usually bookmakers charge between 5% and 10%. You can read more about what margin is and what its effect on profit is in our article.

## Mathematical expectation and variance in rates

Above, we have already given a definition of the terms expectation and variance, and now it’s time to look at them in practice. For ease of understanding, again, let’s take our coin example. We have already written that the probability of getting heads and tails is 50% each, but in practice one of the sides can come up many times in a row.

So, many bettors believe that every losing bet on an event with a 50% probability of passing only increases the likelihood of winning the next time. That is why the Martingale strategy is so popular among many, it is also catch-up. It assumes the following: with each subsequent bet, the player doubles the amount of the previous one in order to win back and make a profit. But here you need to understand that in most cases such a strategy leads to a loss in the distance just because of the variance.

If you rely only on the mathematical expectation, then after a loss there should come a win, but this does not happen, and the deviation from the mathematical expectation is especially noticeable at a short distance. For example, if a player makes 10 bets, he can easily lose 7 of them. After 50 bets, he may already have 22 wins and 28 losses, and after 100 – 46 wins and 54 losses. Of course, it can be vice versa, here it is already a matter of chance.

As you can see, the result evens out over the course, but 100 bets is too short a distance for evaluating the results. You need to look at 1000 and the balance turns out to be even at best, and often negative because of the margin. So how do you beat the bookmaker? – Now we will tell you.

## Why does a player need mathematical analysis

Mathematical analysis is very important in making a prediction for the match and determining the probability of passing certain events. It is in this way that analytics’ coefficients are calculated in bookmakers. Many professional bettors compete with bookmakers in the analysis of matches and independently calculate the probability of outcomes for themselves using mathematics.

In particular, the calculation takes into account the current form of the team and each of its players separately, the average number of shots, corners, missed chances, cards and many other factors. Based on all this, the bettor makes his own forecast with a percentage probability for each outcome. What is it for? – You will find out now.

## Gambling on value bets

A value bet is an underestimated, according to the bettor, event in the line of the bookmaker’s office. Simply put, the player, according to his own calculations, sees the probability of one team winning at 60%, and the bookmaker at 50%. Accordingly, the odds for this will be higher, so such a bet is profitable from the player’s point of view.

Many professional bettors play exclusively on value bets, and this is a really profitable strategy at a distance with one “but”: the player must know the formulas of the theory of probability on bets, what is mathematical analysis and how to apply it in relation to each specific match. You can read more about value bets in our article.

## Should you trust the theory of probability in betting?

Finally, we come to the answer to the most important question: **can you trust the theory of probability in betting?**

If you use value bets, then you can and even should. The most difficult thing is to correctly identify the events that the bookmaker estimates incorrectly. When betting, you must have your own margin, which can bring profit over the long term. If you place every bet on an outcome that you think is 10 percent or more likely to pass than the bookmaker suggests, this is a good bet.

The main problem here is that it is very difficult to give an objective assessment of the upcoming match, and statistics do not always help with this. In any case, the subjective component influences the forecasting, that is, how the analyst sees this match. You need to understand that the result of a future match will not depend on the results of the head-to-head meetings of these rivals earlier. Of course, it is worth considering, but not as a major factor.

Based on all this, we come to the main idea: the player must take into account the theory of probability in the bets, because it will definitely help him in the long run. If the bettor will correctly determine the rates with inflated odds, this will bring him long-term profit, when we are not talking about 10 or even 100 bets, but about 1000 or more.

The average average player will not bother with all these calculations, he bets based only on his vision of the situation and only a few factors. But an experienced professional player differs in that he is not just well versed in the sport he bets on, and is also able to calculate different options from a mathematical point of view, he understands the laws of probability theory and uses it for his own purposes.

Finally, I would like to say that it is precisely because of the theory of probability that an ideal win-win strategy in sports betting has not been developed, and will not be. It will not be possible to find a ready-made solution, you need to get it yourself by trial and error and by improving your skills.