The Main Misconception of Players in Sports Betting

Despite the fact that success in online sports betting depends not only on luck and pure statistical probability, but, like everything else in the world, bets are also governed by the laws of physics. Before you decide that this statement does not make sense, we need to return to 17th-century Switzerland and check whether one of the most controversial principles in gambling — the law of large numbers — is applicable to sports betting.

What does the law of large numbers mean?

There is no need to understand physics and mathematics very well or to be an expert in science in order to understand how the law of large numbers (abbreviated LLN) works, it is quite simple and can be easily tested in practice.

LLN is part of the theory of probability and considers the result of the same experiment on a large number of repetitions. The more times you repeat an action, the closer its results are to the expected value.

Imagine tossing a coin. There are only two possible outcomes, “heads” or “tails”, and each outcome theoretically has a confirmation percentage of 50%. Now, if you flip the same coin 10 times and record the results, it is likely that 50%-th result is unlikely. In a 10-fold experiment, the result can be even 10 consecutive “heads” and not a single “tails”. However, if you continue to throw, for example, 100 times, the results will begin to level out. If you roll 1000 times, you get an even more balanced number. The more you flip a coin, the closer the results are to an average of 50%.

The coin toss is the easiest experiment to validate the law of large numbers, which is often called the “Bernoulli scheme”, named after Jacob Bernoulli, a Swiss mathematician and mechanic of the 17th century AD. Bernoulli was born into a family of mathematicians and is known among other things for his phrase: “In the end, there is equilibrium in the universe.”

Player’s error

So, let’s put Bernoulli’s theory into practice. Given that repeating a coin toss will produce 50% of the “heads” and 50% of the “tails” in the long run, this certainly means that after 10 consecutive throws with the loss of the “heads” the “tails” should fall for the eleventh time, right? Not at all.

We tend to rely on the law of large numbers to predict the outcome of gambling because of our need to explain the world through repetitive patterns. This theory has been used countless times in casinos, especially in roulette, the results of which are also divided into two possible outcomes. Players, as a rule, apply the “Bernoulli scheme” in roulette, believing that if some result happened too many times in a row, then it will certainly be the opposite in the next rotation. This is described as an error in the dependence of the probability of the result of an experiment on previous outcomes, although theoretically according to the LLN, everything is correct, in practice it is not confirmed.

You have probably heard about this theory, it is also called the “player error” or “Monte Carlo false conclusion”. An incredible story, in whose honor the name of the theory takes place, occurred in the chic Monte Carlo casino on August 18, 1913.

At some point at night, the roulette ball stopped several times in a row on the black compartment. After the eighth time, some discerning players became interested and started betting money on “red”, because according to the “player’s mistake”, “black” significantly exceeded their chances to win again.

Since the “black” fell several more times, almost all the men and women in the casino closely watched the roulette wheel, while even more players now manically set to “red”. All of them acted according to instinct based on the player’s error. It is hard to believe, but the ball stopped on the “black” after a record 26 consecutive spins, no matter what. The entire amount lost that night was never publicly announced, but according to rumors, it exceeded one million French francs, (the official currency of Monaco at that time).

It was a complete revelation of the theory and a constant reminder that a kilogram of practice is worth a ton of theory. It also shows that you cannot predict future results based solely on past results.

Example

As for 2019, almost two hundred matches were held between irreconcilable rivals in the Spanish championship Real Madrid and Barcelona. More precisely — 198. Such a number may bring us somewhat closer to understanding the law. We will take draws as a result that does not give advantages to either side, therefore we will not take them into account. So, the royal club scored 83 victories in the history of the oppositions before 2019, their rivals from Catalonia — 77. Each of these clubs had ups and downs, but the number of victories in general shows us the relative parity between the rivals.

Liverpool and Arsenal played even more matches between themselves before that time — 224 meetings, and there is some equality. Liverpool won 86 victories, cannoneers — 78. The history of the meetings of the Milan clubs also represents the relative equality of victories and draws. Milan has 57 wins with 65 defeats and 56 draws.

Looking at such results, bettors may be mistaken that in the case of equal teams this law also works on a small sample. That is, if on the next weekend in Europe several confrontations are played between the leading teams — for example, Chelsea — Manchester City, Borussia Dortmund — Bayern, Roma — Lazio, then the hosts can win and repeat bets every time a similar caliber team is played in leading continental championships. Indeed, based on the law of large numbers, teams of equal strength in the entire set of matches held among themselves should ultimately yield equal results.

Of course, this is a delusion. After all, the law of large numbers works with significant quantities, in a small period it is not indicative. So once over the five years, “Roma” beat its principal rival “Lazio” 6 times, losing once and reducing three meetings to a draw. Perhaps the same successful segment will be in a couple of years in Laziale.

Does the law of large numbers apply in sports betting?

The reason we are analyzing the Law of Large Numbers (LLN) is to find out if it can be applied to sports betting, where various parameters besides statistical probability can influence the event. The strange thing is that the less likely we are to predict the result, the more we are tempted to follow the LLN. In fact, it is known to most bettors system “Martingale” is completely based on this law, as in the theory of probability of winning your next bet is increased with each successive losing.

How can this be applied to sports betting? The popular betting system was conceived as a “progressive draw strategy.” All you have to do is bet on consecutive matches and double your bet every time you lose. This is especially popular for national team competitions such as the European Championship or the World Cup. Almost all matches (with the exception of the last group matches) in such cases are scheduled at different times.

Draw bets mean you bet your money at odds of 3.00 or higher in matches with strong favorites. You do not need to analyze news, latest reports or other statistics, just bet the initial bet on a draw and wait for its confirmation. If the first match does not end in a draw, you must make another bet on a draw and double it.

It is unlikely that the whole tournament will end without a single draw, but you also cannot know when it will happen for the first time. For example, at the 2014 FIFA World Cup, the first draw was recorded in the 13th match, which took place between Iran and Nigeria. If someone followed the “progressive draw” strategy and started with a bet of 10 units, they would have to bet, for example, 40,960 units on a draw, knowing that they had already lost 40,950 units. There are two questions here: do you have a big enough budget to continue following this strategy after 10 lost bets? And even if you do, are you really prepared to risk losing even more?

How and where else can you apply the “Law of large numbers”?

This law can be applied not only in sports betting, but also in almost all gambling games. Here are some clean examples of the expected deviation. Many have already guessed that casino games, such as roulette, would be the most obvious example. The statement that the even or odd sequences, as well as red or black are aligned in the course of one game session, is erroneous here and may well leave such a “strategist” without money!

A vivid example of this is the year 1913, when a black number fell in a row as many as 26 times on a roulette table in Monte Carlo casino. After the 15th repetition, all the players began to bet on red, believing that the chances of losing another regular black are simply astronomical. By doing so, they clearly demonstrated their irrational belief, where one spin somehow affects the next. Therefore, the concept of “player delusion” is also known among the players as the “Monte Carlo False Conclusion”.

Another example of a “fallacy” for many players is slot machines that operate on the principle of a random number generator with a set PRP (percentage return to the player). The “mistaken” players consider and are convinced that if they invested a lot of money in the machine, then after a series of losses a big victory must come.

Such players can often be found in casinos or slot machines, and watch them keep other players out of their slot machine and ask them to “hold” the slot machine while they go for the next amount of money. But it should be understood that such a tactic is simply not real and a priori cannot be winning, because in order to achieve the coveted PRP, the player will have to play a huge number of times! For an example with the same million, this will require at least 30 days of continuous play on one machine.

Resume

The law of averages says: “Something will happen very soon, if not immediately,” while the law of large numbers expects correction to take place over a longer period.

The law of average values ​​can be used to calculate the most likely result of a single action that is not associated with any previous or subsequent result. As previously shown, this is a misinterpretation or application of percentages or statistics.

The law of large numbers says that in any situation, the results over a long period of time will approach the percentage expectations, since more results are known, but because of the potentially huge numbers, they may never reach the ideal figure.

And moreover

We believe that instead of the laws of averages or large numbers, one should probably just stick to the difference between dependent and independent events and their probabilities.

Removing a card from the deck of cards without replacing the probability of the 2nd draw depends on the result of the 1st, 3rd draw depends on the result of the 1st and 2nd, etc.

And if you flip a coin, the result of the 2nd coin toss does not depend on the 1st, the result of the 3rd does not depend on the 1st and 2nd, etc. This means that for independent events, the results of previous events do not play any role for the current event. The consequences for the races are obvious: since individual races on a race day are independent of each other, the results of the days of previous races do not affect the likelihood of the next race.

It is entirely possible to do without any law if you consider whether events are independent of each other or not. For example, the sixth race does not depend on the first five races; therefore, the outcome of the sixth race does not depend on the first five races. This means that nothing changes the fact that the favorites won in these first five races or not. If the five previous races were not won by the favorite, this will not change the chances of the favorites in the last race.

A similar consideration applies to the full season: the result of the 1000th race of the season, at least in general, does not depend on the results of previous 999 races. Of course, there is some form of dependence on previous results for each horse, but this has nothing to do with the question of how likely it is that this race is won by the favorite.

Or, to put it in other words: the law of large numbers is the correct description of the behavior of independent events, while the law of average values ​​creates a completely incorrect relationship between independent events.

Thus, all that a bettor must really do is to ask yourself: what the outcome of the upcoming race depends? Everything that this result does not depend on, the forecaster can and must completely ignore and forget.