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Betting System: The Bettor Error or The Gambler’s Fallacy

11 Mins read

Goodbye nice martingales and other pseudo statistical proofs in random domains of betting systems…

Let’s flip a coin.

I tossed this coin once and it landed on tails. Do you think it will come up heads the next time?

I have tossed this coin 10 times in a row and it always landed on tails. Do you think it will come up heads with it the next time?

I tossed this coin 30 more times and it always landed on tails. Do you think it will come up to heads the next time?

There is a good chance that over the course of my launches, following any betting system, you will start to think that next time it will surely stop falling on the same side!

The betting systems make us tend to believe that if, in a random draw, an unlikely result is obtained a large number of times, subsequent draws are likely to compensate for this deviation and give the opposite result many times. In the example above, if pulling a coin I get a lot of times tail, we’ll believe have better luck pulling heads during or subsequent draws.

In reality, the prints are independent of each other. Previous results do not affect the odds of the next throw. With a perfectly balanced piece, so we have at all times an even chance of getting tail or heads.

The gambler fallacy is when a person assumes that a deviation from what usually happens or in the long term will be corrected in the short term. This error looks like this: X appears, but in fact, X is not supposed to appear on average or over the long term. Therefore, according to a betting system or the player intuition, X will eventually no longer appear.

This betting systems error is made in two common ways. In either case, a person assumes that some results must appear, simply because what happened before is a departure from what they expected on average or over the long term.

The first concerns events whose probabilities of occurrence are independent of each other. For example, a throw of a correct coin (two-sided and not rigged) does not affect the outcome of the next throw. Therefore, every time the coin is tossed there is (ideally) a one in two chance that the heads side will appear and the same percentage chance that the tails side will appear.

Suppose a person flips a coin 6 times and gets the heads side each time. If he concludes, following a betting system, that the next pitch will be tails because he thinks it should be, then he will have made the bettor error. This is because the results of the previous 6 throws have no bearing on the result of the 7th. There is a 50% chance that the heads side will appear and also a 50% chance that the tails side will appear, as is the case with any other throw.

The second involves cases where the probabilities of occurrence are not independent of each other. For example, suppose a boxer has won 50% of their fights in the past two years. Let’s assume that after several fights, he’s won 50% of his matches this year, lost his last six fights, and dropped six.

If a person believes he will win his next six fights because he has considered his losses and is “doomed” to a win, then he would have made the betting system fallacy. After all, this person would not have taken into account that the results of one match can influence those of the next. For example, the boxer could have been injured in a match, which would reduce his chances of winning his next six fights.

It should be noted that all betting systems predictions about what is likely to happen are wrong. If a person has hard evidence to support their predictions, then the predictions will be reasonably accepted. For example, if a person flips a normal coin and rolls nine heads in a row, it would be reasonable to conclude that he or she will most likely not get another consecutive set of nine more heads in a row. 

This reasoning would not be fallacious if its conclusion is drawn from a betting system understanding of the laws of probability. In this case, if he understands that he will not get another consecutive series of nine more heads, because the chances of such an event happening are lower than the chances of getting less, then his reasoning would be good and his conclusion would therefore be justified. 

Therefore, determining whether the betting system error is made often requires some basic understanding of the laws of probability.

Moreover, the reverse effect of this cognitive bias is just as dangerous!

After a very large number of Tails, some may be tempted to forget the one in two rules and think that they are not risking much by betting that this coin will fall on Tails repeatedly!

Ditto for red and black in roulette at the casino, moreover this bias is also called “Monte Carlo bias”!

How am I affected by this betting system fallacy at work?

If a team member has consistently delivered their first 5 deliverables late, you might think it will almost certainly be the same next time around, and you might be tempted to plan the rest of the project around that “predictable” delay, without even consulting him.

However, he might have had specific and different difficulties each time and will not encounter any on the production of this deliverable.

Ditto for an executive director you invited to all the steering committees and who has never been there. You might think it will be the same next time and not prepare for his coming (by not anticipating his likely questions for example) but he might surprise you and come this time.

How to avoid the betting system fallacy as much as possible?

Explaining to your interlocutors, the independence of random events that occur is necessary (but not always sufficient).

It is also necessary to train people to see each event as a new beginning and not a continuation of previous events.

Studies have shown that age has a positive effect on the ability to manage this bias of betting systems. So make sure you have more experienced people, alumni, on the team to counter this bias.

Finally, by getting together and discussing the situation together with the team, a better decision can be made.

Can an understanding of the betting system be of use to you?

I don’t really see any situation in which you can take advantage of this cognitive bias for good reasons while respecting your ethics as a project management professional. However, this understanding of betting systems might be useful at the online casino.

Betting systems relying on the laws of probability can harm your capital

Bettor error is a well-known phenomenon where the player’s perception of the events unfolding in front of him is somehow going to be offset by future games. This kind of betting system thinking can lead players into a losing streak that will get out of hand if they continue to bet on losing odds while waiting for the opposite outcome, which is to win.

It can also lead to players going bankrupt when they find themselves in a winning streak that they see as a fair return from their previous losses, or from the losses of other players who are at the table.

How does this affect online baccarat players? Some players trust betting systems more than their own intuition and understanding of the game. In fact, some betting systems that have been designed for this game and others with similar betting styles, such as blackjack, are based on the mistaken assumption that the game should swing in favor of the player as often as it does for the house.

Thinking that the law of probabilities applies to a casino game is what leads players to suffer more big losses than they should if they simply accept the small losses and adjust their playing style. All casino games, whether played in a physical casino or with a live dealer, or through a live video feed like those featured in some baccarat and other gambling casinos, are slightly in favor of the house, no matter what betting system the player uses.

This is an unrelated factor that should immediately make players realize that the only way to overcome this advantage is to play and bet smartly with each hand instead of depending on an imaginary sense of balance or a promising betting system when it comes to wins and defeats.

Keep your play style in mind, adjusting it as needed. Avoiding hope that the game will swing in your favor at some point will prevent you from making the bettor mistake. You have to remember that no betting system is perfect. Players will fail if they rely solely on live Baccarat betting systems rather than their skill, luck, and knowledge of the game they are playing.

Does the betting system mistake affect your game? Let’s find out

A person makes the bettor mistake when he assumes that when an unusual situation occurs, or an event will occur in the long term, he will be able to handle it, or that the event in question will end quickly. The betting systems error is made in two ways. In both cases, the person believes that the result is the consequence of an unforeseen event. 

The first way involves events the possibilities of which are independent of each other. Take for example a coin toss. Each time the coin is tossed, the chances of the heads and tails appearing are equal. Suppose a person has flipped the coin six times and the result has always been headed. If he concludes that the result of the seventh throw will be tails, then that would be an error, as the previous results do not affect the result of the last throw. 

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However, it is good to note that not all betting systems predictions are wrong. If the predictions are accompanied by concrete evidence, it would be reasonable to accept their veracity.

For example, when a person makes nine throws and gets the heads side each time, and assumes that he will never get the same side for the next nine throws, that reasoning makes sense. In summary, determining the betting system error requires judgment and a basic understanding of the laws of probability.

The betting system anecdote

On August 18, 1913, at the Casino de Monte Carlo, the black player came out 26 times in a row at roulette, a record unmatched since.

That day, the players who used any betting system, paradoxically lost more than ever…

Indeed, as it became evident around the play mat that something unique was happening, panic began to take players by the throat.

With each new exit of the Black, and particularly from the 15th according to the witnesses, the players doubled or tripled their bet on the Red, piling up small fortunes there, and therefore lost more and more since the Black continued to go out against all odds and all betting systems.

And that was their mistake relying on any betting system: in the application of the fallacious theory of the evolution of chance, very widespread in society, players thought, especially from the 20th draw, that there was only one chance out of millions that Black came out again, and therefore bet very hard on Red.

Only on that day, Black was released six more times, for a total of 26!

In the end, the Casino had a record of earnings, the biggest in its history, and a number of regulars lost real fortunes…

The betting system problem

The mistake of these players and their betting system was to believe that previous draws had an influence on subsequent draws.

This is a very common mistake among players, but also among most of our compatriots, resulting from a fundamental misunderstanding of the principles of chance and statistics.

Indeed, through an anthropomorphic movement of thought, the players attribute to a “just” machine the same possibilities of statistical drift as to an “unjust” person or machine.

Let us clarify these terms: a “fair” machine is, for example, a perfectly balanced roulette wheel, that is to say that it does not present any bias that could favor one result over another with each given draw. An “unfair” machine is the reverse; it is a system that allows the draws to be influenced to favor certain results.

Players and betting systems forget that a roulette wheel is as just as a coin to toss, it is just more complex.

Betting systems and the Independence of events, or “roulette has no memory”

With a fair system, therefore, each draw is independent.


Draw n ° 1: the ball has a 50% probability of hitting Red and 50% on Black.

Draw n ° 2: always 50% for each

Draw n ° 3: always the same…

Draw n ° 19: the ball still has a 50% chance of going to Red and 50% of going to Black.

Betting systems forget that The wheel and the ball have no memory

Contrary to general intuition and all betting systems, there is therefore absolutely no reason to consider that a future roulette draw will be influenced by a probability that would result from a previous draw (or a series of draws).

The betting system who almost succeeded

Joseph Jagger, a big bettor, still in the same Casino, had hired assistants who carefully noted all the draws of all the roulettes.

After several weeks of observation, he ended up discovering that one of the wheels had a bias in its draws and favored nine squares over the others.

He began to bet bigger and bigger sums each day on these nine numbers, quickly amassing very large wins.

As the Casino was unable to correct (and therefore modify) a roulette wheel overnight, the Director decided one night when the player had gone to sleep, to swap the roulette wheel with another in the Casino…

The next day, the player resumed his bets, more important than ever, on the same table, convinced that roulette would still favor him.

He did not realize that something had changed and ended up losing all his winnings…

This story perfectly illustrates the phenomenon described previously: a machine or a betting system must be “unfair”, in this case deregulated and biased, in order to be able to predict fluctuations in the course of random draws.

A “right” machine or system simply does not allow this.

Betting System: The Bettor Error or The Gambler's Fallacy

The “run”, the “zone” or “I’m hot”

There is another belief widely held among players, which says that you have to “exploit your luck” and that you must not give up a “good run” or a “good streak”. 

That is to say that if the player wins the bet several times in a row, he will consider himself lucky, “hot”, “in the zone”, and will try to take advantage of this moment of luck and bet harder than he normally would.

The error is once again to misunderstand the nature of chance and to believe that we recognize a variation in its distribution that will work in our favor. The draws are independent, as seen previously, and even if a player wins with the Red several times in a row, that doesn’t mean he’s in a lucky period and that he’s going to win again on that number afterwards, in any case that doesn’t mean he or any betting system can predict it.

A “fair” machine like roulette has no memory, and therefore does not remember previous draws as we have seen, but it does not remember the player’s history either! Roulette does not change its behavior or its operating rules according to the betting system variations in luck of a bettor…

The betting system paradox

Suppose a roulette player wins several times in a row by playing his lucky number.

Based on the mistaken belief of the betting system that was first described, he should consider that the chances of that number coming out again are getting lower and so start playing another number.

According to the belief that was mentioned next, he should consider that he is “hot” or in a good “run”, that he is in the “zone”, and should, therefore, continue to exploit his luck in betting again on the same number!

In either case, players still have as many chances of losing and winning as in other non-series periods, and their beliefs or betting systems have absolutely no influence whatsoever on chance constant in its unpredictability on a machine or a so-called “fair” system.

The solution

If we want our chances of winning to be greater, and therefore favorable in the long term, we must ‘paradoxically’ only play with ‘unfair’ systems, that is to say which allow elements of non-chance in the game.

As for example in video poker, where the hand which is given has value only if it is revealed, allowing the expert player to make his opponent fold before chance (which is egalitarian for all) does not come into play.

If you play “fair” systems, like Lotto, for example, you just have to remember that chance has no memory, that each draw is independent.

First of all, with each Lotto draw, there is just as much chance that a “random” sequence of 6 numbers will emerge compared to your “chosen” sequence of 6 numbers, quite simply because your chosen sequence has the same statistical weight. 

Its 6 numbers only have meaning for you, in relation to your history or your culture, whereas they are just as “random” as the other sequence which has no meaning for you.

Then, each draw is independent of the previous ones, and the series formed that can be seen from time to time (such as “it’s been 8 times that the zero came out, it won’t come out the next time”) do in fact allow no predicting the next draws. 

The next time, zero will always have as many chances to come out as the previous one, because the rules of the game have not changed and the number of balls neither!

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