Both the Gambler’s Fallacy and the Hot Hand Fallacy are common in gambling.

When you’re on a winning run in roulette, what should you do? Also, Baccarat! A round of Blackjack, perhaps? We can see certain trends emerging. You’ve entered a trance and can feel that the reds will keep coming. Not till the sixth red light! Or the sixth red. Also, red seven. Also, red eight. You can feel the spell slipping away, and it’s time to think about arithmetic again. You have some recollection of learning about probability in junior high. There have been seven reds in a row, hence it is statistically impossible for there to be another red number. Right? Perhaps not; see Gambler’s Fallacy for more on this.

What bets will you make on the next round of roulette? You ride the wave of success? Maybe you’re betting against it. Simply said, that’s just math. Surely?

The Basic Logic-Abuse of Bettors

The mathematical answer is, of course, that it doesn’t make any difference. In the following spin, there is an equal chance of landing on red or black. Probability of success is 50%. A real-time roulette wheel, especially one that is online, does not keep score. There’s no way the wheel is broken, biased, or tampered with.

But then what would be the point?

For games of chance, players all have their unique habits. However, knowing your fallacies is essential when encountering streaks, whether good or negative.

Mistakes Gamblers Often Make

The hypothetical gambler in my story gets jittery after the sixth red, then clammy after the seventh, and finally so sudorific after the eighth spin that perspiration falls across the green felt, leaving a swamp of deeper green (or your cup of tea, if you’re playing online roulette).

Imagine then, a run of twenty-six black numbers in a row, one of the most famous examples of a Gamblers Fallacy widespread panic in history. Let’s travel back in time a bit:

The fallacy of the Monte-Carlo gamblers

In 1863, the principality’s dire financial position inspired the construction of the Casino de Monte-Carlo. Princess Caroline, Charles III’s mother, proposed opening a casino to bring in money and win favor with the people who had long been overtaxed to support the royal family’s lavish lifestyle. The prince was able to amass so much wealth from the casino after convincing a successful casino manager in Germany, Francois Blanc, to modernize and operate it that he was able to eliminate income tax for all Monegasque citizens.

Well-known as it is, this policy is still in effect, but now it helps oligarchs and professional tennis players instead of suffering farmers. Almost a third of the population of Monte Carlo is made up of millionaires. Consider that just one in every 35% of Londoners is a millionaire. Plus, Facebook is more popular among the wealthy than Twitter is. However, that is beside the point.

A party of visiting dignitaries got a little too crazy at the roulette table one August day in 1913, as the Mediterranean sun poured in through the big windows of the Salle Blanche Terrace. As word of the increasing streak spread, people clustered around a single roulette table. Black numbers kept coming up, and the Benedictine-drinking nobles finally saw their chance to win big at the live dealer casino. They finally gave up after 15 straight black digits since obviously the following spin would be red. Indubitably. After placing their red wagers, they realized that increasing their bets by two, three, or even four times for a black spin was hopeless. That has to be prescribed by some natural law; heck, even gravity’s had to sputter out a red tout-suite.

By the eleventh round of frenzied red bets after the twenty-sixth black, the casino was stuffed to the gills with millions of francs. In what way?

Developing into one’s potential. Sin of the gambler.

To state the obvious, the top hat-wearing high rollers knew very little about basic arithmetic.

A European roulette wheel has 18 red numbers, 18 black numbers, and one zero. Therefore, the odds of landing a red are 18 in 37 (or 48.6%) and the odds of landing a black are 18 in 37 (or 48.6%) on every spin. Choosing between red and black is statistically equivalent to flipping a coin (although a shaky one that comes up heads or tails only once every 37 spins).

They realized that it was statistically likely to acquire a same number of reds and blacks after x number of spins. They likely realized that streaks of black or red spins were to be expected, but that the rule of averages would eventually cause the number of black and red spins to become roughly equal.

And certainly the rule of averages would kick in after fifteen consecutive black spins…

First, it’s not the Gambler’s Code or the Gambler’s Law or even the Gambler’s Jurisprudence (NB: I shall construct this, and it will be fundamental in the literature on Gambler’s Jurisprudence); rather, it’s called the Gambler’s Fallacy. Keep an eye out!)

The dictionary defines a fallacy as “a mistaken belief, especially one based on unsound arguments.”

Second, no matter what your dad says to you after a few beers, the “law of averages” is not a genuine law. (There is no such thing as Sod’s law.) The Law of Large Numbers in probability theory asserts that “as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean.” This is a common misconception and misuse of this law by the general public. An infinite number of coin flips will eventually result in a 50/50 split of outcomes, but it will take an infinite amount of time to get there. In case you were wondering, this is how the RTP works for your preferred online games and how much money you can anticipate to win. The “law of averages” is not a magic bullet that will save the day.

Like a coin, the roulette wheel has no long-term memory. Every round stands on its own.

Therefore, our Monte Carlo high rollers failed in this infamous occasion due of their own shaky understanding of probability theory.

But imagine if they had jumped on the winning streak like it was a freight train. Surely the scorching run of black numbers would never stop if the wheel, the dealer’s magic hands, or the stars that were beginning to shine in place of the swiftly lowering sun all had anything to do with it. Have faith in the sizzling.

What’s the deal with the hot hand phenomenon?

The hot-hander’s belief that a streak would continue stands in contrast to the gambler’s fallacy. In this scenario, black digits performed exceptionally well. It was obvious to even a dummy that the dark figures were destroying tires.

The earliest studies of the Hot Hand phenomenon analyzed the predictions of basketball observers for made baskets. The results indicated that, despite their being no statistical difference, the crowd tended to expect a successful shot immediately following a previous success rather than a miss. Most people therefore put their faith in the winning streak.

Since basketball requires a high level of talent, it seems sense to give those intangibles like form and confidence a chance. In games of chance, however, a “hot hand” will always be present. After a successful round at roulette, gamers tend to wager on additional numbers, thinking they’re lucky. Similar to how lottery players may repeatedly utilize “hot” numbers, an increase in sales is common after a lottery retailer has generated a winning ticket, suggesting a “lightning strikes twice mentality.”

Apophenia

The word “apophenia” is used in the field of psychology to describe the “human tendency to perceive patterns in random data that simply do not exist.”

Yet, why?

It has been discovered that humans are apofiendsTM. The tendency to look for trends and patterns may be ingrained in our minds as a result of our evolutionary history. After all, things aren’t always at chance. The distribution of life forms and resources on Earth is influenced by several variables, including geography and climate. The ability to identify trends like this was crucial for thriving in the cutthroat business world of the 1990s.

This inclination may account for certain people’s compulsion to gamble. There is a primal human pleasure in riding a “hot streak” of successive victories. During a streak like this, it’s easy to lose sight of how much luck actually plays a role and how much control we have.

Sandra Hubscher writes about our “deficiencies” in evaluating randomness:

By its very definition, randomness must include some order. We tend to look for trends and then read too much into them.

We believe that order may be established out of chaos.

Even with the occurrence of seemingly random events, we have a natural tendency to think that the past has a role in what will happen next.

Battle of the Untruths

Which logical fallacy so triumphs? Is there one that does less damage than the other? Which logical error used by gamblers is more common?

Considering that both hot hand and falsity are central to their definitions, these inquiries may appear out of place.

It’s natural for humans to use the apophenic eye while betting on games of chance because of how deeply established the sense of patterns in randomness is in our psyches. Which of these two trends, though, are we most inclined to follow?

Canadian psychologists conducted an experiment in which they split participants into three groups and had them predict whether the next coin flip would be heads, tails, or a tie. Both the Heads, Tails, Heads, Tails, Tails, Tails, and Tails sequences and the Tails, Heads, Tails, Heads, Heads, and Heads sequences were displayed to the participants. The eighth spin was preceded by instructions to “bet” on the outcome as if it were a real wager.

Both the person flipping the coin and the person recording the outcomes were schooled in the fine art of casual spontaneity for their roles in the experiment.

The first set of participants heard the experimenter exclaim, “Wow,” in shock. To paraphrase, “I am really throwing a lot of heads.”

Transparent? Absolutely not. She inquired about their wagers. She did a coin toss.

Critical trials’ Meryl Streep huffed, “Wow,” at the second group. A large percentage of “heads” have been produced by this coin. Next, repeat the previous steps.

She remained silent while the last group approached, then took their wagers. The wrinkles in her face were undeniable evidence of the intensity of her performance.

As a result, the attention of the first group was (subtly) drawn to the individual tossing the coin. The second set was instructed to look at the coin. To serve as a comparison, the third group served as the control.

Which way would you have bet if it were your money on the line? Why?

Do you have any idea what the results of this experiment were?

The findings imply that under neutral conditions, once we become aware of an implausible sequence, we expect it to stop any minute. The gambler’s fallacy is inevitably invoked here.

But when we (implicitly) identify this “streak” to a person or an item, we become more confident in the streak’s continued success. Our first impression is that the person flipping the coin is either very good or very lucky, and that the coin itself is magical.

We need to put order into the “random” pattern.

To replicate these findings with a new set of subjects, the researchers switched the flipper before the eighth critical spin. The “sympathetic magic” was suddenly not there.

Though not necessarily unreasonable, these “strategies” strike me as being intellectually flawed. We humans give significance to everything. What would be the point if we gambled without any emotion or strategy? It doesn’t matter how you arrive at your decision while placing a wager on roulette or the bonus round of an online slot machine, where the stakes are double or zero with the flip of a coin. The streak of odd numbers cannot possibly continue, therefore if you think the dealer has miraculous hands, you should go with it.

That’s the exciting part!

Nothing would be meaningful if we didn’t give significance to everything.

The results of the experiment highlight a key feature of human decision making: the fact that many individuals display a degree of inherent pessimism or, to use a more pleasant term, caution. Our natural skepticism kicks in if someone is currently riding a winning streak. Unless we discover reason to be hopeful. In the absence of solid proof, we turn our gaze skyward.

For What Purpose?

Despite their illogic, these strategies are acceptable while participating in games of pure chance like roulette, online slots, and so on.

Why?

There is no right or wrong approach, as long as you keep in mind that the results are random and each spin or flip has no bearing on the outcomes of subsequent ones. Isn’t it true that games become more enjoyable when they have deeper significance?

Just what does this study prove? Is there hope for gambling in the future given our apophenic tendencies?

Efforts should be made to keep teaching. According to research published in the journal Evolution and Human Behavior:

Therefore, treatments that teach participants about the features of random devices may lessen the propensity for cognitive illusions that lead to gambling. We anticipate that future research will aid in… reducing the impact of compulsive gambling on individuals and communities.

To combat compulsive gambling, several experts suggest learning more about the gamblers fallacy and the nature of chance. Do you have any thoughts? Leave your thoughts in the comments!

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