Gamblers Fallacy vs Hot Hand Fallacy

by Dale Shelabarger Updated:

How do you play when you’re on a streak in roulette? Or Baccarat? Or Blackjack? The patterns are starting to develop. And you, under a trance, sense the reds will keep on coming. Until, that fifth red. Or sixth red. Or seventh red. Or eighth red. You feel the magic dissipating, you remember mathematics. You remember high school probability. There have been seven reds in a row, therefore the laws of probability dictate that it is universally unlikely for another red number. Right? Maybe not, as we'll discover in the Gamblers Fallacy below.

So how do you play the next spin of the roulette wheel? Do you ride the hot streak? Or do you bet against it? Because that’s mathematics. Surely?

Gamblers Fallacy Fundamentals

The answer is of course, in numerical terms, that it doesn’t matter. The probability of getting red or black in the next spin is 50/50. One in two. A live roulette wheel has no memory, especially an online one. There’s not even a chance that the wheel is busted or biased or has been tinkered with.

But where’s the fun in that?

Everyone has their own routines when it comes to games of chance. But when you are confronted with streaks, good or bad, it is important to know your fallacies.

The Gamblers Fallacy

In my scenario, the hypothetical gambler is twitchy on the sixth red, clammy on the seventh, before the eighth spin has such a sudorific effect on the poor punter that sweat cascades onto the verdant felt, leaving a swamp of darker green (or if you’re playing online roulette, your cup of tea).

Imagine, then, a streak of twenty-six consecutive black numbers and one of the most notable examples in history of a Gamblers Fallacy mass hysteria. Let us go back in time:

The Monte-Carlo Gamblers Fallacy

The Casino de Monte-Carlo was built in 1863 as a solution to the grave financial situation of the principality. In fact, it was Charles III’s mother, Princess Caroline, who suggested that a casino could generate revenue and endear the royals to their subjects, who had been long overtaxed to fund the family’s profligate ways. After persuading a successful casino manager in Germany, Francois Blanc, to update and operate it, the casino brought so much money into the prince’s coffers that income tax was abolished, relieving every Monegasque citizen of their long-suffered burden.

Famously, this policy remains today, no longer to the benefit of struggling farmers but of oligarchs and highly ranked tennis players. Nearly one in three residents of Monte Carlo are millionaires. To put that in perspective, only one in thirty-five Londoners are millionaires. Also, millionaires prefer Facebook over Twitter. But that’s mostly irrelevant.

One August day in 1913, the Mediterranean sun beaming through the large glass windows of the Salle Blanche Terrace, a roulette wheel spun a group of vacationing dignitaries’ wild. They crowded around a single roulette table as word spread of the mounting streak. As black number followed black number, the Benedictine swilling aristocrats knew that this would be their moment to beat this live dealer casino. Fifteen consecutive black numbers was their breaking point; surely the next spin would be red. Indubitably. They placed their red bets, doubling, tripling, quadrupling their stakes for another black spin was surely impossible. Some natural law must surely dictate that; even the law of gravity must cough up a red tout-suite.

By the twenty sixth black, and eleven rounds of hysterical red bets, the casino had engorged itself by millions of francs. On what basis?

The maturity of chances. The gambler's fallacy.

The chapeau adorned high rollers possessed a vague understanding of rudimentary mathematics - To state the obvious:

There are 18 red numbers, 18 black numbers and one zero on a European roulette wheel. Therefore, on each spin you have an 18 in 37 (or 48.6%) chance of landing a red, and an 18 in 37 (48.6%) chance of landing a black. To land on red or black is practically a coin toss (albeit an unreliable coin that lands on its side one in thirty-seven flips).

They understood that after x number of spins, it was statistically probable to get an equal number of reds and blacks. They probably understood that there would be a small streak here or there but that ultimately, after further spins, the law of averages would dictate that any disparity in the number of black and red spins would even up.

And after fifteen black spins in a row, the law of averages would surely kick in…

Firstly, it is called the Gamblers Fallacy, not the Gambler’s Code, or the Gambler’s Law or even the Gambler’s Jurisprudence (NB: I shall invent this and it will be seminal in the literature on Gambler’s Jurisprudence. Watch this space.)

The definition of fallacy is “a mistaken belief, especially based on unsound arguments.”

Secondly, the “law of averages” is not a real law, no matter what your father tells you after a few pints. (Sod’s law is not a real law either.) It is, rather, a layman’s misunderstanding and misapplication of probability theory’s Law of Large numbers, which states that “as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean.” In layman’s terms, the more coin tosses you perform, the closer you will get to an equal number of heads and tails and the timeframe, frankly, is infinity. This, incidentally, is how the RTP works with regard to what you can expect to win from your favorite online games. The magical “law of averages” will not right the ship.

The roulette wheel, like a coin, does not remember. Each spin is independent of the last.

So, in this notorious instance, our Monte Carlo high rollers were failed by their own tenuous grasp of probability theory.

But what if they’d ridden the streak like a freight train? Surely something about the wheel, or the dealer’s magic hands, or the stars starting to gleamingly appear in lieu of the quickly setting sun, meant that this hot streak of black numbers would never end. Trust in the hotness.

The Hot Hand Fallacy (Or Phenomenon?)

As a counterpoint to the gambler’s fallacy, the hot-hander believes that a streak will continue. In this case, the black numbers were hot. Any simpleton could see that the black numbers were burning up rubber…

The first research into Hot Hand analysed observer predictions of hoop shots in basketball. Results showed that the spectators more often predicted a good shot directly following prior success rather than a miss even though there was no statistical difference. Thus, most observers trusted in the hot streak.

As basketball involves a good deal of skill, it seems reasonable perhaps to put credence into form and confidence and other such intangibles. But hot hand can always be found in games of chance. Research shows that roulette players will often place bets on more numbers after a winning round, because they feel they are on a roll. Similarly, lottery players may reuse numbers that they consider to be “hot” and lottery ticket sales often substantially upsurge soon after the store has produced a winning ticket, reflecting a “lightning strikes twice mentality.”


There’s a term in psychology literature called “apophenia” which describes the “human tendency to perceive patterns in random data that simply do not exist.”

But why?

Humans, it turns out, are apofiends™. The compulsion to perceive patterns and streaks could be a fundamental aspect of our psychology, an adaptive trait arising out of evolutionary necessity to survive. After all, not everything is random. On our planet, the distribution of plants, animals and water sources are not simply random; it is shaped by myriad geographical and environmental factors. To recognize patterns such as these was to formulate strategies to survive and navigate a hostile, competitive environment.

This predilection could partially explain why people are compelled to gamble. The sensation of riding a perceived “hot streak” on a slew of consecutive wins is a base human thrill. During a run such as this, suddenly our good luck, our agency, our superpower obfuscates sensible perspectives on randomness.

On our “deficiencies” to properly assess randomness, Sandra Hubscher writes:

Fight of the Fallacies

So which fallacy wins out? Is one less destructive than the other? Which gamblers fallacy is more popular?

These may seem like odd questions to ask of terms which, by their nature, center around falsehoods (or potential falsehood in the case of hot hand).

The perception of patterns in randomness is ingrained in the human psyche, so it is only natural for us to apply the apophenic eye when gambling on games of chance. But which of these two patterns are we more likely to buy into?

In an experiment, psychologists in Canada asked three groups of participants to call the toss of a coin after a run of four heads or tails. Each person was shown a sequence of either Heads, Tails, Heads, Tails, Tails, Tails, Tails or Tails, Heads, Tails, Heads, Heads, Heads, Heads. Before the eighth spin, the participant was told to bet on the next outcome in earnest, as if placing a true bet.

The experimenters, one to flip the coin and one to record the results, were trained in the art of off-the-cuff easiness.

“Wow,” the experimenter gasped to the first group of partakers. “I am really throwing a lot of heads.”

Transparent? Not at all. She asked for their bets. She flipped the coin.

“Wow,” the Meryl Streep of critical trials huffed to the second group. “This coin is really coming up with a lot of heads.” Then, the same routine.

She greeted the final group with silence before taking their bets. No doubt, the power in her performance came through the crumpled contours of her face.

Accordingly, the first group’s focus was (subtly) directed to the person flipping the coin. The second group’s focus was directed to the coin itself. The third group was the control.

If it were you placing a bet, would you have gone heads or tails? Why?

Can you guess what happened in this experiment?

The results suggest that after we start to detect a mildly improbable streak, in neutral circumstances, we are inclined to believe that it will end any minute. This is a natural reversion to the gambler’s fallacy.

However, when this “streak” is (subtly) attributed to either a person or an object, we are more likely to show faith in that streak continuing. Instinctively, we see the coin flipper as skilled, or perhaps just lucky, and the coin charmed.

We must find rhyme and reason in the “random” streak.

When the experimenters followed up on these results with a new group, they swapped the flipper just before the critical eighth spin. Suddenly, the “sympathetic magic” was gone.

If you ask me (which you didn’t), these “strategies” are logically fallacious but they are not necessarily illogical. We ascribe meaning to everything. If we gambled in a detached and unthinking manner, what would be the point? When you’re choosing your next roulette bet, or having double or nothing on the spin of a coin on an online slot bonus round, it doesn’t really matter through what avenue you come to your decision. If you think the dealer has magic hands, or that the run of odd numbers simply cannot continue then go with it.

That’s all part of the fun.

If we didn’t ascribe meaning to everything, then very little would have meaning.

The experiment shows an important aspect of human decision-making; that many people have a baseline pessimism, a cautiousness if that’s more palatable. If a hot streak is on, we are programmed to be skeptical of it. Unless we can find some evidence for optimism. In lieu of proper evidence, we look a little more toward the stars.

What’s the Point?

Fallacies they may be, but they are perfectly reasonable routines for playing roulette or online slots or any other game of total random chance.


As long as you remember that the outcomes are random, and each spin or flip does not influence future spins or flips, then there is no better or worse strategy. In fact, isn’t gaming more joyful when imbued with meaning?

What does the research mean? What does our apophenic proclivity portend for the future of gambling?

A concerted effort must be made to continue to educate. A study in the Evolution and Human Behavior Journal concludes:

“Thus, it is possible that interventions to teach subjects the properties of random devices might reduce the propensity to cognitive illusions that lead to gambling. We hope that further work will help… to alleviate suffering caused by pathological gambling."

Some academics say that a concerted effort to educate ourselves about the gamblers fallacy and the nature of randomness could help tackle problem gambling. What do you think? Comment below.

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