Gambler’s Fallacy and Randomness

The Gambler’s Fallacy is the mistaken belief that a random event is less or more likely to happen based on the results of a previous event or events. Let’s take a deeper look into Gambler’s Fallacy and Randomness.

A Players Belief System

Recreational gamblers often have beliefs based on myths or gut feelings. The Gambler’s Fallacy believes that probability changes based on previous events. For example, the roulette ball has landed on red six times. Believing the gambler’s Fallacy assumes the ball will likely land on black on the next spin.

Most people gamble on independent events. However, their belief system does not embrace the math and the truth behind each wager. The relationship between the Gambler’s Fallacy and Randomness is crucial to understand. Remember: Previous events don’t affect the probability.

Every Wager is a Single Event

Example #1 – Roulette

Gambler's Fallacy and Randomness
Roulette table.

You have 18 black pockets, 18 red pockets, and two green pockets on a roulette wheel. That’s 38 total possible events. (Let’s not admit that triple zero roulette exists, shall we.) So the probability of the ball landing on black is 18/38, or 47.37%. That probability will always be there. And it doesn’t change based on what happened on the previous spin.

Example #2 – Dice

Consider rolling a pair of dice, and both land on 6. The odds of this happening in a fair roll are 1/36. The odds of each die landing on a six are 1/6.

Gambler’s Fallacy assumes that the odds of both dice landing on six again on the next roll are lower than 1/36. So, don’t bet on boxcars (hard 12).

Gambler's Fallacy and Randomness

In reality, on each roll, the odds of the dice landing on double 6’s are still 1/36 – even if that was the previous roll. So regardless of how many times we roll the dice, the dice can’t remember what they landed on last time.

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Embrace the Math, Not the Myth

Essentially, there is no way for the last dice roll to affect the next one, the last number in roulette to affect the next one, or even if quad aces dealt in video poker affect the next deal. So never assume that these independent events affect each other. (You know what assuming means, right?)

Some people imagine that because the odds are so great against any event happening a certain number of times in succession, it is not very likely to happen again when it has happened so many times.

if you will toss a coin and put down all the times that it comes one way five times running, you will find that in just half those cases it will go the same way again. Note all the times that it goes six times one way, and you will find that in half of them it will go seven.”

From “Hoyle’s Games,” by Edmond Hoyle

Why Do So Many Gamblers Believe in the Law of Small Numbers?

Players often assume that streaks even out in the short term. But the short-term results mean nothing from a small sample. This unfortunate expectation is called the law of small numbers.

In gambling, the law of small numbers is when players believe that a few observations will reflect the general outcome. Why is it so prevalent in recreational gamblers’ belief systems? Because human beings don’t do well with accepting randomness. It exists because people favor certainty over doubt, explanation over ignorance, causation over association, and patterns over randomness and skill. For sports bettors, failure to truly appreciate its significance can be costly. 

Gambling Fallacy and Patterns

Of course, casinos are aware of Gambler’s Fallacy. Here are a few things that subtly pokes the demon in all of us:

Roulette – roulette players live the Gamblers’ Fallacy. Every table has a tall lighted sign keeping track of the last 10 or 12 numbers that have appeared on the wheel. The number “5” hit twice in a row? Better not bet on it next, right? It doesn’t matter to the table, especially with very few roulette tables skewed or unbalanced.

Gambler's Fallacy and Randomness
Roulette display.

Video Keno, Keno – some players will work hard to track the numbers hit more often. Players can buy video keno systems to ensure their success! But, listen, random = random. ‘Nuf said.

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Stadium Gambling – games such as craps & baccarat will display the previous winning results, thinking that keeping track will give you insight into the future plays – but it doesn’t.

Slots – Imagine a scenario where someone is on a losing streak at a slot machine, so they move to another machine. When that person gets up, someone sits down at that machine because they believe the machine’s “luck” is about to turn. (It’s due!) The odds for both players aren’t going to change for the reasons they believe they will. Random number generators (RNGs) do not account for the results of previous spins – the results are genuinely random to protect the integrity of the game and the casino operations.

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Baccarat – Every casino under the sun uses a bright, flashy display screen overhead to tantalize superstitious baccarat players. These “big boards” are equipped to display various “roads” which list the table’s previous results. Folks who believe previous trends can predict the future feverishly follow the watching the lighted sign provided like roulette, scribbling in their notebooks to decide which bets to make next. These big boards are nothing more than a way for casinos to prey on what is known as the Gambler’s Fallacy.

Gambler's Fallacy and Randomness
Baccarat display board.

The 53 Frenzy

The gambler’s Fallacy can also lead to financial ruin and problem gambling. Once upon a time, the Venice Lottery 2005 caused quite a stir and trouble. Hundreds of Italians started placing bets on the number 53 purely because the number hadn’t been the winning number for an abnormally long time.

Venetians bet a considerable amount of euros on the number “53” because the odds of 53 showing up had somehow increased. Some even parted with life savings. It became a national obsession, leading to many suicides, murders, and bankruptcies.

Summary and Conclusion

  • The gambler’s Fallacy is the mistaken belief.
  • Players show this by expecting results based on the events of previous wagers.
  • The gambler’s fallacy view is one of chance as a fair and self-correcting process.
  • You should understand why this reasoning is flawed to avoid the gambler’s Fallacy.
  • When resolving the gambler’s Fallacy, remember that sometimes, a sequence of improbable outcomes can indicate that the events in question are not genuinely random or independent.