The gambler’s fallacy: What it is and why it ruins good bets

If you were to believe that a coin was to land on heads simply because the previous five flips had landed on tails, you would be a subject of the gambler’s fallacy.

Also known as the Monte Carlo fallacy, the phenomenon first originated at the Monte Carlo Casino in the summer of 1913. This saw black land 26 times in a row on a roulette wheel. Gamblers believed red would be sure to land, so they continued wagering high stakes on it. However, this meant they lost millions as the ball continued to fall on black.

What is the gambler’s fallacy?

Imagine you’re playing roulette. Black has landed five times in a row. Surely red has to land soon, right? Well, maybe. But maybe not.

Because black has landed five times in a row, you bet on red for the sixth spin, with the false logic that red must have a greater chance of landing this time, since black landed five times in a row before hand. However, black lands again. Uh oh. You’ve lost your bet. That, in a nutshell, is the gambler’s fallacy.

The gambler’s fallacy is the false belief that an outcome is more or less likely to happen due to past events.

However, if a game is truly random, past outcomes have zero impact on the next outcome. The fact that black has landed five times in a row has no bearing on what will land next.

Here’s another example. You flip a coin seven times. Each time, it lands on heads. For the eighth flip, you think it will be tails because, surely, heads cannot land eight times in a row? Well, it can.

Each time you flip a coin, there is a 50/50 chance that it will be either heads or tails. Just because it has landed on heads seven times in a row does not increase the chances of the eighth flip being tails. It is still a 50/50 chance.

Why does it ruin good bets?

Past outcomes do not impact events with random outcomes. Thinking otherwise can skew your bets, and it has no real basis or logic.

This means gamblers will misjudge random and independent outcomes, potentially resulting in more losses.

If we use the earlier roulette example, a gambler may be under the false impression that there is a greater chance of red landing on the sixth spin after black landing five times in a row.

As a result, they decide to up their stakes for the next bet, and instead of wagering €20 on this spin, they bet €50. However, black lands for a sixth consecutive time, and instead of losing €20, they’ve lost €50. This is how it can ruin your bets.

What’s the difference between betting on games of luck and skill?

Humans are ingrained to identify patterns, and will make judgements on outcomes based on past events or skill in an attempt to gain an advantage.

Nevertheless, truly random games have no element of skill. It is purely random, and the chances do not change based on prior outcomes.

Since many games are based on skill, it is easy to carry the same logic into games that have random outcomes. Sports wagering is different, as there is an element of skill that determines the outcome.

Games of chance vs. games of skill

Games of chance	Games of skill
Roulette	Sports Betting
Slot Machines	Poker
Dice	Fantasy Sports
Lottery	Blackjack (partially)

Football match case study

While it is not a foregone conclusion that Liverpool were to beat a lower-league side, say Carlisle United, for example. The gulf in ability means that the chances of Liverpool winning are much greater.

However, it is not as simple as that, and there are many other factors to consider, such as team selection. Take the FA Cup 4th-round tie in February 2025.

Plymouth Argyle vs Liverpool

• Date: 09/02/2025

• Venue: Home Park

• Pre-match odds: Plymouth 14/1, Draw 7/1, Liverpool 23/100

• Implied winner probabilities: Plymouth (6.67%), Draw (12.5%), Liverpool (81.3%)

• Match results: Plymouth Argyle 1-0 Liverpool

Championship side Plymouth Argyle managed to unexpectedly beat Liverpool 1-0. Many weren’t expecting it, proven by the implied winner odds for Plymouth being just 6.67%. The odds indicated that Liverpool had an implied probability of 81.3% to win the match.

However, the fact that Liverpool heavily changed their lineup and rested key players had a big impact on the result. This outcome was not purely random.

When considering dice rolls, the lottery, and roulette, the outcomes are random. That’s why the gambler’s fallacy occurs: the search for a chain of linked results and outcomes, based on a small sample of outcomes.

How to steer clear of the gambler’s fallacy

You must focus on logic and understand that prior results do not determine coin flips, dice, and roulette outcomes. As a result, always remember that every single coin flip has a 50/50 chance of landing on either heads or tails.

For casino games that are more based on skill and strategy, it is a good idea to look at data trends, analytics, and strategies to find an edge. However, it is important to remember that a win is never guaranteed.

The bottom line is to focus on true probabilities of outcomes and ignore irrational patterns.