May 19, 2023

The Fallacy of Hot and Cold Numbers in Roulette

Roulette, the quintessential game of chance, has been a staple of casinos for centuries. The simplicity of its rules, combined with the thrilling suspense of the spinning wheel, has captivated gamblers for generations. A common question that often arises, however, is which roulette number hits most? Are there 'hot' or 'cold' numbers that are more likely to appear? Let's delve into the world of probability and chance to answer these questions.

The Rules of Roulette

To understand the dynamics of roulette, it's crucial to know the basic rules of roulette. In European roulette, the wheel consists of 37 slots, numbered from 0 to 36. The American version, meanwhile, includes an additional 'double zero' (00) slot, bringing the total to 38. Players can place bets on individual numbers, ranges of numbers, the colors red or black, or whether the number will be odd or even.

When the wheel is spun, a ball is released into it. The ball eventually loses momentum and falls into one of the slots, deciding the winning number and color.

The Concept of Hot and Cold Numbers

The terms 'hot' and 'cold' numbers are often used by roulette players to refer to numbers that appear frequently (hot) or infrequently (cold) over a certain number of spins. Some gamblers swear by these concepts, asserting that they provide valuable insight into the game's trends and patterns.

However, the reality is that each spin of the roulette wheel is an independent event. The outcome of a spin doesn't influence the outcome of the next spin. This is a fundamental principle of probability theory and the key to understanding why there are no hot or cold numbers in roulette.

Probability and Independence in Roulette

In probability theory, two events are considered independent if the outcome of one event does not affect the outcome of the other. This is precisely the case with each spin of the roulette wheel. The wheel has no memory of past spins, and each number has an equal chance of being hit on any given spin.

In European roulette, the probability of any specific number coming up is 1 in 37, or approximately 0.027 (2.7%). For American roulette, with its additional slot, the probability is 1 in 38, or approximately 0.026 (2.6%).

The Gambler's Fallacy

The belief in hot and cold numbers in roulette can be attributed to what's known as the Gambler's Fallacy. This is the mistaken belief that if something happens more frequently than normal during a given period, it's less likely to happen in the future (or vice versa). In the context of roulette, a player might think, "The number 32 hasn't come up in a while, so it's due to come up soon."

But remember, the roulette wheel has no memory. Each spin is an independent event. The odds of hitting 32 are the same on every spin, regardless of what has happened in the past.

Law of Large Numbers

One might wonder, "If every number has the same chance of appearing, why don't we see an even distribution of numbers over a series of spins?" This is where the Law of Large Numbers comes into play.

The Law of Large Numbers is a theorem in probability theory that describes the result of performing the same experiment a large number of times. It states that as a sample size grows, its mean gets closer to the average of the whole population. In roulette, this means that over a large number of spins, each number should come up roughly the same number of times.

However, "a large number of times" is much larger than most people think.# Let's find some statistical analysis of roulette spins to illustrate the point about the Law of Large Numbers search.

In reality, to see an even distribution of numbers, we would need to spin the wheel a significantly large number of times. As a matter of fact, a statistical analysis was performed on millions of 300-spin simulations of both single-zero and double-zero roulette. The results revealed that the most frequent number in these 300-spin simulations hit anywhere from 9 to 25 times, while the least frequent number hit anywhere from 0 to 6 times.

The probabilities of these occurrences varied considerably. The average number of wins on a single-zero wheel for any number in 300 spins was calculated to be around 8.11. These statistics illustrate the Law of Large Numbers in action. Over a smaller number of spins, there can be wide variations in the frequency of different numbers. However, as the number of spins increases into the thousands or even millions, these frequencies will start to converge toward the expected average.


While the allure of 'hot' and 'cold' numbers can be enticing, it's important to remember that roulette is fundamentally a game of independent chances. Each spin is a separate event, with every number having an equal chance of being hit. Belief in the fallacy of 'hot' and 'cold' numbers can lead to flawed decision-making and potential losses.

The Law of Large Numbers assures us that over a significant number of spins, each number should appear roughly the same number of times. However, in the short term, we can still see significant variations, which is part of what makes roulette exciting and unpredictable.

In the end, when spinning the roulette wheel, it's best to remember the words of the renowned physicist Richard Feynman, who said, "The first principle is that you must not fool yourself, and you are the easiest person to fool." So, play responsibly, and remember that each spin is a new game of chance.

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