The gambler's fallacy and the myth of hot streaks
Why a number is never "due", why red does not become likelier after a run of black, and what roulette really tells us about random streaks.
The gambler's fallacy is the belief that a random result becomes more or less likely because of what happened before. Casino games are full of this thinking, and roulette is the classic example.
Each spin starts from zero
A roulette wheel has no memory. Each spin is independent of all earlier spins, and every pocket has the same chance each time. On a single-zero wheel, a given number comes up with a chance of 1 in 37 (2.70%), and red or black has 18 chances in 37 (48.65%). On a double-zero wheel, a given number has 1 chance in 38 (2.63%).
These chances do not change after a run of reds. If the ball has landed on red ten times in a row, the chance of black on the next spin is still 18 in 37.
"Due" numbers
People often think that a number that has not appeared for a long time is "due", as if the wheel owes it a visit. It is not. Suppose the number 17 has been missing for 50 spins. On spin 51 its chance is still 1 in 37, because the ball cannot know what came before.
The same error can run in reverse. Believing that a streak will continue ("red is hot") is as unfounded as believing it will end.
Why streaks still happen
Streaks are normal in random sequences. A run of ten reds sounds shocking, yet on a single-zero wheel it has a chance of roughly 1 in 1,350 from any given starting spin. Over thousands of spins at many tables, such runs will appear from time to time. They are part of random behaviour, not a sign that the wheel has changed.
Humans are good at spotting patterns, even in noise. That is where "hot" and "cold" numbers come from. They are an impression, not a feature of the wheel. Lists of recent numbers show what happened. They do not show what will happen.
Betting systems
The same mistake sits behind many betting systems. Doubling the stake after each loss, for example, assumes a win must be on its way. It is not. Such a system only changes how a stake is spread over time. It cannot change the odds of a single spin, and it can lead to very large losses or run into table limits.
Every spin carries the same house edge, 2.70% on a single-zero wheel, whatever came before. The honest way to treat a streak is to ignore it, and to set limits that do not depend on it.
18+ only. This article is for information, not advice to gamble. Responsible gambling.
