What is the gambler's fallacy?
It is the mistaken belief that a random event becomes more or less likely because of what happened before. After a coin lands heads five times, many people feel tails must be more likely next. It is not. The coin has no memory, so the next flip is still exactly 50/50.
The famous Monte Carlo example
In August 1913 at a casino in Monte Carlo, the ball on a roulette wheel landed on black 26 times in a row. As the streak grew, gamblers piled money onto red, convinced it was overdue. Red did not come until the 27th spin, and many players lost very large sums.
Why it feels so convincing
We expect short sequences of random events to look "balanced". We imagine that a fair coin should alternate more than it really does. In truth, real random sequences contain streaks far more often than people expect. In 50 flips there is roughly a 55% chance of seeing at least six heads or six tails in a row.
What does even out?
Over a very large number of flips, the proportion of heads settles close to 50%. That is the law of large numbers. But it does not happen by the coin "correcting" itself. Early streaks simply become a smaller share of the total as more flips are added. The raw difference between heads and tails can actually keep growing.
See it for yourself
- Flip a coin many times on our coin flip page and watch your best streak and percentages.
- Use the coin flip odds calculator to work out how likely a streak of any length is.