The Gambler's Fallacy — Linking Independent Events
You flip a coin and heads comes up five times in a row. Is it now tails' 'turn'? If it felt that way, you've fallen into the gambler's fallacy.
What Is the Gambler's Fallacy
The Gambler's Fallacy is the mistaken belief that, in mutually independent events, 'an outcome that has come up less often for a while is now due.' It is also called the Monte Carlo fallacy.
A fair coin or roulette does not 'remember' past outcomes. Even if heads came up five times, the probability of heads on the next flip is still exactly 1/2. This is because each trial is independent. Yet human intuition expects the opposite outcome, insisting that 'the balance must be restored.'
The 1913 Monte Carlo Incident
The most famous case happened at the Monte Carlo casino in Monaco on August 18, 1913. On the roulette, the ball fell on black a full 26 times in a row.
As black kept coming, gamblers bet ever-larger sums on red, saying 'now it's red's turn,' and lost millions of francs as black continued. The probability of 26 in a row on a single-zero roulette is roughly 1 in 68.4 million — extremely slim — but the fact that black had already come up 25 times did not in any way raise the probability that the next would be red.
The 26-in-a-row streak itself is an astonishingly rare event when viewed after the fact. But the core of the gambler's fallacy is that the probability of the next single spin after 'a streak that has already occurred' is always the same original probability.
The Gambler's Fallacy in Investing
Thoughts like 'it fell 3 days in a row, so tomorrow it'll rise' or 'this month was a loss, so next month is due for a recovery' are typical. A market's day-to-day ups and downs are not completely independent, but predicting short-term moves as 'turns,' like a coin flip, has weak grounds.
The opposite-direction illusion also exists — concluding that an asset that has risen for a long time is 'due to fall,' or one that has fallen for a long time is 'due to rise.' Such attempts to time the market are a common psychological root of market-timing failure. That's why this site does not predict rises or falls at specific points, and instead focuses on showing, with data, what the outcome is when you hold for a long time.
Preguntas frecuentes
Q. Are the gambler's fallacy and the hot-hand fallacy opposites?
They are illusions in opposite directions. The gambler's fallacy sees 'it came up a lot, so now the opposite is due,' while the hot-hand fallacy sees 'it succeeded in a row, so it will continue.' Both share the trait of forcibly imposing a nonexistent rule onto independent or largely random events.
Q. Then is 'regression to the mean' also the gambler's fallacy?
No. Regression to the mean is the tendency for ordinary values to follow extreme values — a statistically real phenomenon. The difference: mistaking that 'the probability of an individual independent trial changes' is the gambler's fallacy, while seeing that 'the average of many trials finds its place over the long run' is regression. It's important not to confuse the two.
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