The gambler’s fallacy: nothing is ever “due”

On August 18, 1913, the wheel at Monte Carlo ran 26 blacks in a row; the room, certain red was “due”, bet heavier with every spin — and lost millions of francs. They were wrong for a precise reason: spins are independent, so after any streak red is still 18/37 = 48.65%. A 26-run is astonishing to see (≈ 1 in 67 million for a fixed window) — but given it’s underway, continuing is a coin flip. That distinction is the entire fallacy.⚙ computed

The two probabilities people merge

P(streak happens) — small, and the one intuition feels. P(next spin | streak so far) — always 48.65%, and the only one you can bet on. Our streak pages compute both, including the figure nobody else does: the chance a long run visits your session (7+ reds: 48% per 200 spins).

Why the fallacy is expensive

Every “bet bigger, it’s due” impulse is a size-up at unchanged odds — which is exactly what Martingale formalizes. A million simulated sessions show where that leads: 32.6% of bankrolls dead, edge paid in full. The wheel doesn’t remember; your bankroll does.

The mirror error: hot numbers

“17 has hit three times tonight — it’s hot” is the same mistake reflected: past clusters don’t raise future frequency on a maintained wheel. Clusters are what uniform randomness looks like at small samples — the balanced wheel design guarantees no honest sector runs rich for long.

Frequently asked

What is the gambler’s fallacy?

The belief that independent random events “balance out” short-term — that after many reds, black becomes likelier. On a fair wheel every spin stays 18/37 for each color regardless of history.

Did the Monte Carlo 1913 streak really happen?

Yes — it’s the textbook case that named the fallacy: roughly 26 consecutive blacks while the floor doubled down on red. The casino’s profit that night came entirely from players betting against independence.