The Gambler's Fallacy: When the Monte Carlo Wheel Hit Black 26 Times

By the fifteenth black in a row, the story goes, the crowd around the table had stopped watching and started betting. Red had to come. It had been gone too long, the wheel owed it, and anyone with a stack of francs and a feel for averages could see that. Black came up again. And again. On 18 August 1913, at the Casino de Monte-Carlo, the ball is said to have landed on black 26 times in a row, and the gamblers who kept piling onto red lost millions of francs doing it.

That night gave its name to one of the most persistent mistakes in gambling, the Monte Carlo fallacy, better known as the gambler's fallacy. It is the belief that a random outcome becomes more likely because it has not happened for a while, or less likely because it just has.

What happened at Monte Carlo on 18 August 1913

I should be honest about the sources first. The streak is repeated everywhere, from statistics lectures at MIT to BBC features, but the account most writers lean on comes from Darrell Huff's book How to Take a Chance, published by W. W. Norton in 1959 with illustrations by Irving Geis. I have not found a contemporary 1913 newspaper report of the night. The date and the count of 26 are consistent across every telling. The details of who bet what are not, and I would treat any precise loss figure you read as decoration.

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What the versions agree on is the shape of it. As the blacks stacked up, players became convinced the run had to break, and they bet harder on red the longer it went on. That is the whole fallacy in one room. Each extra black made them more confident in red, when the wheel itself had not changed at all.

Monte Carlo already had form for this sort of legend. In 1891 an Englishman called Charles Deville Wells had a run of wins there big enough to clean out the cash reserve at his table, which is what "breaking the bank" originally meant. Fred Gilbert turned it into the music hall song "The Man Who Broke the Bank at Monte Carlo", and the performer Charles Coborn reportedly paid £10 for the rights. Wells later went to prison for fraud, which is a story for another day. For a sense of how gambling looked to ordinary British players in that era, my piece on gambling life before the internet goes further back.

How unlikely were 26 blacks in a row?

A European roulette wheel has 37 pockets: 18 red, 18 black and a single green zero. The chance of black on any one spin is therefore 18/37, a little under half. The chance of black twice running is 18/37 × 18/37, and so on, multiplying once for every spin.

You will often see the night described as a 1 in 66.6 million event, or 1 in 67 million. Both figures are real, they just answer slightly different questions. If you ignore the zero and treat each spin as a coin toss, 26 identical results come out at 1 in 2 to the power 26, which is 1 in 67,108,864; that is the version in the MIT lecture notes. If you keep the zero and ask how likely it is that, once the ball has landed on a colour, the next 25 spins match it, the answer is (37/18) to the power 25, about 1 in 66.6 million. Ask specifically for 26 blacks from a standing start and you get roughly 1 in 136.8 million.

Whichever number you pick, it is tiny. It is also beside the point for anyone standing at the table after the twenty-fifth black.

Why the 27th spin was still a near coin toss

Once 25 blacks have already happened, they are history. The question a player faces is only about the next spin, and the next spin has the same odds as every other: 18/37 for red, 18/37 for black, 1/37 for zero. The wheel has no memory, the ball has no sense of fairness, and nothing in the physics keeps a tally. The rarity belonged to the whole run of 26, which had already happened, not to the one spin people were betting on.

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The usual objection is the law of averages: over thousands of spins, red and black do come out close to even. That is true, but it does not work by correction. A run of blacks is never paid back by a run of reds. It is simply swamped by the thousands of later spins, so it shrinks as a share of the total while staying exactly as large in absolute terms. Red never needed to catch up, and it never did.

The same logic runs through every game decided by a random number generator. A slot that has not paid a big win for an hour is not "warming up", and a progressive jackpot that has gone months without paying is not overdue, which I go into in progressive jackpots explained.

Why our brains keep making the mistake

Psychologists have a good explanation for why this feels so convincing. Amos Tversky and Daniel Kahneman described the representativeness heuristic: we expect even a short sequence of random results to look like the long-run average, so a long run of one colour feels wrong, as if the sequence is not "random enough" and must fix itself. The feeling is strong and almost universal, which is why the fallacy shows up in roulette, lotteries, coin tosses and, outside gambling, in investment decisions too.

It has a mirror image, the hot-hand fallacy, where people believe a streak will continue rather than break. The term comes from basketball. In 1985 Thomas Gilovich, Robert Vallone and Tversky studied shooting records and concluded the hot hand was a cognitive illusion. In 2018 the economists Joshua Miller and Adam Sanjurjo published a paper in Econometrica showing a subtle statistical bias in that analysis, and once corrected, the data gave some support for a real hot hand in basketball. That debate is about human players, who can genuinely have good days. A roulette wheel cannot.

There is also an inverse gambler's fallacy, a term associated with the philosopher Ian Hacking. You walk into a room, see someone roll a double six, and conclude they must have been rolling for ages to get it. One unusual result tells you nothing about how many attempts came before it.

Where the fallacy still shows up

Look at any physical roulette table today and you will usually find an electronic board showing the last dozen or so results, often with the reds and blacks colour-coded. Online live tables show the same history strip. It is presented as information, but the only thing it can help you do is fall for the mistake the 1913 crowd made. I have never seen a casino take one down, which tells you something about whose side the board is on.

Betting systems built on doubling up after a loss, such as the Martingale, lean on the same belief that a colour is due. They do not change the house edge, which on a single-zero wheel stays at 2.70% on every spin, and a long streak like the Monte Carlo one is exactly what breaks them. If you notice yourself chasing a pattern on a results board, that is a good moment to look at the responsible gambling tools your casino offers, from deposit limits to time-outs. The board will still be showing its numbers when you come back, and the next spin will still be 18 in 37.

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