What happened. On 18 August 1913, at the Monte Carlo Casino, the ball landed on black 26 times in succession. As the run went on, players bet more and more heavily on red, reasoning that red was "due". It was not: on an unbiased single-zero wheel the chance of black on the 27th spin was exactly what it had been on the first: 18 out of 37, about 48.6%. The episode gave the gambler's fallacy its other name, the Monte Carlo fallacy.

How unlikely was it, really?

On a European wheel 18 of 37 pockets are black. The probability of 26 blacks in a row is

Probability of the 1913 run
$$P(\text{26 blacks}) = \left(\frac{18}{37}\right)^{26} \approx 7.3 \times 10^{-9} \approx \frac{1}{137\text{ million}}$$

Counting a run of either colour (26 reds would have been just as remarkable) doubles the probability: about 1 in 68 million. That is the figure usually quoted.

Two things are true at once. The run was extraordinary. And it carried no information: the probability of black on the next spin was unchanged, because the wheel has no memory. Rare events happen; casinos run many thousands of spins a day, and over a century of play somewhere a 26-run is expected.

What the players did

Secondary accounts agree on the date and the length of the run; they disagree on details. One account says players began betting against black after about 15 repetitions, another after 10. The total lost is reported as "millions of francs" without a verifiable source. No contemporary 1913 newspaper report has been located by the sources this page relies on, so the betting details should be read as tradition rather than record.

The behaviour itself is well documented in modern data. In 18 hours of casino security video from Reno, Nevada (July 1998), 139 players placed 24,131 bets. After one to four identical even-money outcomes, bets were split roughly 50/50. After six or more, 85% of bets went against the streak. The wheel in that study showed no bias.

"Subjects act as if every segment of the random sequence must reflect the true proportion: if the sequence has strayed from the population proportion, a corrective bias in the other direction is expected. This has been called the gambler's fallacy." Amos Tversky and Daniel Kahneman, "Belief in the Law of Small Numbers", Psychological Bulletin 76(2), 1971, p. 106.

The same mistake in 2026

Every online roulette lobby shows a "hot and cold numbers" board. It is the 1913 table with better graphics. A number that has come up five times in the last hundred spins is a number that came up five times; its chance on the next spin is 1/37, like every other number. A number that has not appeared in 200 spins is not "due"; the chance it stays absent for another 200 is $(36/37)^{200} \approx 0.4\%$, small, but exactly as small as it was before the drought started.

Under the UK Gambling Commission's Remote Technical Standards, a licensed online roulette game must use a random number generator that is "acceptably random", verified by an approved third-party test house, and games that adapt or compensate based on past results are prohibited. The board is a display of the past, not a forecast.

Sources

  1. Wikipedia. "Gambler's fallacy", Monte Carlo Casino, 18 August 1913, citing BBC, "Why we gamble like monkeys", 2 January 2015. en.wikipedia.org/wiki/Gambler%27s_fallacy (accessed 24 October 2026).
  2. Owen, A. M. (2011). "The Monte Carlo fallacy." Medical Journal of Australia, 195(7). mja.com.au (account of players switching after about 10 spins).
  3. Tversky, A. and Kahneman, D. (1971). "Belief in the Law of Small Numbers." Psychological Bulletin, 76(2), 105–110. doi:10.1037/h0031322
  4. Croson, R. and Sundali, J. (2005). "The Gambler's Fallacy and the Hot Hand: Empirical Data from Casinos." The Journal of Risk and Uncertainty, 30(3), 195–209. doi:10.1007/s11166-005-1153-2
  5. UK Gambling Commission. Remote Gambling and Software Technical Standards, RTS 7A. gamblingcommission.gov.uk

Frequently asked questions

What happened at Monte Carlo in 1913?

On 18 August 1913 the roulette ball at the Monte Carlo Casino landed on black 26 times in a row. Players bet increasingly on red, believing it was due, and lost heavily. The event is the origin of the name 'Monte Carlo fallacy' for the gambler's fallacy.

What are the odds of 26 blacks in a row in roulette?

On a single-zero wheel the probability is (18/37) to the power 26, about 1 in 137 million. Counting a 26-run of either colour, about 1 in 68 million. On the 27th spin the chance of black was still 18/37.

Was red 'due' after 26 blacks?

No. Each spin is independent. The wheel does not keep a tally and does not correct itself. Over millions of spins the proportions converge to 18/37 by dilution, not by compensation. Betting on red after the streak carried exactly the same house edge as any other bet.

Is the 1913 story true?

The date and the 26-black run are reported consistently by secondary sources, including an encyclopaedia entry citing a BBC article and a 2011 medical-journal essay. Details such as when players switched to red and how much was lost vary between accounts and are not backed by a located contemporary report.