Gambler's fallacy, in full
The best-known case supplies the second name. At the Monte Carlo Casino on 18 August 1913, a roulette ball fell on black 26 times in a row. Players crowded the table betting heavier and heavier on red, reasoning that red had become overdue, and lost very large sums. Every spin was independent of the one before it. On a single-zero wheel the chance of red stayed 18/37 throughout, no matter how long the black run had already run.
The intuition underneath is not stupid, only misapplied. Long runs really are rare in advance, and 26 blacks in a row has probability (18/37)^26, roughly 1 in 137 million. The mistake is applying that rarity after the run has already happened. The wheel keeps no record of the previous 26 spins, so the 27th starts again from 18/37. Rarity of a whole sequence is not evidence about the next element of it.
Hot and cold lottery systems run on the error in both directions at once. A cold number gets called due because it has not appeared lately, a hot one gets called lucky because it has, and since draws are independent neither claim says anything about the next result. Vibe Numbers does not publish hot or cold predictions. Numbers here are picks, presented as picks.
- Probability
- Monte Carlo fallacy, Fallacy of the maturity of chances
A worked example
A fair coin lands heads nine times running. The probability of that specific run, measured before the first flip, was (1/2)^9 = 1 in 512. The probability the tenth flip is tails is 1/2, unchanged by the nine. Both statements are true simultaneously. Ten heads in a row has probability 1 in 1,024 in advance, but standing where you are, after nine, one flip remains and it is still a coin.
Sources
At the Monte Carlo Casino on 18 August 1913 a roulette wheel came up black 26 times in succession, and gamblers lost heavily betting against the streak, which is the origin of the alternative name Monte Carlo fallacy.
Wikipedia — Gambler's fallacy
See also
Where it comes up on this site
Gambler's fallacy: frequently asked
No. The draw has no memory, so a number missing for months carries exactly the chance it always did.
Yes, on 18 August 1913, which is where the second name for the error comes from. The run itself was extraordinary and cost nobody anything. What emptied pockets was the reasoning around it: as the count of blacks climbed, players raised their stakes on red, spin after spin, on the conviction that a correction was now owed to them. The wheel owed them nothing. On a single-zero wheel red was 18/37 on the twenty-seventh spin exactly as it had been on the first.
Not always. Cards dealt without reshuffling are dependent, so tracking what has gone is genuinely informative. The fallacy bites on independent events: roulette spins, coin flips, lottery draws.