Steelman
Gambler’s fallacy
Also called Monte Carlo fallacy, maturity of chances, “It’s due”.
Believing past random results make a different result “due”.
What it is
Believing that in a series of independent random events, an outcome that has happened less often than expected recently is more likely next, or one that has happened more often is less likely.
The pattern
A fair coin has landed heads five times in a row. Therefore tails is more likely than 50% on the next flip.
An example
“Red has come up eight times in a row on this roulette wheel. Black is due, so I’m putting everything on black.”
If the wheel is fair, each spin is independent. The chance of black is exactly what it always was.
Why it fails
Independent events have no memory. A fair coin still has a 50% chance of heads after any streak. Long-run averages even out because a streak gets diluted by many later results, not because later results compensate for it.
When it’s not a fallacy
Most lists skip this part. Calling a fair point a fallacy is a mistake too.
It can be fair when
- The events aren’t independent. When cards are dealt without being replaced, the remaining deck really does change; that’s why card counting can work in blackjack.
- A long streak is used as evidence that the device is biased. Then the rational bet is on the streak continuing, not reversing.
Try one
A question from the app. The wrong answers are its usual look-alikes.
Gaming Discord. Kai: “Patch notes say every card pack has the same 1% shot at a legendary, no matter how many you’ve opened.” Rui: “I’ve opened 90 packs without one. I’m buying ten more tonight. After a dry run that long, the next ten are where it finally lands.” Kai: “Post a screenshot if it hits.”
What’s the flaw?
The patch notes say each pack’s odds are the same 1% whatever came before, so 90 empty packs don’t make the next ten any luckier. Rui is treating a dry run as a debt the game has to pay back.
A fair reply
“Each pack is still 1%, so the next ten are no luckier than the first ten were.”
Often confused with
- Regression fallacy
Regression to the mean is real: extreme results tend to be followed by less extreme ones. But that means “closer to average”, not “the opposite is due”.
- Sunk cost fallacy
Chasing losses at the casino often combines both: “I’ve lost so much already” (sunk cost) and “a win is due” (gambler’s fallacy).
Where the name comes from
Named for the gambler who’s sure a losing streak has to turn. “Monte Carlo fallacy” is after the famous casino in Monaco. “Maturity of chances” pictures a missing result ripening with every miss until it has to drop. “It’s due” is how it sounds out loud, as if chance kept a schedule.
On 18 August 1913 at the Monte Carlo Casino, the roulette ball landed on black 26 times in a row, and gamblers lost millions of francs betting that red was “due”. The mirror-image “hot hand” belief, that a streak will continue, is also a fallacy in games of pure chance. In skill-based sports, though, the evidence is mixed: a 2018 re-analysis by Joshua Miller and Adam Sanjurjo found significant evidence of streak shooting in the data of the classic 1985 study that had dismissed the basketball hot hand.
Sources
- The Gambler's Fallacy, The Fallacy Files
- Gambler's fallacy, Wikipedia
- The Hot Hand Fallacy, The Fallacy Files
- Hot hand, Wikipedia
In the app
Practice spotting it on arguments that sound real.
Steelman has more examples of gambler’s fallacy, how to answer it in a real conversation, and practice rounds that mix it with its look-alikes, so you learn the difference, not just the name. Coming soon to iPhone and Android.
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