Gambler’s Fallacy Gambler's Fallacy
The mistaken belief that, in independent events, something that hasn't happened for a while is "due." Every slot spin is independent through the RNG, so previous results do not affect the next spin's probability.
| English | Gambler's Fallacy |
|---|---|
| Classification | Math & Probability |
| English | Gambler's Fallacy |
| Also known as | Monte Carlo fallacy |
| Category | Math & Probability |
| Key point | Independent events are unrelated to past results |
| Famous case | 1913 Monte Carlo roulette, 26 black results in a row |
| Opposite misconception | Hot hand fallacy (belief that a winning streak will continue) |
Overview
The Gambler’s Fallacy is the mistaken belief that, in independent events, “an outcome hasn’t happened for a while, so it’s now more likely to happen” (or the reverse). In reality, for events that are independent each time, like coin flips, roulette, or slot spins, past results have no effect on the next probability.
The Monte Carlo example (1913)
There’s a reason this fallacy is also called the “Monte Carlo fallacy.” On August 18, 1913, black came up 26 times in a row on a roulette wheel at the Monte Carlo casino in Monaco. The probability of that happening was about 1 in 68.4 million. People bet heavily on red, saying “red is due now,” and lost a lot of money. But the probability of red on each spin was always the same, regardless of earlier results.
The Gambler’s Fallacy in slots
The result of every slot spin is decided independently by the RNG (random number generator). That’s why all of the following thoughts are examples of the Gambler’s Fallacy.
| Common thoughts | In reality |
|---|---|
| “The bonus hasn’t hit in 300 spins, so it’s due soon” | The bonus probability on the next spin is the same as it was at the start. |
| “It just paid big, so it won’t hit for a while” | The probability is the same right after a big win, too. |
| “Two scatters showed up, so the next one will be three” | A near miss is also an independent random result. |
| “This game is hot right now” | Slots have no memory. |
Figures like RTP and hit rate are averages over a very long period. They don’t apply to short stretches in the sense of “a win has to come soon to match the average.”
The hot hand fallacy
The opposite mistake to the Gambler’s Fallacy is the “hot hand fallacy.” It’s the belief that “I’ve won several times in a row, so I’ll keep winning.” Researchers explain that people tend to expect streaks from human actions (like an athlete’s shots) and balance from inanimate processes like roulette or coins. Both are wrong for independent events.
Why it’s worth knowing
The Gambler’s Fallacy can easily lead to the thought “I can win it back soon.” Even when you enjoy a game with a free demo, knowing that every result is independent helps you understand how the game works more accurately.