Gambler's Fallacy Demonstrator
Interactive proof that past results don't affect future outcomes
Coin Flip Simulator
Flip a fair coin repeatedly and see the results. No matter the history, each flip is always 50/50.
Click to flip
The Truth:
No matter what just happened, the next flip is ALWAYS 50/50.
If you've flipped 10 heads in a row, the chance of heads on flip #11 is still exactly 50%.
Common Gambling Fallacies
"It's Due!"
Myth: "Red hasn't hit in 15 spins, it must be due!"
Reality: Each spin is independent. Previous results don't affect future outcomes. Red is still exactly 48.6% (European roulette).
"Hot/Cold Numbers"
Myth: "Number 17 is hot, it's been hitting all night!"
Reality: Past frequency doesn't predict future results. Hot and cold numbers are just random variance.
"Balancing Out"
Myth: "I've lost 10 in a row, I'm due for a win!"
Reality: Each bet is independent. Your luck doesn't "balance out" in the short term. The house edge persists forever.
"The Streak Must End"
Myth: "The dealer has won 5 hands, they can't keep winning!"
Reality: Streaks can continue. The probability of the next hand is unchanged by what came before.
What IS True
Law of Large Numbers: Over MILLIONS of trials, results approach expected probability. But this doesn't mean short-term "catch-up" happens.
Understanding the Gambler's Fallacy
What is the Gambler's Fallacy?
The gambler's fallacy is the mistaken belief that if something happens more frequently than normal during a period, it will happen less frequently in the future (or vice versa). This is false for independent events.
Why It Feels True
Our brains are pattern-seeking machines. We expect randomness to "look" random, with even distribution. But true randomness includes streaks, clusters, and apparent patterns that mean nothing.
Examples in Gambling
- Roulette: Each spin is independent. Past spins don't matter.
- Dice: The dice have no memory. 6 sixes in a row? Next roll is still 1/6.
- Slots: Each spin is independent (by law). "Loose" or "tight" machines don't exist in the short term.
- Cards (with shuffling): After a shuffle, previous hands are irrelevant.
When Past DOES Matter
Card games without replacement:
- Blackjack card counting works because cards aren't replaced
- Poker probabilities change based on seen cards
- Any game where the sample population decreases
The Monte Carlo Fallacy
On August 18, 1913, at the Monte Carlo Casino, black came up 26 times in a row at roulette. Gamblers lost millions betting on red, assuming it was "due." It never was.