The Gambler's Fallacy: Why 'Due' Numbers Don't Exist
The most expensive cognitive bias in gambling — and how to stop falling for it.
The Most Expensive Mistake in Gambling
The Gambler's Fallacy is the belief that past random events affect the probability of future random events. It's the reason people bet on "due" numbers, chase colors at roulette, and think cold slot machines are about to pay out.
It's wrong. And it costs people billions.
The Classic Example
A roulette wheel lands on red 10 times in a row. What's the probability of the next spin being black?
Answer: 47.37% (on an American wheel)
The same as it always is. The wheel doesn't know what happened before. It has no memory.
Why Our Brains Get This Wrong
Humans are pattern-seeking machines. We evolved to find patterns because it helped us survive. But this instinct misfires with random events:
- We see RRRRRRRRRR and think "B is overdue!"
- We see lottery number 7 hasn't appeared in 30 draws and think "it's due!"
- We see a slot machine that hasn't paid out and think "it's ready to hit!"
None of these intuitions are correct.
The Math
For independent events, the probability of each outcome is fixed:
| Previous Results | P(Red Next) | P(Black Next) |
|---|---|---|
| 10 Reds in a row | 47.37% | 47.37% |
| 10 Blacks in a row | 47.37% | 47.37% |
| Alternating R/B | 47.37% | 47.37% |
| Any sequence | 47.37% | 47.37% |
The previous results are irrelevant. Period.
Where It Costs You Money
- Lottery — Tracking "hot" and "cold" numbers is meaningless
- Roulette — Electronic boards showing recent results exploit this fallacy
- Slots — A machine that hasn't paid out is not "due"
- Sports betting — "This team is due for a win" ignores the actual matchup
The Reverse Gambler's Fallacy
Equally wrong: believing that a streak will continue because of "momentum" or "hot hands" in games of pure chance. In roulette, dice, and lottery, there is no momentum.
How to Protect Yourself
- Understand that each event is independent
- Ignore "history" boards at roulette tables
- Never choose lottery numbers based on what hasn't been drawn
- Make every decision based on the current odds, not past results