Key facts
- The gamblers fallacy is the belief that a result becomes more likely because it has not happened for a while. On a fair wheel every spin is independent, so the chance of red is 18 in 37 (48.65%) whatever came before.
- Ten reds in a row from a standing start is about a 1 in 1,347 event, but after nine reds the tenth is still 48.65%.
- Long streaks are normal: in our simulation a run of 8 or more of one colour appeared in 47.1% of 200-spin stretches.
- Hot and cold numbers are noise. Over 100 spins each number averages 2.7 hits, yet some number hits 6 or more times 91.9% of the time, and about 2.4 numbers never appear at all.
- Results do not even out in money terms: over 37,000 spins the red share is very close to 48.6%, but the typical gap between red and its expected count grows to about 96.
What the gamblers fallacy is
The gamblers fallacy is the belief that a random outcome becomes more likely because it has not happened recently, or less likely because it just did. At a roulette table it sounds like "black has come up seven times, red is due". It is wrong because a roulette wheel has no memory. Victoria's gambling regulator puts it in one line: "Each game on a poker machine or spin on a roulette wheel is independent." And: "What happened before doesn't affect what happens next."
On a single zero wheel, 18 of the 37 pockets are red. That is the chance of red on the next spin, every spin, forever: 48.65%.
The odds after a streak
The confusion comes from mixing up two different questions. "How likely is a run of ten reds?" is a question about the future, asked before any spins. "How likely is red, given nine reds just happened?" is a question about one spin.
| Reds so far | Chance of this whole streak, from scratch | Chance the next spin is red |
|---|---|---|
| 3 | 11.5% (1 in 8.7) | 48.65% |
| 5 | 2.7% (1 in 37) | 48.65% |
| 7 | 0.64% (1 in 155) | 48.65% |
| 9 | 0.15% (1 in 655) | 48.65% |
| 10 | 0.074% (1 in 1,347) | 48.65% |
By the time you are watching the ninth red, the rare part has already happened. The tenth spin starts fresh. The same applies in reverse: after nine reds, black is not more likely either.
Long streaks are normal
People treat a long run as a sign that something must change. In practice long runs happen all the time. We simulated 100,000 stretches of 200 spins on a single zero wheel and recorded the longest run of one colour (a zero breaks the run):
| Longest run of one colour in 200 spins | How often |
|---|---|
| 6 or more | 94.5% |
| 8 or more | 47.1% |
| 10 or more | 13.7% |
So a scoreboard showing eight blacks in a row is close to a coin flip in any couple of hundred spins. It tells you nothing about spin 201. This is precisely the moment a Martingale strategy player doubles again, because surely red is due; it is also the moment the doubling ladder runs out.
Hot and cold numbers
Casinos often show recent results next to the wheel. Tasmania's approved roulette rules even define the device: a winning number display, "recording and displaying the present and most recent winning numbers spun at the table". Players read those boards for hot numbers (hitting often) and cold numbers (absent for ages). Here is what pure chance produces on a fair 37-pocket wheel.
Hot numbers, 100 spins. Each number should appear 2.7 times on average. In our simulation of 100,000 sessions:
| Hottest number in 100 spins | How often |
|---|---|
| Hit 6 or more times | 91.9% |
| Hit 7 or more times | 53.9% |
| Average hits for the hottest number | 6.7 |
A number hitting seven times in 100 spins looks hot. It happens in more than half of all sessions with a perfectly fair wheel.
Cold numbers. The chance a particular number misses a stretch of spins, in our calculation:
| Spins | Chance one chosen number never appears | Numbers you can expect to be missing |
|---|---|---|
| 37 | 36.3% | 13.4 of 37 |
| 74 | 13.2% | 4.9 |
| 100 | 6.5% | 2.4 |
| 200 | 0.42% | 0.2 |
After 37 spins, about a third of the board is "cold" by definition. Betting the cold numbers does not change their odds: each is still 1 in 37 next spin.
Pundit tip: if you catch yourself saying "due", swap it for "1 in 37". It sounds less exciting because it is accurate.
Does it even out in the long run?
The law of large numbers is real, but it is not a correcting force. It works by dilution, not by payback. Percentages settle down as spins pile up; the raw gap between what happened and what was expected does not shrink at all. It typically grows.
| Spins | Red share, 95% of the time between | Typical gap from the expected red count |
|---|---|---|
| 37 | 32.5% and 64.8% | 3.0 reds |
| 370 | 43.6% and 53.7% | 9.6 reds |
| 3,700 | 47.0% and 50.3% | 30.4 reds |
| 37,000 | 48.1% and 49.2% | 96.1 reds |
A player waiting for red to "catch up" after a black-heavy hour is waiting for something the maths never promised. The only thing that reliably evens out is the house edge, which collects 2.70% of everything bet on a single zero wheel. See our European roulette guide for where that number comes from.
The fallacy outside roulette
The same error drives "this pokie hasn't paid in ages". The VGCCC's guidance on poker machines says it directly: "There is no pattern, cycle or 'due win'." Each spin of a pokie is picked by a random number generator, as our how pokies work guide explains, and electronic roulette works the same way; the testing rules behind that are in our random number generator casino guide.
Why it matters for your money
The gamblers fallacy is not just a curiosity. It is the belief that keeps people betting bigger after losses: "it has to turn". The VGCCC's myths page notes that people sometimes think they can spot patterns in games like keno or roulette, and answers: "This isn't possible." If you find yourself chasing losses, our gambling help page lists free, confidential support, including Gambling Help Online on 1800 858 858.
Roulette is legal in Australia at licensed casinos only; online roulette cannot be offered to Australians, as covered in our online roulette Australia guide.
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Frequently asked questions
What is the gamblers fallacy?
It is the mistaken belief that past results change the odds of independent future ones, for example that red is due after a run of black. On a single zero roulette wheel the chance of red on any spin is 18 in 37, about 48.65%, no matter what has happened before.
Are hot and cold numbers real in roulette?
No. A scoreboard of recent numbers always shows some numbers hit several times and some not at all, because that is what random results look like. In our simulation of 100-spin sessions, the most frequent number averaged 6.7 hits against an expected 2.7, with no bias in the wheel.
Does roulette even out in the long run?
Percentages settle down; counts do not. Over 37 spins the share of reds commonly ranges from about 32% to 65%, and over 37,000 spins from 48.1% to 49.2%. But the typical difference between the actual and expected number of reds grows from about 3 to about 96.
Is the hot hand the same as the gamblers fallacy?
It is the mirror image. The gamblers fallacy says a streak must end; the hot hand belief says it will continue. On an independent game both are wrong, because the next spin has the same odds either way.
Can a casino wheel be biased?
Approved Australian rules control the equipment and the spin. Tasmania's and the ACT's rules require the ball to be spun against the wheel and to complete at least three revolutions, and in Victoria's approved rules it is four, or the spin is void. You cannot detect bias from a scoreboard of recent numbers, which is what the fallacy relies on.
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