Gambler's fallacy
It’s a quietly shocking experience: looking at two solid months on a chart, and noticing a market index seems to go up almost every single day. Surely, this is unnatural—“due” for a correction, right?
Yet even seasoned traders fall into patterns of gut intuition that the math simply shreds on contact.
Donuts, banter, and the notion that some people simply get lucky more often than others. In trading, the equivalent is spotting someone on a streak—and doubting its reality. Enter the gambler’s fallacy: the mistaken belief that, after a string of similar outcomes (like market gains every day for weeks), some mysterious force makes the opposite more likely.
But the laws of probability don’t care about your feelings or “fairness.” A flipped coin is still 50/50, regardless of the last result. In the markets, a stock going up day after day is not "due" for a drop—future moves are not forced to compensate for the past.
Why Runs Feel So Unlikely
Let’s get specific. Suppose a market index (or coin) flips up every day for two months. Start flipping coins yourself: the probability of 40 heads in a row from a fixed starting point is vanishingly small. But across 250+ flips (a year of trading days), how likely is at least one big run?
Most people gut-estimate based on the fixed-point odds—ignoring that each toss, each trading day, is a new opportunity for a run to begin. So, when flipping a coin a million times, there are nearly a million possible starting points for a (for example) 100-heads-in-a-row streak. Intuitively, we vastly underestimate how often we should expect to see unbroken streaks in random processes, whether coin tosses or trading days.
Streaks in the Markets: Not So Rare
What does this tell us about financial markets? Think of every “market up” as a “heads.” Runs then become not just possible, but mathematically inevitable given enough time. In a typical trading year (about 250 days), a week or more of consecutive up-days isn’t at all improbable. In fact, the expected length of the longest run in n coin flips is approximately one less than the base-2 logarithm of n:
So for 256 days, the expectation hovers just below 8. A full week of unrelenting gains? That’s what the averages predict.
The Harder Question
Suppose instead of the longest possible streak, the query is subtler: “How long will any single run last, on average?” Here we land on an expected run length of 2 days for a fair coin or a 50/50 chance, which feels more “normal.”
But traders often conflate these two questions—expected length of any run, versus expected length of the record-breaking run in a sequence. The result: persistent surprise each time a chart features more green (or red) than "should" be possible.
Fibonacci, Recursion, and Why Streak Calculation Is Tricky
The math of streaks in random sequences is trickier than it first appears. If streaks could start independently anywhere, calculations would be easy. But they’re not independent: a run starting at position 2 overlaps with one starting at position 3, creating intricate statistical dependencies. This leads to recursion relations—ultimately connecting to a concept called the k-step Fibonacci number. In this system, each number is the sum of the previous k numbers, so the longer the streak considered (k), the faster possible outcomes grow.
For financial nerds, this means that the more days in your streak, the more rapidly probabilities shift, but still never to the point where monster streaks are likely unless the number of flips gets very large.
Human Bias and the Search for Pattern
Why do so many traders and investors routinely fall for the gambler’s fallacy? The answer is hardwired into our psychology. The brain craves equilibrium—when a market runs to one side, we itch for the “other shoe” to drop. This bias is so prevalent that it endures even among experienced professionals, who intellectually know better.
Why? Because the difference between probability and “fairness” is emotionally unacceptable. The gambler’s fallacy thrives wherever short-term imbalances appear—leading to contrarian trades, unforced errors, and needless second-guessing of valid strategies.
A classic counter-argument: “Aren’t markets mean reverting? Shouldn’t streaks be shorter?” While volatility (how violently prices change) does often revert to the mean, actual price does not. In other words, there’s no deep law that forces markets to fall after rising—or rise after falling. Studies and widely used models like Black-Scholes simply don’t find persistent mean reversion in price itself; if anything, prices behave pretty “randomly” over moderate periods, despite popular models that forecast otherwise.
Some models (like the Heston) build in mean-reverting volatility, but give little practical guidance for day-to-day trading. When volatility is far from its historical average, expect it to pull back, but don’t confuse this with directional predictability.
Autocorrelation: When Psychology Creates Big Moves
What about autocorrelation—the idea that today’s move predicts tomorrow’s? Classic behavioural finance (think Robert Shiller) argues that markets sometimes show autocorrelation, especially over short stretches. This causes “fat tails” in return distributions: the markets have more sudden, violent swings than a simple random-walk model would predict.
But even here, the effect is not longer streaks, just sharper, more dramatic single moves. “Crashes” are real—an emotional selloff amplifies itself—but rarely do such effects produce record-breaking strings of losses or gains.
Regression to the Mean vs the Gambler’s Fallacy
There’s a subtle but important distinction between regression to the mean and the gambler’s fallacy. Over very long sequences, a fair coin (or market series) will have an average close to 50/50. But that doesn’t mean “corrections” are due after every streak; rather, the rare streaks are increasingly diluted as more and more data accumulates—not “reversed” by force of nature.
Contrarian Strategies: Why Trading “Against the Run” Isn’t Automatic Alpha
There’s real danger in over-applying contrarian strategies just because "the run can't last." The expectation that a streak must end at a specific time is a recipe for repeated whipsaws. While contrarian thinking can yield insights, it’s critical to distinguish structural edge from a pure belief that the universe owes you a break.
The Professional’s Take: Managing by the Math
So what does all of this mean for traders who must convert statistical wisdom into real-world results? Process, not prediction, is paramount:
Optimal play (sound probability-driven trades) does not guarantee steady, daily profits. It guarantees only that, in the long run, wins will outnumber losses—by as much as possible given your edge.
Even the best processes cannot eliminate the existence of ugly streaks: “Sometimes you play correctly and lose... a lot, in a row.” This isn’t a sign to abandon your method—unless your process was never robust in the first place.
Avoid overfitting and over trusting mean-reversion/contrarian logic where it’s statistically unsound.
Surprising runs are normal: Over hundreds of trading days, weeks-long winning or losing streaks will happen—even in a fundamentally fair system.
Human intuition is a poor guide: It drastically underestimates long streaks, over-believes in immediate corrections, and sees patterns where math sees only noise.
Volatility reverts, price does not: Volatility’s tendency to revert won’t shrink or break streaks of up or down days. Don’t conflate the two phenomena.
Process over prediction: Stick with strategies that honour probabilistic logic, not gut feelings of “overdue” reversals. Accept streaks as part of the game—not omens, warnings, or opportunities in themselves.
The truest skill is to detach from the emotional tug-of-war of streaks. Recognize them for what they are: natural, even expected, in any large sample of data. Fight the urge to believe in “cosmic fairness”—markets have none. Equip yourself with process, probability, and emotional resilience.