Two rows of coin flips sit on the screen. One came from a fair coin. The other was written by someone trying to look random, or rather by a program that imitates them. Most people pick the wrong one, and the reason is not that the fake is clumsy. It is that real chance is streakier than our gut believes.
Each strip is 100 flips, read left to right like text, a solid square for heads and an empty one for tails. Pick the one that came from a real coin. Then look at what gave it away.
Write 50 flips that look random. Tap heads or tails, as you would if you were making it up.
A fair coin has no memory. After four heads it is still 50/50 on the fifth. That single fact has a strange consequence: in a run of 100 flips, long streaks are not rare at all. I worked out the exact odds by counting every possible sequence.
| In 100 fair flips | Chance it happens |
|---|---|
| A streak of 5 or more | 97% |
| A streak of 6 or more | 81% |
| A streak of 7 or more | 54% |
| A streak of 8 or more | 31% |
The average length of the longest streak is about 7. A sequence of 100 flips that never goes past four in a row turns up only around 3% of the time. Yet when we make up a random-looking sequence, we almost never write down a streak of six, because it feels like the coin is "broken".
People expect a short sequence to look like the long-run average, a fairly even mix with no pattern. Kahneman and Tversky called this the representativeness heuristic in the early 1970s. The coin does not know it is supposed to look balanced. Only the long-run share settles toward half; a short stretch can lean on one side for a while.
The result shows up in experiments on how people write "random" sequences. They tend to switch sides more often than a fair coin does. With 99 gaps between 100 flips, a real coin switches about 49 or 50 times, give or take 5. The faked strip above switches around 70. That surplus of switching is a better clue than any single pattern, and you can see it in the numbers after each guess.
The same instinct makes us read meaning into clusters. A run of heads, a string of good days, or three similar songs in a row on a shuffled playlist can look suspicious even when nothing is wrong. A Spotify engineer wrote on the company's R&D blog that a truly random shuffle can play songs by one artist back to back, which listeners read as a bug, so the app spreads them out instead. The shuffle that feels random is deliberately less random.
The famous 1985 study of basketball "hot hands" argued that fans over-read streaks in shooting. Later work has argued that real streakiness may exist after all, so the question is still debated. The safe lesson is narrower: before you explain a streak, ask how often chance alone would make one of that length.
When you next see a streak, check the odds first. If a run of six or seven in a hundred tries is normal, then a run that long is no evidence of anything.
Odds computed exactly by counting all sequences of fair flips. Sources: Kahneman & Tversky, "Subjective probability: a judgment of representativeness" (1972); Bar-Hillel & Wagenaar, "The perception of randomness" (1991); Gilovich, Vallone & Tversky, "The hot hand in basketball" (1985); Miller & Sanjurjo (2018) on streaks; Spotify R&D blog, "How to shuffle songs?"