Spotting a Fabricated Coin-Flip Sequence

A classic interview task: hand someone two sequences of 200 "coin flips," one genuinely generated by a coin and one typed out by a human trying to imitate randomness, and ask which is which. Almost everyone gets it right, and the giveaway is always the same — the fake sequence looks too balanced. Humans writing fake flips subconsciously avoid long runs of the same face, because a run of six heads in a row feels like a mistake, not like randomness. But in a real sequence of 200 fair flips, a run of six or more of the same face is not just possible, it is expected — the probability of the longest run being under five flips is quite low. Genuine randomness is streakier than intuition allows, because each flip is independent of the last: the coin has no memory of how many heads it just produced, so nothing stops a long streak from happening.

The simplest way to test a sequence is to measure its longest run of identical outcomes and compare it to what pure chance produces. For $n$ independent fair flips, the expected length of the longest run grows roughly like $\log_2 n$: for 200 flips, this puts the expected longest run at around 7 to 8, with real sequences frequently reaching runs of 9 or 10. A hand-typed fake sequence, by contrast, rarely contains a run longer than 4 or 5, because the person consciously or unconsciously interrupts anything that starts to feel like a pattern.