Five heads in a row, so tails must be due. Why that feeling is wrong.
Five heads in a row does not change the probability of heads on the next toss; it stays one half. A coin has no mechanism for storing past results. People nonetheless feel that balance must be restored and judge from that feeling. This is the gambler's fallacy.
It is true that the ratio approaches half over many tosses. That happens not because past imbalance is compensated but because, as trials accumulate, the early imbalance becomes a smaller share of the whole. The run of five does not disappear; it is diluted. Separating those two explanations changes how you judge.
At 1%, it feels as though a hundred attempts should produce one hit. In reality, the chance of getting nothing in a hundred attempts is over a third. Low-probability trials carry both a high expected count and far wider variance, so planning from the average alone goes badly wrong.
Shown a genuinely random sequence, people feel it is too clustered to be random, because real randomness naturally produces runs. Sequences people invent to look random contain too few runs. A result feeling strange is therefore not evidence that anything was manipulated.
The usable principles are simple: do not predict the next result from the last, plan low-probability attempts around a near-worst case rather than the average, and set a limit before starting. This explains how probability works; it is not advice about which games to play or how much.
Each button runs this keyword on that search engine