In a run of n coin flips the longest streak of the same face lands near log₂n — about six or seven in a hundred flips — so a streak that looks rigged is usually the ordinary case.
There are many places in a long sequence for a streak to start, and the chance of at least one long streak appearing somewhere grows with the number of opportunities even though each individual flip stays at fifty-fifty.
It is a description of what randomness looks like, not a test of it. A genuinely biased coin also produces long runs, so a long streak on its own neither proves nor disproves anything — that needs a goodness-of-fit test over many flips. It also tempts people into the opposite error: believing a streak must end soon, when the next flip is always fifty-fifty.
Estimate with the rule, then check it against the calculator that models it properly.
Open Dice Roller & Coin Toss →In a run of n coin flips the longest streak of the same face lands near log₂n — about six or seven in a hundred flips — so a streak that looks rigged is usually the ordinary case. There are many places in a long sequence for a streak to start, and the chance of at least one long streak appearing somewhere grows with the number of opportunities even though each individual flip stays at fifty-fifty.