Is a coin that just landed heads five times 'due' for tails?
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Is a coin that just landed heads five times 'due' for tails?
The short answer
No. A fair coin is not 'due' for tails after a streak of heads. Every flip is independent and stays 50/50, because the coin has no memory of what it did before.
How it works
Each flip of a fair coin is its own separate event with a one-in-two chance of heads and a one-in-two chance of tails. The coin cannot remember its last result, so a run of five heads does nothing to the next flip — it is still 50/50. Over hundreds of flips the share of heads does drift close to one-half, but that happens because the huge pile of new flips swamps the old streak, not because tails 'catches up' to balance it.
What people get wrong
Many people believe that after several heads in a row, tails becomes more likely because the coin 'owes' some tails to even things out. This is the gambler's fallacy. A fair coin keeps no record of past flips, so the streak changes nothing — the next flip is exactly 50/50, and betting that tails is 'due' wins about half the time, never more.
The catch
It is true that the long-run proportion of heads settles near one-half, so the average really does even out. But that is dilution, not correction: the gap between the total number of heads and tails is not pulled back to zero and often grows larger — it just becomes a smaller and smaller fraction as more flips pile up.
Questions kids ask
If the coin keeps no memory, why does the average end up near 50/50?
Because new flips outnumber the old streak. After thousands of flips, five extra heads from one early streak is a tiny sliver of the total, so the overall share of heads sits close to one-half. Tails never had to 'catch up' — the streak just got buried.
Does this mean a long streak of heads is impossible?
No. Long streaks happen by chance and are perfectly normal for a fair coin. Five or even ten heads in a row is allowed — it just tells you nothing about the next flip, which is still 50/50.
Is there ever a case where past flips do matter?
Yes, but only if the coin is not fair or the flips are not independent — for example a weighted coin, or a machine that always flips the same way. For an ordinary fair coin flipped normally, each result is independent and the past does not matter.
For grown-ups
This is the gambler's fallacy. Coin flips are independent trials, so P(tails) = 1/2 regardless of history. The law of large numbers guarantees that the relative frequency converges to 1/2, but it makes no promise about the absolute difference between head and tail counts, which is not driven toward zero. Convergence happens by averaging over many trials (dilution), not by a compensating force.