counting · paradox
Gambler's fallacy
A long run of heads. Is the next flip due? That feeling is the gambler's fallacy.
A long run of heads. Is the next flip due?
Your flips
One trial: the streak, then the next coin
Flip the coin yourself. A smile is heads and a star is tails. The trial row stays separate.
After that streak, the next flip is
Lock a guess, then run the next flip.
0Current heads streak
—Next flip was heads, after that streak
—Next flip was tails, after that streak
Each flip is its own event. A fair coin stays at one half, whatever the row so far shows.
A long run of heads is uncommon, and it does not use up the heads.
After five heads in a row, the next flip is still heads about half the time. The same is true after any fixed streak.