Flip a fair coin over and over. Which three-in-a-row pattern shows up first? It feels like a coin toss between them — it isn't. (Penney's game.)
H
T
Tap “Flip” to start a race.
Simulate many races
HHT first—
HTH first—
Cumulative across all runs this session.
Why isn't it 50/50? Once you flip two heads in a row (HH), the very next tail
finishes HHT — but HTH can never sneak in first from
there, because any tail after those heads completes HHT. That asymmetry tilts the race:
HHT wins with probability 2/3, HTH only 1/3.
The expected number of flips to first see HTH is 10; for HHT it's 8.