Scheltrum

Flip 3 Coins at Once

This page flips 3 coins at once. Eight sequences, all equally likely: three of a kind lands 25% of the time and all 3 heads exactly 1 time in 8.

Flip it

heads tails heads longest run

Each flip is an independent 50/50 draw from your browser's random number generator. A run of five or six the same way is normal in 100 flips — that is what surprises people most.

The numbers on 3 flips

  • 8 possible sequences, each with a 12.5% chance.
  • All 3 heads: 1 in 8, or 12.5%. All 3 tails, the same.
  • Three of a kind either way: 25%.
  • A 2-1 split either way: 75%.
  • More heads than tails: exactly 50%, because an odd number of flips cannot tie.

HHH is no rarer than HTH

Every one of the 8 sequences carries the same 1 in 8 chance, HHH included. What makes three heads feel special is that only one sequence produces it, while two heads and a tail can arrive three ways: HHT, HTH and THH. The totals are uneven. The sequences never are.

Odd one out

Three people each flip once and whoever differs from the other two is picked. It resolves 75% of the time; the other 25% is all three matching and you go again. That works out at 1.33 rounds on average, which is why it beats taking turns.

Three flips choose one of eight

Label eight options with the eight sequences and a single round picks between them evenly. It is the by-hand version of a number from 1 to 8. For a longer run try 5 flips, and the coin flip page covers every other count.