Scheltrum

Flip 2 Coins at Once

Press once and this page flips 2 coins. There are 4 equally likely sequences, HH, HT, TH and TT, so one head and one tail turns up half the time and two heads a quarter.

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.

All four outcomes

Sequence Heads Chance
HH 2 25%
HT 1 25%
TH 1 25%
TT 0 25%

Why a split beats a pair

The four sequences are equally likely, but two of them give one head and one tail. A split therefore comes up 50% of the time, while two heads is 25% and two tails is 25%.

This is where people go wrong. They count three results, two heads, two tails and one of each, then assume a third apiece. HT and TH are separate flips of separate coins, and squashing them into a single outcome is the entire mistake. Two more figures worth keeping: at least one head is 75%, and both coins matching is 50%.

Two flips settle nothing

Half the time 2 flips tie at 1-1, which makes them useless as a best-of. An odd count always produces a majority, so use 3 flips when someone has to win.

Picking one of four

Because the four sequences are exactly even, you can label four options HH, HT, TH and TT and flip twice to choose between them with no bias at all. For a plain yes-or-no, heads or tails does it in one, and the coin flip page handles any other count.