Scheltrum

Coin Flip

The coin above lands heads or tails with an even chance each time. The pages under it flip several coins at once and count the results, from two flips up to a thousand.

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.

Every page in this section

The odds, exactly

One flip is 50 per cent heads, 50 per cent tails. Two flips give four equally likely orders, so two heads happens once in four. Three flips give eight orders, so three heads in a row is 1 in 8, or 12.5 per cent. Each extra coin halves the chance of an unbroken run.

Streaks are ordinary, not evidence

Flip twenty times and a run of five or more identical results appears somewhere in the sequence 45.8 per cent of the time. In ten flips, a run of four or more turns up 46.5 per cent of the time. That is close to half in both cases. A streak on twenty flips is what a fair coin looks like, and over a thousand flips a run of ten identical results is more likely than not, at 62 per cent.

Nothing is ever due

After six heads the next flip is still 50/50. The coin holds no record of the six. What is true is that a run gets diluted rather than corrected: keep flipping and the six are outnumbered by later flips, so the average drifts back towards half. Tails are never owed.

Even splits are rarer than people expect

Ten flips land on exactly five heads only 24.6 per cent of the time. Twenty flips land on exactly ten heads 17.6 per cent of the time. The even split is still the single most likely result, and it still loses to everything else put together, which is why ten flips so often reads 6-4 or 7-3.

Real coins are slightly unfair

A tossed and caught coin carries a small same-side bias. A 2023 study of 350,757 human tosses found the coin landed on the side that started facing up about 50.8 per cent of the time, caused by wobble in the toss rather than a weighted coin. Spinning a coin on a table is worse. The tool above has no physical bias at all.

The coin pages

  • Heads or tails and yes or no – one flip, labelled two different ways.
  • 2, 3, 5 and 10 flips – small batches, where the split still swings hard.
  • 100 and 1000 flips – big enough to watch the ratio settle near half.