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Hablox

What actually evens out when you flip a coin

Flip a coin long enough and the share of heads settles on a half. The GAP between heads and tails does the opposite — it usually grows. Both things are true at once, and only one of them is what people mean by 'it evens out'.

What actually evens out when you flip a coin — the interactive part

After 10,000 flips
50.10%
5,010 heads
Expected
50.00%
Heads minus tails
20
the gap grows even as the share settles

The first 20 trials, one square each

12 / 20

counteddid not

Share of flips that came up heads

Trials run so far (log scale)

This chart as text
  • After 10 trials: 0.3
  • After 100 trials: 0.53
  • After 1,000 trials: 0.505
  • After 10,000 trials: 0.501
  • Exact answer: 0.5
The share of flips that came up heads, as more trials are run
10 trials
30.0%
100 trials
53.0%
1,000 trials
50.5%
10,000 trials
50.1%
exact answer
50.0%

Runs a fresh set of trials. Moving a slider keeps the same random draws, so only the thing you changed changes.

After 10,000 flips is 50.10%, 5,010 heads. Expected is 50.00%. Heads minus tails is 20, the gap grows even as the share settles.

Calculated by our own tested code

The gambler's fallacy, precisely

After ten heads in a row, tails is not 'due'. The coin has no memory, and nothing pushes the counts back together. What happens instead is that the ten-head lead stops mattering: it is enormous against ten flips and invisible against ten thousand. The proportion converges because the denominator grows, not because the numerator corrects itself.

Check your understanding

You flip 10,000 times and heads leads by 90. What is the most likely next 10,000?

Pick one to check yourself.