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Coin Flip

Flip once to decide something, or raise the count and watch heads and tails converge: slowly, and not the way most people expect.

What a hundred flips actually look like

A fair coin gives heads half the time, and almost everybody misreads what that means. It does not mean the counts stay close together. Flip a hundred times and a gap of ten between heads and tails is unremarkable; flip ten thousand and the typical gap grows to around a hundred. The gap widens as you flip more, not narrower. What converges is the proportion: 55 out of 100 is 55%, while 5,100 out of 10,000 is 51%, even though the second is off by a hundred flips and the first by only five.

This is why the gambler’s fallacy is a fallacy. After six heads in a row, tails is not owed anything. The coin has no memory, no record of what it just did, and the seventh flip is 50/50 like the first. Runs of six happen roughly once in every sixty-four stretches of six flips, which is to say constantly. The reason long runs stop looking strange is not that some force corrects them; it is that the later flips dilute them into the proportion.

The other thing worth knowing is that a real coin is not perfectly fair, and not for the reason people assume. The bias is not in the weight of the faces but in the flip: a coin caught in the hand lands the same way up as it started slightly more often than not, around 51% by the best-known measurement, because it precesses rather than tumbling cleanly. A coin allowed to bounce on a table is a different and messier story. This page has no such physics: it asks the browser’s cryptographic generator for a bit and shows you the result, at exactly 50/50.

For settling an argument, one flip is the whole tool. The counter exists for the other use: showing somebody what randomness looks like when you can see a hundred of them at once, which is far streakier than the smooth alternation people imagine when they picture “random”.

Frequently asked questions

Is it really 50/50?

Yes. Each flip takes one bit from the browser’s cryptographic random source, and the two outcomes are exactly equally likely. Unlike a physical coin, there is no spin, no catch and no table to complicate it.

I got six heads in a row, is it broken?

No. A run of six has about a one in sixty-four chance in any given six flips, so it shows up regularly. If it never happened, that would be the suspicious result: real randomness is streakier than people expect.

Is a real coin fair?

Close, but not exactly. A flipped coin caught in the hand lands the same way it started about 51% of the time, because it wobbles around its axis instead of tumbling end over end. The weight of the two faces has almost nothing to do with it.

Can I flip more than one coin at a time?

Yes. Set the count and you get every individual result plus the running tally of each side. Up to 1,000 at once, which is enough to watch the proportion settle while the gap between the two counts keeps growing.

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