Coin flip

How a fair coin works

A fair coin has two sides, and both come up with equal probability — 50/50. This tool does not manipulate anything: the side is chosen by a cryptographic generator directly in the browser. The animation only shows the decision that has already been made, so it does not affect the result.

Each toss is independent of the previous ones. The coin 'does not remember' what came up last time: after five heads in a row, the probability of a head again is exactly 50%. This property is called the independence of trials, and it is precisely because of it that long streaks are not an anomaly, but a normal part of randomness.

50/50 probability: what it means in practice

In a series of one hundred tosses, you should not expect exactly 50 heads and 50 tails: the usual variation is a few units in either direction. The longer the series, the closer share towards half, but the absolute difference can still grow. The law of large numbers refers to proportion, not equality of count.

Why a run of five heads is normal

The probability of seeing five identical sides in a specific set of five throws is 1 in 16. In a series of a hundred throws, there are already 96 such "fives," so at least one series of five identical sides in a row occurs almost always — about 97% of the time, and a series of exactly five heads — about 81%. People tend to see a pattern or a "glitch" in this, even though it is just ordinary randomness.

A common mistake is to think that after a series of heads, a tail "should" come up. The coin does not try to even out the score: it simply continues to come up with a 50-50 probability.

Where a coin toss will come in handy

• to settle the dispute over who pays for coffee or washes the dishes;
• choose one of the two options when the arguments are equal;
• to determine the first player in a board game;
• to test intuition about series and probabilities;
• to conduct a fair draw between two participants.