Flip a coin

What are the odds of heads or tails?

Exactly 1 in 2 for each side, on every flip. The coin has no memory, so after five heads in a row the next toss is still a 50/50. What is unlikely is the whole run: five heads in a row, judged before the first flip, happens about once in 32 attempts.

Runs are more common than most people expect, which is why the streak counter is fun to watch. Flip a few dozen times and you will usually see a streak of four or five of the same side. That is normal randomness, not a broken coin.

Are real coin flips really 50/50?

Almost, but not quite. In 2007 the mathematicians Persi Diaconis, Susan Holmes and Richard Montgomery published a physical model of the coin toss showing that a flipped coin tends to wobble in a way that keeps its starting face up slightly more of the time. Their estimate was a small bias of about 51% towards the side that was facing up when the coin left the thumb.

A team led by František Bartoš tested the idea on a large scale in 2023. Volunteers recorded 350,757 flips, and the coins landed on the same side they started on roughly 50.8% of the time. They found no sign that heads or tails as such was favoured; the lean came from the starting position.

A digital flip has no starting side, no thumb and no wobble. Each result here is drawn fresh by your browser's secure random generator (more on that in how random a spin really is), so it behaves like the perfectly fair coin that textbooks describe.

How does best of three work with a coin?

Best of three means the first side to win two tosses takes it, so the contest ends after two or three flips. It is popular because a single toss can feel abrupt, and a short series gives the loser a moment to accept the result.

There is a shortcut: set the selector to 3 coins and flip once. With an odd number of coins one side always has the majority, so a result such as "2 heads, 1 tails" settles it in one press. Choose 5 coins for best of five. The odds are the same as playing the series out one toss at a time.

When do people use a coin toss?

• Sport. Football referees toss a coin before kick-off so the captains can choose ends or the kick-off, and cricket captains toss to decide who bats first.
• Settling small disputes. Who drives, who picks the film, who gets the last slice. Agree on the stakes first and accept the result.
• Choosing who starts. Board games, card games and video game matches often begin with a toss. For three or more players, the who goes first wheel handles everyone at once.
• Breaking a tie between two good options. If both choices are fine, a coin saves the time you would spend going back and forth.

Coin, wheel or dice?

A coin is ideal when there are exactly two outcomes. If you would rather see the words on screen, or might add a third option later, the yes or no wheel gives the same odds with labelled slices. We compared the maths of both in coin flip vs wheel probability. For more than two outcomes, roll a dice instead.