Does luck really exist?

When you toss a coin in the air, nobody can say whether it will land heads or tails. But toss the same coin a thousand times, and almost everyone knows that heads will come up very close to half the time. Individual events can't be predicted, yet the total is remarkably regular. That is one of the most surprising ideas in maths.

This journey first teaches you to count the possible outcomes, and then to turn that count into a probability. After that you'll see why experiments get closer to the theory in the long run: the law of large numbers. There's also a very common trap in thinking: if a coin has come up heads five times in a row, is the next toss more likely to be tails? The answer surprises a lot of people.

Finally, you'll put experimental and theoretical probability side by side. You'll be able to tell where what we call "luck" is genuinely uncertain and where it is surprisingly regular.