Coin Run Detective — Probability

Spot the real coin pattern

Story: Imagine two kids make a list of coin flips. One uses a real coin. The other just makes up a pattern that “looks random.” Which list will fool you?

Look at these two sequences of coin flips. One was typed by a person trying to “be random”. The other was made by a real coin.

Two sequences below — one was made by a person trying to "be random", the other by a computer. Which one is truly random?

Which sequence is the real coin flip?

Most people pick the wrong one because they expect random results to go H T H T H T. Real randomness is usually messier than that.

Big idea: random does not mean neat

When you flip a fair coin, each flip is still 50-50. But 50-50 does not mean:

heads and tails must take turns
you cannot get 3 or 4 of the same in a row
the next flip has to “fix” the earlier flips

It only means that after lots and lots of flips, the total number of heads gets closer to half.

Short run: a few flips can look wild, uneven, or streaky.

Long run: many flips settle down and get closer to half heads, half tails.

Try it yourself

0 Heads

0 Total

— % heads

Last 20 flips:

Flip 30 coins. Then 100. Then more.

If you see a run of 4 or 5, that is not a broken coin. That is normal.

Why people guess wrong

When people try to make a fake random list, they usually avoid long runs. They think H T T H H T looks better than H H H T T T.

But a real coin does not care what happened before. If heads happens four times in a row, the coin is perfectly happy to do that.

That is why real coin lists often have more runs than human-made lists.

What does 50-50 look like?

Use the flipper and watch the heads percentage.

After a small number of flips, the percentage can be far from 50%.
After 100 flips in our demo, it was 53.0%.
After 10,000 flips, it was 50.2%.

This is the Law of Large Numbers in a kid-friendly sentence:

The more times you try something random, the closer the total gets to what you expect.

It does not mean the coin remembers past flips.

Quiz time

You flip a coin 5 times and get H-H-H-H-H. What is the probability the next flip is Heads?

You see a sequence: H H T T H H T T H H. Is this more likely to come from a person or a real coin?

In 100 coin flips, we saw a streak of 9 in a row. Is that surprising?

If you flip a fair coin 10000 times, roughly how many times do you expect Heads? (Hint: think about 50-50.)