I was listening to a podcast today, the Hidden Brain podcast. It was about coincidences and how we, as people, think they have special meaning; but in reality the mathematics behind coincidences is that they aren’t that unusual after all. We tend to confuse probability with unlikelihood, and attribute meaning to it when we encounter it. We’re not good judges of randomness.

Anyway, the podcast went on and then gave the listener a chance to use probability in order to demonstrate their *own* magical powers. Here’s how the trick goes:

First, you get a group of people together and tell them you’re going to have a coin flipped 30 times. But before you do, give everyone a piece of paper and enter in columns of numbers 1 through 30. Each person in the group should then make a prediction of what a coin toss of 30 times in a row will look like. For example:

1. Heads

2. Tails

3. Tails

4. Head

5. Tails

6. Tails

7. Tails

8. Heads

9. Tails

10. Heads

And so forth.

One person refrains from writing their prediction. It is this person who is going to flip the coin 30 times in a row and write the results on their own piece of paper. They do this while you leave the room. So, in effect, everyone but one makes a prediction of 30 coin tosses, and then that one records the results of the actual tosses. You can’t see the results of anyone – predictions nor actual result – since you are in a separate room.

You then re-enter the room and gather up all the predictions plus one actual result (the reason why you have one person refrain from making a prediction *and* recording the actual result is so that you cannot tell due to a duplicate set of handwriting who has two sets of results – a real one and a prediction – because otherwise people will accuse you of doing this and narrowing your odds to 50/50 [1]).

**You gather up the results, look them over, and correctly announce which one of the sheets of paper contains the actual tosses from amongst all of the predictions.**

It’s an amazing magic trick!

So how is it done?

It’s done by using mathematics, and more specifically, probability and statistics. For you see, in the example above, the heads and tails alternate with regularity. Heads, then tails, then heads twice, then tails, then heads, then tails, and so forth. The results flip back and forth quite often because as we all know, flips of a coin are 50/50. It’s either heads or tails, and maybe we get two or possibly three results in a row. That’s what our predictions would reveal.

But in reality, a 50/50 occurrence in a coin flip will have long sequences of heads or tails. That is, we might get 5 or 6 heads in a row followed by 5 or 6 tails in a row. It’s unusual to sit down and flip a coin that often and get that result, but given 30 coin flips that’s almost inevitably what you will see in real life.

So what you have to do is look for the result with the longest sequences of heads and tails because that’s the one that will occur in real life, whereas everyone’s prediction will only have short sequences of heads vs. tails.

And that’s how you use probability and statistics to do a magic trick.