With three children, I have my own laboratory at home for performing psychological experiments. Before anyone calls social services, there is an ethical committee standing by (their mother).

This evening, I tried out one of my favourites: testing the perception of randomness. Here is the setup: I gave the boys two pieces of paper and a 20 cent coin. I was to leave the room, then they had to decide which of the two sheets of paper would be decided by the boys and which by a coin. Having made their choice, they then had to write down on one of the sheets their best attempt at a “random” sequence of 100 heads (H) and tails (T). Having done that, they were then to toss the coin 100 times, writing down on the other page the sequence of heads and tails that came up. I would then return to the room and guess which one was determined by the toss of the coin, and which by the boys.

I identified which sequence was which in less than 30 seconds. How did I do it?

The trick is to look for the longer sequences. Much like the gambler at the roulette wheel, the kids assume that a run of heads cannot last too long. One of the sheets had three runs of 5 in a row and two runs of 4, while the other had only one run of 5 and one run of 4. I correctly picked that the sheet with more long runs was determined by the coin toss.

Try it yourself sometime. If you see a run of 6 or more (which is in fact quite probable in a sequence of 100 coin tosses), you can quite confidently pick that as the coin toss, unless your subject has been well schooled in probability.

Our intuition struggles with randomness. We tend to assume randomness is more regular than it is. On the other hand, we also try to find patterns where there is only randomness, whether it is the man in the moon, clouds that look like things, the face of Mary on a piece of toast or, perhaps, an explanation for the disappearance of MH 370.

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{ 4 comments… read them below or add one }

Great. A random chance to plug my favourite Radiolab episode: Stochasticity. You might have to google it.

@Dan ahh yes, Stochasticity is one of the classics! It does include this heads/tails test.

Can you calculate the p-value for the Chisquared Test for each setup’s numbers and possibly a histogram of frequency of sequences of length “n”, with the expected values as well?

@Zebra a new post is up with some histograms (no Chi-squared test though).