# Five Coins

The odds of a flipped coin coming up heads five times in a row is 1 in 32. If you’ve flipped a coin four times and it’s come up heads all four times, the chance of the fifth flip coming up heads is 1 in 2.

A lot of people struggle with that, conceptually. That’s the heart of the Gambler’s Fallacy: the belief that past events can influence raw in-the-moment probability. After all (some people think), if there’s only a 1 in 32 chance of getting five heads in a row, then surely this fifth flip coming up heads must be very unlikely!

Of course, you’re not evaluating the difference between getting five heads in a row versus the probability of getting one tails. You’re evaluating the probability of getting five heads in a row versus the probability of getting exactly four heads and one tails, in that order. And the chances of those two outcomes are equal – 50/50. So if you want the past four flips to “count,” then you have to count them both ways.

This all doesn’t really matter to the current flip, though. The thing that makes “five heads in a row” unlikely has already happened, so you’re only really asking “out of every time four heads get flipped in a row, how many times is the next flip also heads?” Which is again, 50/50.

Here’s what I notice about people.

If someone has 8 hours to complete a task, and they get distracted for 6 of them, they’ll stress. They’ll think the job can’t be done in 2 hours, that they’re a failure, that they’ve already lost. But if you just gave them 2 hours, they wouldn’t feel that way.

The past flips already happened; they don’t affect the present chances of success. They are what they are, good or bad. Call it.