Anti-Buzz: Pick a number …

by Andrew Emmott on September 25, 2012

in Anti-Buzz

Any number. Any number at all.

The Anti-Buzz: You can’t.

Time to switch gears and get super nerdy again.

I wrote earlier this year about how probability is counter-intuitive to most people, and then went on, (perhaps too long), about a famous problem. Here’s something a little more down to earth. Like the peanut butter sandwich, it is yet another common pedagogical game that is used to surprise the audience and charm them into believing a complicated idea – in this case, getting them to believe that their intuitions about probability are inherently bad. I share it with you now because it can also make for a pretty great party trick. It also demonstrates a weird quirk of the human brain.

Scaling this down to impress a stranger is easy, but I will explain the classroom version. The instructor has each student get out a piece of paper and a coin. Students are instructed to choose one of the following: Flip the coin 100 times and record the sequence of results, or fake it and just write down a sequence of results and never flip the coin. The instructor leaves for a few minutes, returns, and with high accuracy is able to discern the real sequences from the fakes.

How? Because as it happens, humans tend to be very bad at faking randomness. If you know what to look for, you can spot it. In the case of a hundred real coin flips it is extremely likely that, somewhere in there, there is going to be a “run” of at least five of the same results, (five heads in a row or five tails in row). I probably don’t need to try very hard to convince you that if you spit out a “random” sequence of heads and tails, you probably wouldn’t ever say the same result five times in a row. If the sequence doesn’t contain a long run, it’s a fake.

This exercise can illuminate several bad intuitions.

First, if you have a hard time believing that a run of at least 5 is very very likely in a sequence of 100, you are probably focused on how unlikely it is if you were to flip the coin just five times. Well, it’s actually not that unlikely – 1/16 to be exact. (No! It’s 1/32 you say? Remember: all heads or all tails – again, intuition can get very angry and wrong when odds are involved). You can probably imagine that, on average, you’d have to try the five-flip-trial about 16 times before it worked. Well, with 100 flips you are actually trying five flips 20 times, and you can get a run in overlaps as well. So really, when you break it down like that, it’s not so weird sounding, right?

Now imagine you were participating in this exercise and trying to summon a random sequence from your brain. Why are you so unlikely to make a run of five? Because, even in room full of technical students who know better, one of the most fundamental wrong intuitions about probability is that an event occurring makes it less likely to happen again. And maybe you roll your eyes because you think you know better? Not when you are asked to simulate randomness yourself. Even with the knowledge above, even shoe-horning a run of 5 into your new simulation, you’re still going to be guilty. It’s because you are focused on the big picture. You are trying to produce a believable sequence and in so doing, you are always looking back at what you just spat out, influencing your next “random” decision, typically working toward the goal of being “fair” and trying to give heads and tails an equal share of the pie.

Don’t believe me? You can play rock-paper-scissors against a computer that learns your tendencies. If you’ve ever played a long series of games of rock-paper-scissors against an opponent and discovered that you could often beat them, (or perhaps you were on the receiving end of this), it’s because you were exploiting the fact that they aren’t capable of being random. Maybe you could second guess them, maybe you were good at imagining what they were thinking. The point is that people aren’t arbitrary. They make decisions and they justify them.

I suppose there’s a cutthroat business lesson here about learning to predict your opponent and crushing them like a flimsy pair of scissors, but that’s certainly not what I’m after, (though by all means go ahead). The inverse, of course, is not to be a bushwacked pair of scissors, boxed into ineffectiveness by your faulty intuitions.

Perhaps take solace in the fact that people aren’t random. Take joy in the fact that we instinctively try to be fair and just, even to coins. Be proud that we work with intent, that we seek reasons, that we aim to do our best.  Or if all of that is too sappy then go with the opponent crushing thing.

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