HANNAH FRY: So today we're going to talk about rock-paper-scissors
and I reckon everyone knows how to play it
Scissors beats paper, paper covers rock, rock blunts scissors, so three--
BRADY: Wait, I always thought it smashed them? Dr. FRY: Oh, I thought it blunts them
Actually, if anything, it would probably sharpen them, right?
There are three strategies, each one of them loses once and wins once
So it looks like there's no strategy that you can play to win, but I'm going to show you
about a new paper that had just come out where it gives you some top tips of how to win
So it's a group of Chinese scientists, where they run an experiment
where they got 360 students to play games of rock-paper-scissors with one another
300 rounds in every game, which took up to 2 hours,
which is astonishing, students playing rock-paper-scissors for 2 hours
Okay, so normally if you have rock-paper-scissors
and some of you had rock (R) up there, and rock is beaten by paper (P), which is then beaten by scissors (S)
So none of these strategies dominate the other,
so really all you can do is play each strategy with an equal probability: 1/3, 1/3, 1/3, okay
Now, if you were playing against a computer, who was choosing these perfectly randomly,
then that would be the best thing for you to do -- just to pick each strategy with equal probability
But the thing is, humans are quite predictably irrational, so to say, in the way they choose their strategy
So, in recording what one of these students did in playing rock-paper-scissors
the scientists came up with two quite important findings of how people try to beat each other
Okay, so the first one is that people who win tend to repeat their strategy
So, for example, if I beat you by playing rock, there is a very high chance, or high probability
that I will play rock again the second time. If it worked once, it's going to work again, right?
The second thing that they found out is that losers change
BRADY: To anything in particular, or...? DR. FRY: Well,
so this is a thing that you can exploit, essentially
so if you know-- so this gives us, I suppose, two strategies that we can use
So the first tip is that if you lose, that means the other person just won, right?
So let's imagine that your opponent won by playing rock
Now, the chances are that they're going to play rock again, you should then play paper
so you just lost on scissors, so you should play paper
which means that, basically, even though paper beats rock
(so the cycle goes around like this: paper beats rock and so on)
you should go the other way around the triangle
Let's imagine that you played scissors, the other person played rock,
what you should do is you should go backwards around this triangle and play paper the next time
because of the high chance that they're going to play rock again
So that's the first thing: Go backwards, I guess
Or another way to say it is -- essentially, you've just played scissors, they've played rock
so play the thing that didn't come up in that, if you lose
Now the second thing, is that if you've just won
now, they're going to expect you to play the same thing again, right?
which means, that they're going to play the thing that you would beat the thing that you just played
so you need to play the thing that would beat that would beat the thing that you just played
which is equivalent to saying, you need to play what they just played
you want to [laughs] let's go again
[both laugh]
BRADY: I like the easy way better, so you should play what they just played
DR. FRY: You should play what they just played, yes
So let's imagine, then, you just won -- you played rock, right? -- and you just won on rock
that means that they played scissors, now they're going to think that you're going to play rock again,
which means that they're going to play paper, which means that you should play scissors
and so again, you basically end up going backwards around the triangle
so play what they just played, and the game go backwards
or an easier way to say it then is to play what they just played.
So in general, if you're cycling through rock-paper-scissors, your best strategy is to go backwards
and go scissors-paper-rock, and cycle through that way
BRADY: How much-- Is this mathematics or is this psychology? This is--
I can't tell if this is all to do with probability, or it's just about knowing how humans think
DR. FRY: Well, I think that a balance of the two, so it's rooted in game theory
which is the mathematics of looking at decisions and strategies,
so in any situation where you're competing against someone,
and you best move is dependent on what the other person is playing, you can frame in game theory
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