How To Use Science To Win At Rock-Paper-Scissors?

Rock-Paper-Scissors is a children’s game. What does it have to do with science? Well, there are branches of science that figure out how games work. One such branch happens to be game theory.

And that’s where our story begins. Game theory researchers have been trying to figure out a winning strategy for the typical rock-paper-scissors game, and have come up with intriguing results.

The results turn out to be surprisingly counterintuitive, yet simple. If you are interested in winning a random game of rock-paper-scissors at a party or two, read along. But remember to credit science if you do indeed end up dominating your friends.

This essay is supported by Generatebg

Rock-Paper-Scissors – The Rules

For starters, it makes sense to revisit the rules of the most common version of the game. It involves 2 players, and 3 elements – rock, paper, and scissors. Each player calls one of the three available elements simultaneously. And the stronger element wins over the weaker element. Typically, the cumulative best out of 3 rounds wins.

Rock is superior to scissors, scissors are superior to paper, and paper is superior to rock (illustrated by the triangle in the image above). You’ll notice that no element is outright superior to the other two elements. This is what makes the game fun as winning involves the role of chance.

Science Applies Game Theory

Whenever chance is involved, mathematicians tend to barge into the scene. That is exactly what happened with game theory and rock-paper-scissors. Theoretically, each of the three elements in the game has an equal probability of occurrence (1/3).

Therefore, the rational player should choose one of the three randomly. And this should indeed be the best approach according to classical game theory. But human beings almost never fit the theoretical definition of rationality, and this approach doesn’t describe real-life game behaviour well.

So, researchers tried to apply a bounded rationality model known as evolutionary game theory, where microlearning models are employed. Unfortunately, this didn’t tie well to observed reality either. All in all, the application of game theory just didn’t seem to fit empirical observations.

Experimental Research

Having faced challenges with applying game theory, some Chinese researchers decided to conduct an experiment with 360 participants. They split the participants into groups of 6 and conducted a series of rock-paper-scissors games.

They came up with two key empirical observations that didn’t fit the theory of chance:

1. When a player won a round,  more often than not, the player chose the same winning element for the next round.
2. When a player lost a round,  more often than not, the player chose to avoid the same losing element for the next round.

For instance, if a player won a round by calling ‘Rock’, she was likely to call ‘Rock’ again in the next round. And if she lost the round by calling ‘Rock’, she was likely to avoid calling ‘Rock’ again in the next round. This behaviour is due to the psychological nature of human beings. Since we are just interested in winning at rock-paper-scissors here, I’ll skip the rabbit hole of psychoanalysing humanity.

The Winning Strategy For Rock-Paper-Scissors

Based on the empirical observations, the researchers came up with 2 conditional responses, also known as heuristics in decision theory. After testing, they confirmed that the strategy performed better than game theory in maximizing win rates.

Here’s the winning strategy in the form of two heuristics:

1. If you win using one element, for the next round, go for whatever element your opponent just lost with in the current round.
2. If you lose using one element, for the next round, go for whatever was not called by either of the players in the current round.

Why Does It Work?

Now, let me explain why this strategy works. Assume that you called ‘Rock’ and your opponent called ‘Scissors” — you win. For the next round, your opponent is likely to (psychologically) expect that you call ‘Rock’ again. So, they are likely to call ‘Paper’ to beat your likely ‘Rock’ call. Therefore, anticipating this, your chances increase if you call ‘Scissors’ (to beat their likely ‘Paper’ call). This is the logic behind the first heuristic.

Now, asNow, assume that you called ‘Rock’ and your opponent called ‘Paper’ — you lose. For the next round, your opponent is likely to call ‘Paper’ again. Therefore, anticipating this, your chances increase if you call ‘Scissors’ (to beat their likely ‘Paper’ call). This is the logic behind the second heuristic.

Besides the logic that I just presented, it is important to note that these are empirically tested strategies that give an edge based on human pyschology.

Of course, if both players are aware of this knowledge, the game gets more complicated, and a random choice ‘likely’ ends up being the better choice. But if you are the only person who knows this, you should obtain an edge over your opponent. Best of luck!

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Credit: Wang et al. (original research paper), Hannah Fry (analysis), and Brady Haran (presentation).

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Further reading that might interest you: What Really Happens When You Divide By Zero? and The Fascinating Reason Why Temperature Has No Upper Limit?