For the fundamental model system of Rock-Paper-Scissors (RPS) game, classic game theory of infinite rationality predicts the Nash equilibrium (NE) state with every player randomizing her choices to avoid being exploited, while evolutionary game theory of bounded rationality in general predicts persistent cyclic motions, especially for finite populations. However, as empirical studies on human subjects have been relatively sparse, it is still a controversial issue as to which theoretical framework is more appropriate to describe decision making of human subjects. Here we observe population-level cyclic motions in a laboratory experiment of the discrete-time iterated RPS game under the traditional random pairwise-matching protocol. The cycling direction and frequency are not sensitive to the payoff parameter a. This collective behavior contradicts with the NE theory but it is quantitatively explained by a microscopic model of win-lose-tie conditional response without any adjustable parameter. Our theoretical calculations reveal that this new strategy may offer higher payoffs to individual players in comparison with the NE mixed strategy, suggesting that high social efficiency is achievable through optimized conditional response.

Summary: The optimal win strategy should be choosing one of the three options randomly, but that’s not what happens. Winners tend to stick with the winning choice. Losers tend to move on to the next choice in the rock, paper, scissors name - in that order - because that’s how they memorized the cycle.

I thought there was another study awhile ago that showed throwing paper for your first time with someone would give a slightly higher chance than pure random. I think the hypothesis was that rock, being assumed to be the strongest article in the trinity of choices, would be picked more often in a random sampling. Subconsciously people would prefer that choice to play from a position of strength.

After this initial random throw, then the rest of this new article would come into play.

The best way to win RPS is making the scissors shape and letting it slightly stick out from behind your head during the countdown.
When the countdown is over choose paper.
This is a tried and true method. Works 90% of the time unless you are up against an idiot who doesn’t notice the scissors.

That sounds brilliant and I totally want to try it but… Do people prepare for Rock Paper Scissors behind their heads? Is that a typo for ‘hand’? Either way, I don’t get it.
I always played RPS by shaking a fist like this: https://www.youtube.com/watch?v=E7OCzz_XuiI (PS: That was the first youtube hit. I make no promises about the video’s comedic value.)

I guess it’s a regional thing. We used to hold our hands behind our heads while chanting something like: “Rock, paper scissors. One of us will win. 1, 2, 3”. That gave the other player enough time to see the scissors and come up with a counter.

Yeah, our method was always much simpler, three shakes of a closed fist while saying either “1,2,3” or “Ro-Sham-Bo” (probably spelling that wrong). On the third syllable, both would simultaneously put their fist into the chosen shape.

Just to be nit-picky here: the game-theoretically optimal strategy (of picking completely at random) is only the optimal one if you value all payouts equally and believe that you can’t predict your opponent’s choice. If you can’t predict your opponent’s choice, then what you do won’t matter because your opponent is picking randomly and thus you will each win equally. If you think you can and are willing to risk a loss to try out your theory in hopes of a bigger win (or just extra excitement from having a strategy other than random choice), then you should try to predict it.

I think one of the places that classical game theory consistently fails is when it discounts outcomes that are essentially identical. In other words, calling something a NE because no one can improve their risk-adjusted payout by deviating doesn’t tell the whole story when deviating has a chance to improve your payout. There’s a difference between an outcome with 100% chance of 0 payout, and one with a 1% chance to pay 10 and a 10% chance to pay -1. That’s waved away by saying “utility” but then mathematical payouts are always assumed to approximate utility. Imagine if nothing beat rock, but rock beat nothing, and one player was the “defender” who won when both play paper or scissors, and the attacker wins when they play something different (but rock is always a tie). How often would people play rock?