Rock-paper-scissors, but in another way
(The Rich, the Civilian and the Thief)

Author: István Scheuring

Recommended age: 10-99

Number of players: 10-40

Space needed for the game: classroom or a large enough space for players to move

Difficulty level: 1

Playing time: 10-15 minutes

Preparation time: 5 minutes

Accessories: 3 cards for each player, small enough to hide in their palms. The cards should show letters or symbols, such as R (rock), P (paper) and S (scissors). If we use an alternative frame story, then we should use those respective letters or symbols.

Short description: Because of the circular winning rule in the rock-paper-scissors game, those cards which are relatively rare will increase in number in the next round. Thus all cards remain in the game for a long time, except if one of them disappears because of random effects. Then only one type of card remains.

Preparations: Every player receives 3 different cards (with letters R, P and S, or symbols, or letters/symbols according to the alternative frame story).

Course of the game: Similar to the well-known game, rock beats scissors, scissors beats paper and paper beats rock. We ask everybody to shuffle their cards with closed eyes and take one of them in their right-hand palms. The other two cards remain in their left-hand palms. Then we ask the players to move around freely, and to choose a pair if hearing a sign (for example clapping). (If there are an odd number of players, the leader can join, or one player can “rest” in each round.) The pairs show each other their right hand cards. Those who have lost, change their right hand card to the one that beat them. For example, if player A has Scissors in her right hand, and player B has Paper, then player B will lose and change her Paper card to a Scissors card in her right palm. Naturally, if both players have the same card in their right palms, then nothing happens. Then the players move again, and after the sign, they find a new partner and the same happens as before. The game leader stops the game after every 3-5 rounds and asks the players to close their eyes. Then she asks those who have Rock in their right palm to put their hands up. She counts the players with Rock cards, and records this number on a paper. Then she does the same with Scissors and Papers. Then the game continues as before. It is worth playing 20-30 rounds to have 8-10 cases when the number of actually played R, S and P cards are recorded. The leader and the players can analyze the recorded values together. The best practice is to draw a figure from the data. It will look something like this:

Figure 1.

We can have two observations based on the figure: 1. It is highly probable that neither strategy will disappear. 2. If a strategy (card) is used by many players, then the number of this card will decrease soon, while the number of the card beating this card will increase. Naturally, any of the cards can disappear from the game for stochastic reasons, especially if there are only a few players. Such disappearances will be followed by the disappearance of the loser strategy of the two remaining strategies.

The alternative frame story has a direct biological analogy, too. The thieves can easily steal from the rich, because the rich have too much to look after, so T beats R. But thieves are not successful against civilians, since the latter are capable of keeping an eye on their less valuable property. That is, C beats T. Finally, as the rich have much more property than civilians, R beats C.

Biological background: The game explains that in cases when the success of a strategy (behavioral type) depends on the presence or absence of other behavioral types, and these strategies are in a circular winning relation, then these strategies remain in coexistence for a long time. What is more, the frequencies of these types typically change cyclically. This is because the rare strategies increase in number at the expense of the more frequent one, which loses against this rare one. It is beneficial (on the short run) to be rare. The excellent biological example of this phenomenon comes from a small Central American lizard (Uta stansburiana). Males follow three different mating strategies. These highly heritable behaviors are correlated with the throat color of males. The orange-colored males (the rich) maintain a high territory and own more than one female. The blue-throated males (civilians) have a smaller territory and own only one female, who they strictly guard. Finally, the yellow-throated males (thieves) don’t own territory, but try to fertilize females guarded by the others. More than twenty years ago it was pointed out that the frequencies of the different strategies change continuously in this population following a 6-years cycle. This type of selection mechanism maintains behavioral and genetic diversity.

References: Sinervo, B.; C.M. Lively (1996). "The rock–paper–scissors game and the evolution of alternative male strategies". Nature. 380 (6571): 240–243. doi:10.1038/380240a0