RoShamBo

Just recapping, RoShamBo is a two-player game that each player at the time of action has in the same opportunity chose one of three options (stone, paper or scissors). Equal options tie. In other cases, it obeys the following order: Stone wins Scissors, Scissors wins Paper, Paper wins Stone.

In the first instance, we can observe that the relation of this game does not obey the distributive property of Mathematics.
For example: x > y, z > x, then z > y … true!
But in this game: stone WINS scissors, scissors WINS paper, then stone WINS paper … false!

Factors that produce uncertainties in people are the main characteristics of all types of interactions between players, but not of games. For, looking only at games as logical systems, victory in RoShamBo should be arbitrary if players did not try to anticipate the decisions of their opponents.

Thus, by analyzing the RoShamBo system we have three interaction configurations.

1. Both players choose one of the options randomly. In this case, we can imagine the faces of a conventional dice as each of the options (stone = 1 or 2, paper = 3 or 4, scissors = 5 or 6). If we consider the players “blue dice” versus “red dice”, we can fix for any result of the “blue dice”, that the “red dice” has the same chance to lose, tie or win.

2. One player tries to predict the actions of the other, the other player plays randomly. In a similar way to the above case, we can fix the choices of the player trying to predict the other (imagining this as the “blue dice”), the other player are the “red dice” and has the same chance to lose, tie or win.

3. Each player tries to predict the actions of the other. As we can see, this case favors the player with the highest predictive ability of his opponent. Taking the challenge to what we mean by “meta game”. For example, predict that your opponent after losing twice times with paper, decides to change it to stone. Or, that the player will begin with scissor. These are particular settings of human behavior, which when conditions favor players. The best player has the chance to win > lose, in the same way, the worst player has the chance to lose > win. So if one player knows that the other is possibly better at predicting behavior, it is a good idea to play arbitrarily, and both players will has the same chance to win, tie or lose.