Randomizing on Rock Paper Scissors
Probably one of the most popular games in the world is Rock-Paper-Scissors. It is a game usually played by two people, where players simultaneously form one of three shapes with an outstretched hand. The "rock" beats scissors, the "scissors" beats paper and the "paper" beats rock; if both players throw the same shape, the game is tied.
This game can be analyzed using game theory. If both players play the same shape they both get a payoff of 0. If one player plays a shape that beats the other player's shape then he gets a payoff of 1 while his opponent gets a payoff of 0. This situation yields what Game Theorists call a Mixed Strategy Equilibrium. This means that a player would randomize between rock, paper, and scissors, playing each of these strategies with an equal probability of a third. This makes sense considering that the probability of winning by playing any of the three strategies is the same. Von Neumann and Morgenstern [1] in one of the earliest works on Game Theory, claims that randomization is a deliberate effort of the player to deter the opponent from predicting his moves.
Recent evidence suggests that people are very poor at randomizing [2]. The is apart from the fact that sometimes people don't want to randomize. Try playing the game with someone and you will soon realize that you are not randomizing because you are trying to predict the other player's strategy, rather than trying to conceal your own strategy. This is truer if the game is played several times. If people were to simply randomize then there wouldn't be a "World Rock Paper Scissors Competition" attracting a lot of participants every year.
People have been able to identify certain patterns that are typical of certain groups of people. For example, one article suggests that Males have a tendency to start with a rock. If you are playing a male opponent, you should play paper. If however, you are playing an experienced player who thinks you are a new male player, then he will expect you to play rock and he would play paper. In this case, you should play scissors [3]. This reasoning is never ending, since each player can try to think one level ahead of the opponent. The World Rock Paper Scissors competition also has a guide on how to win the game with similar patterns http://worldrps.com/advanced-rps/sample-page/
An analysis of data can be done to see if, after several plays of the game, people played each strategy equally and further if they randomized their plays.
References
[1] Von Neumann, J., Morgenstern, O., 1944. Theory of Games and Economic Behavior. Princeton Univ. Press, Princeton
[1] Von Neumann, J., Morgenstern, O., 1944. Theory of Games and Economic Behavior. Princeton Univ. Press, Princeton
[2] Armstrong, S. A. (2004). A meta-analysis of randomness in human behavioral research (Doctoral dissertation, Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Science In The Department of Mathematics By Summer Ann Armstrong BS, Southeastern Louisiana University).
[3]https://flowingdata.com/2010/07/30/how-to-win-rock-paper-scissors-every-time/
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