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Rock, Paper, Scissors

I enjoyed the piece on Rock, Paper, Scissors (RPS) in today’s AFR (paywalled but it it was featured in the British press a while back).  Recall the kid’s game  – two parties simultaneously call “Rock”, “Paper” or “Scissors” with the mnemonic “Rock breaks Scissors, Scissors cuts Paper and Paper covers Rock” – so “Rock” beats “Scissors”, “Scissors” beats “Paper” and “Paper” beats “Rock” while the same call of each is a tie.  This game is normally repeated over a series of trials.  Game theory suggests that a randomised strategy of calling each alternative with probability 1/3 outperforms any other strategy  because it gives your opponent no predictability advantage.  But how would you play this game (as a “one-shot” game)  if you wanted to win?  There are many suggested strategies on the internet and there are “expert players” who have skills at detecting non-random responses from their opponents.

Men play “Rocks” most and women apparently play (painful!) “Scissors” most so playing against a naive man a good initial call is “Paper”.  Overall however “Rocks” are played more than “Paper” which is played more than “Scissors”.  Naive players don’t like to make the same selection more than two trials in a row so a “rock” “Rock” is likely to be followed by a switch so, after such a sequence the best option is to choose whatever signal the doubled signal would beat – here “Scissors”.  The US RPS champion starts with a predefined strategy (call this, then this etc depending on whether he won or lost etc) but then switches to improvisation based on pattern recognition and perceptions of an opponents emotional state  in playing. Trash talk is allowed in most tournaments and honesty can be a good policy – I tried this tonight with my son and it worked – I called what I said I would play and then played it. Fooled him as he assumed I would lie.   Facial expressions and the way you pump your hand when starting off (1, 2, 3 , call…) can signal your opponent’s intention.

There is a book length treatment of these issues that I have just purchased from Amazon.  Could I validly include this in a course on game theory? Skilled strategists should outperform those who have studied game theory so there is some a priori benefit from studying the actions of the winners.

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