Is There Strategy in Rock Paper Scissors?: The Definitive Guide

PSI Having run the World Rock Paper Scissors Championships since 2002, being one of the co-authors of the Official RPS Strategy Guide book, and  followed for 3 years by the crew of the new feature length documentary on Rock Paper Scissors, I have come to learn more about Rock Paper Scissors and  gained a true level of respect for this enduring game. Because RPS is often used as a decision making vehicle, in the same way that flipping a coin is often used, confusion seems to have developed about the nature of strategy in the game vs. the idea that it is simply a game of random chance. This is demonstrated on a fairly regular basis with one particular style of email or comment that comes into the worldrps.com website. Now, while the spelling is all over the map, the general message is pretty much the same:

lol… there is no stratigy[sic] in Rocks paper and Scissors. it's a stupid game of randem[sic] chance!!!!

Stalemates

There is no question that Rock Paper Scissors is one of the world's simplest games and that is one of the reasons that has made the game a part of almost every culture in the world. But does this simplicity mean that the game is devoid of any possible strategy? It is often said that RPS is "strategy at its most basic and most profound" or that "To the beginner the choice are few; to the expert the choices are many", but one does not need go down the esoteric and circular referential paths of those last statements to understand the nature of strategy in RPS. The reasons are actually very clear.  So once and for all let's go through 6 reasons why RPS is not a game of random chance and later on a little about how you can put this into action:

The 'Optimum' Strategy Sucks

What initially trips a lot of people up is that from a mathematical point of view the 'optimum' strategy (i.e. the Nash Equilibrium) in RPS is to, in fact, play randomly. The important point though here is that… READ MORE

PSI

Having run the World Rock Paper Scissors Championships since 2002, being one of the co-authors of the Official RPS Strategy Guide book, and followed for 3 years by the crew of the new feature length documentary on Rock Paper Scissors, I have come to learn more about Rock Paper Scissors and gained a true level of respect for this enduring game. Because RPS is often used as a decision making vehicle, in the same way that flipping a coin is often used, confusion seems to have developed about the nature of strategy in the game vs. the idea that it is simply a game of random chance. This is demonstrated on a fairly regular basis with one particular style of email or comment that comes into the worldrps.com web site. Now, while the spelling is all over the map, the general message is pretty much the same:

lol… there is no stratigy[sic] in Rocks paper and Scissors. it's a stupid game of randem[sic] chance!!!!


There is no question that Rock Paper Scissors is one of the world's simplest games and that is one of the reasons that has made the game a part of almost every culture in the world. But does this simplicity mean that the game is devoid of any possible strategy? It is often said that RPS is "strategy at its most basic and most profound" or that "To the beginner the choices are few; to the expert the choices are many", but one does not need go down the esoteric and circular referential paths of those last statements to understand the nature of strategy in RPS. The reasons are actually very clear.  So once and for all let's go through 6 reasons why RPS is not a game of random chance and later on a little about how you can put this into action:

The 'Optimum' Strategy Sucks

Stalemates What initially trips a lot of people up is that from a mathematical point of view the 'optimum' strategy (i.e. the Nash Equilibrium) in RPS is to, in fact, play randomly. The important point though here is that even though this is the strategy with the best expected outcome, it is still not a winning strategy because the player should win 1/3 of the time, lose 1/3 of the time and tie 1/3 of the time. This means that this strategy over the long term has an expected outcome of only coming out even. To further complicate matters, this is assuming that humans are even capable to executing this random strategy because humans can only only approximate what they believe to be randomness. And in trying to approximate randomness, people can unwittingly become predictable or fall into patterns. To illustrate, the average player attempting to play randomly will often have a tendency not to play the same throw two or three times in a row because of a mistaken impression that doing so is not being random. In a true long series random pattern, throws would often clump together in 3 or 4 (or more) strings. Now of course, we could all execute our moves based upon a roll of the dice in order to better approximate randomness, but we discount this since that would turn RPS into a dice game variant since we are going to work under the (logical) assumption that we are asking the players to determine their own moves.

Summary: Even though the optimal strategy is random, it is not a winning strategy even if humans could execute it properly.

 

Same Same but Different

Lisa vs. BartRPS is a perfectly balanced game in the sense that each throw has no advantage over the other throws since each wins to one, loses to another and ties to itself. This allows the nay-sayers to say that it doesn't matter what you play since all moves are equally strong. Yet, minds work the way they work and  there is a perception of inequality in the game because even though the three throws are in perfect balance, the personalities of the throws are different and this has an important effect on people's perception of each throw. It may sound odd to quote from the Simpson's to help illustrated the point but, as is often the case, this show demonstrates great insight into the human psyche. In a famous scene, Bart is playing RPS with Lisa and thinks to himself" Good old rock, nothing beats that" Of course, Lisa is thinking "Poor predictable Bart, always takes Rock". Lisa wins by successfully exploiting her knowledge of Bart's belief in Rock being somehow stronger. This 'funny because it is true' example illustrates that, in RPS, it is a player's perception of the throws that has an effect on the frequency of their distribution. But, if you don't like a cartoon proving the point, turn instead to some cold hard stats. A 1998 Japanese study by Mitsuo Yoshizawa analyzed 11,567 separate throws from 725 people and found that rock was thrown 35% of time, paper 33% and Scissors 31%. Facebook's Roshambull application which is a popular online RPS game has logged a staggering 10 million  throws in over 1.6 million games from real players and their stats come out as 36% Rock, 30% Paper and 34% Scissors. Players clearly have a slight preference for Rock which effects the distribution of the outcomes. Given people's preference for Rock, it is impossible to claim that RPS is a game of chance.

Summary: Even though RPS is a perfectly balanced game, it is people's perception of the personalities of the throws that creates a small imbalance. It also proves that the average players think more like Bart Simpson than they realize 😉

The value of decision changes the dynamics

Cooper Once you put an important decision on the line, it is also less likely that people will treat RPS as a game of chance. The World Rock Paper Scissors Championship is a perfect example of this in action (Most habitual lottery players are another obvious example of how even in true random events people often treat it differently). With a World Championship title and $10,000 on the line, players are trying to get any possible edge against their opponent. This often leads players to over-think their actions or the actions of their opponent.

Summary: When you up the stakes of a match, people who may have the thought the game random, generally stop thinking in such terms immediately.

 

People's history can effect the outcome

In order for RPS to be random, past actions can have no effect on future outcomes.  This is in the same way that a die does not care how many times a three has been rolled in the past, there is still a one in six chance of it happening on the next role.

 

Consider this situation: You are tied at one game a piece in a best of three (let's say the match is for something like: loser shaves their head and you are both overly proud of your locks) and you noticed that your opponent has played scissors twice in a row, in fact they have only played scissors in this match.

Avalanche

Notwithstanding the obvious irony of their move considering the stake at hand (or rather head), at this point, your opponent is baiting you and, in essence, forcing you to make a judgement call about what kind of player they are. Are they crazy enough to play the same throw three times in a row for such large stakes?

 

Or do they just want you to believe they will throw that last scissors to complete the Toolbox Gambit, as it is known in RPS circles? And most importantly, are you going to let any of this knowledge affect your next move?

Summary: Past history in Rock Paper Scissors is often a reflection of future intentions

 

Outside factors can be introduced to the game

A player can change the dynamics of the game by introducing new information that tries to force the opponent to reconsider his next move. This could be achieved by, for instance, actually telling your opponent your next throw "I'm coming out with rock, you knucklehead!". As counter intuitive as this might seem, adding such odd information is hard for your opponent to ignore and forces them to make a judgment call about whether the vocal player is lying or telling you the truth. If the vocal player can correctly deduce what their opponent will do with this information then they can outwit them. But remember, the important point here is not how well this strategy might work, we are using this example to point out that the game must be considered strategic if players are adding and acting upon such new information.

Paper is the Answer

Summary: Adding new complexity into the game can force an opponent to rethink their next move

 

Strategy at it's Most Basic and Most Profound

So now that we have established that RPS is not a game of random chance, we can clearly say that it is a game with some level of skill involved. So does this mean that someone cannot get lucky and win? Of course they can, but luck is a factor in all sports and pastimes, from the roll you are hoping for in Monopoly to the lucky bounce of the puck off a stake into the net. How much of an edge any strategy gives is dependent upon your opponent. It is said that the Stock market is chaotic rather than random in that you never know what it is going to happen next but tendencies and patterns can tease out some meanings and give the smarter investor the edge. And this is how you need to approach the idea of strategy in RPS. In the end, you only need win 50% plus 1 game in order to get that last slice of pizza or become the next World Rock Paper Scissors Champion, so any edge you can get, however slight, might be all you need.

 

 

So what of this learning can you put into practice?

Lead OnNow, while this article is not about how to win more often at RPS (you can find another article that I wrote on that subject here ) Simply knowing that the average player over-indexes on the use of Rock means that even playing a scissors exclusive strategy, should give you a slight edge against an average non-random opponent. If you are playing multiple games against someone who is claiming to play randomly or who is not actively thinking about their throws; a good strategy, after the first throw, is to play the throw that loses to your opponents last throw. Why? Since your opponent is less likely to throw the same throw twice (let's say Rock) then Paper or Scissors will be their most likely next move. So, if you play scissors, you will beat their paper or, at worst, stalemate to their paper.

 

This article is copyright Graham Walker/worldrps and may not be reproduced or re-blogged in full (500 word maximum) and must link back to the original online source at worldrps.com for the full text. Graham Walker is one of the world's leading authorities on the strategy, history and significance of Rock Paper Scissors. He is co-author of the Official RPS Strategy Guide published by Simon and Schuster . He is also featured in the new documentary by Mike McKeown: Rock Paper Scissors. He has written on RPS for Men's Journal and The National Post and has made appearances on CNN, The Today Show, BBC and been interviewed by Rolling Stone, Forbes, Believer, Fortune, New York Times, Boston Globe, Wall Street Journal.