Is stone paper scissors a game of chance?

The surprising psychology of rock-paper-scissors


"No dishes for me tonight," I said after beating my sister in a rock-paper-scissors (RPS) game. I was 10 years old and RPS was our game of fate to make all kinds of decisions. Little did I know that RPS was not a game of chance, but a strategic system with a strong psychological foundation.

RPS probably comes from the Han dynasty in China (206 BC - 220 AD). The game, known in Japan as "Sansukumi-Ken" (Hand, three-way, deadlock) used fingers and hands to represent a variety of different symbols in addition to stones, paper, and scissors, including snails, poisonous millipedes, frogs, and hunters. By the 20th century, RPS had spread westward. English names such as Roshambo, Ick-Ack-Ock, Ching-Chang-Walla or rock-paper-scissors were also used.

RPS is technically a zero-sum hand game (i.e. losing one person is exactly the same as another person winning) played between two people in which each player creates one of three forms with their hand at the same time. The shapes are "stone" (a fist), "paper" (a flat hand) and "scissors" (a fist with the index and middle fingers forming a V).

There are four possible outcomes: 1) a tie; 2) stone crushes the scissors; 3) paper covered rocks; 4) Scissors cut paper. (For those looking for an in-depth discussion of RPS, check this out The official strategy guide for stone paper scissors by Douglas Walker and Graham Walker. Some of the strategies are based on this book and those found on the World RPS Society website - yes, there is a World RPS Society.)

Many people (including myself) may have thought that RPS was similar to flipping coins or tossing dice - a useful way to randomly pick something. However, the game offers a lot more than meets the eye. RPS involves observation, mindfulness, manipulation, emotional intelligence, strategy, and dexterity. Part of this ability is to take advantage of your opponent's non-random behavior.

If people were playing RPS really randomly, it would be impossible to use any strategy. The best thing to do is to just pick your weapon at random. Ultimately, you would have an equal chance of winning, losing, or binding. Several small experiments have confirmed that this strategy - where each player is equally likely to choose the three actions in each round - often seems to be effective.

Then a study from China by Zhijian Wang at Zhejiang University suggested that RPS is indeed a game of psychology more than chance, which makes it possible to take advantage of your opponent's predictable patterns.

Zhijian and colleagues looked at 360 students who were divided into 60 groups. In each group the players played 300 rounds of RPS against each other. The winners were paid out in proportion to the number of wins they won.

On the surface, the results of the study didn't seem surprising: the players in all groups selected each action roughly a third of the time - as if it were random. However, a closer look at their behavior reveals a strategy called "conditional response" or a strategy that turns out to be "win-stay-loss shift".

These results raise further questions as to whether this conditional answer is hardwired to a neural mechanism or a learned process that lies in rationale for decision making. When players try to employ a strategy, they reduce the likelihood that the game will remain random.

Here are psychological strategies used by RPS fans against non-random opponents.

  1. Expect repetition.The winners usually stick with the action that led to their success. We repeat what works. So if you lose with rock (you were playing paper) your next play with paper again and you should go with scissors. In other words, if you lose, you jump two actions ahead of the sequence.
  2. Follow the order if your opponent loses.Losers change their strategy and move on to the next action (clockwise: R - P - S) in the sequence. If you lose with rock (you played paper), next play paper. So you should play scissors. In other words, if you win, move on to the next action in the sequence.
  3. Know the symbols. There may be underlying reasons for your opponent to choose a particular symbol. Rock: Very aggressive, symbolized by the fist. Players subconsciously view rock as a weapon and rely on it when other strategies don't work. Scissors: Some aggression as they are sharp and dangerous, but also useful craft tools. Represent controlled aggression used as a smart throw - often when someone is confident or wins. Paper: the most subtle step. An open hand is passive, peaceful, and kind. Some players will not use this if they fall behind as it can symbolize weakness. Other players identify paper with writing and, as such, the force of pressure is a subtle attack. In these cases, paper can be used to indicate superiority.
  4. Choose rock for rookies. Rock is a typical opening move for beginners, especially men, as rock is associated with strength and steadfastness. Knowing this, a good opening move against a beginner is often paper.
  5. Think ahead, like in a game of chess.Against a more experienced opponent, they will purposely not start with rock, which is too obvious. They can consider you a beginner, expecting rock, and therefore opening up with paper. Against a veteran, you should lead with scissors: at worst, you will be bound.
  6. Manipulate your opponent.Carefully manipulate your opponent to choose a particular action or not to choose a particular action. If you can subtly get your opponent not to throw a stone, go for scissors (will either result in a tie or a win). Manipulation comes in many flavors. For example, tell your opponent what you are going to throw and then actually do it. Since they probably won't expect you to be so fearless and honest, the only thing they likely won't take off is action that hits yours. If you say "rock", your opponent will likely toss rock or scissors, resulting in your win or tie. Another subtle manipulation technique arises from neurolinguistic programming. At the beginning of the game, remind someone of the rules. You might say, "Scissors beat paper, paper beats stone (show a sample of the rock with arm movement), and stone crushes the scissors" (show how the stone crushes the scissors). In magic this is called "power". Now expect them to throw a stone. Of course you will answer on paper.
  7. Remember, nobody likes to be predictable. If someone has already thrown a double (usually because they won it for the first time), it is very unlikely that they will use it a third time. After you've used scissors twice, your next step is either rock or paper. Paper is the best step to win or bind. If they make two stones, follow up with scissors. Two papers, you answer with a stone.
  8. Know the statistics.Statistically, the expected average is 33.3 percent if everything is completely random. It turns out that the most common throw is stone (35 percent), scissors (35 percent), and then paper (29.6 percent). Not sure what to do next? Picking up paper can give you very little advantage.
  9. Be attentive.Watch your opponent's hands before he throws. A tight hand, when raised many times, ends up in a rock. A loose hand turns to paper and the first two fingers lead to scissors. Watch your opponent closely as he or she plays RPS against others. Do they tend to fall back on a particular litter? Is there a pattern? Do they telegraph their litter by moving their fingers early?

As a result of RPS competitions, many complex algorithms have been developed with heuristically designed strategies, sub-strategies, and meta-strategies based on past performance, frequency analysis, history matching, multiple history matching, and even random guessing.

If you were lucky enough to have very good observation skills and lightning-fast reflexes, you would of course have an amazing advantage. When the Tokyo University's robotic hand is playing RPS, it detects it within a ms with a high-speed camera. what shape the human hand makes and delivers the winning shape 100 percent of the time.

What does it all mean in real life?

  • In 2005, Takashi Hashiyama decided to auction a multi-ten million dollar collection of Impressionist paintings, including works by C├ęzanne, Picasso, and van Gogh. He contacted the auction houses of Christie's and Sotheby's. Hashiyama let the companies play RPS to get the auction rights. Christie's consulted the 11-year-old twin daughters of one of their directors who suggested "scissors" because "everyone expects you to choose rock". Treated it as a random game of chance, Sotheby's had no particular strategy and opted for "paper". Christie's won and sold the $ 20 million collection and earned millions of dollars in commission.
  • In 2006, Federal Judge Gregory Presnell of the Middle District of Florida ordered opposing sides in a lengthy lawsuit to resolve an issue with RPS.
  • Warfare often involves RPS situations. For example cavalry over archers, archers over long spearmen (pikemen), pikemen over cavalry.Many modern video games and card-based video games emulate this RPS cycle when choosing possible weapons or unit types. This phenomenon maintains the gameplay and reduces the possibility of a significantly dominant strategy.
  • In 2015, three officers were reprimanded for allowing an underage drinker at a concert to avoid a ticket by winning on RPS.
  • The RPS scheme plays a role in bacterial ecology and evolution modeling. Intragenomic conflicts arise when they are safe Genes (so-called selfish elements) cause their own transmission to the detriment of the rest of the genome. Instead of the traditional medelian frequencies in a general evolution model, we have the RPS dynamics.
  • There are many domestic and international RPS competitions with purses valued at thousands of dollars.

Don't rely on chance whether you're competing for money to finish washing the dishes or to avoid doing pushups: incorporate some of these psychological strategies.

Check out my book Making Lemonade: 101 Recipes for Turning Negatives into Positives.