Games – who doesn’t like them? From our early childhood on we engage in playing. Some of the games have an educating purpose, such as a quiz or a strategy game, some are embedded in a physical activity and we call them sports, and some games we play for entertainment purposes in a social environment, for instance, in form of board or card games. One of the simplest and, hence, most popular games that not only children know how to play is Rock‑Paper‑Scissors (RPS). It is a game that only requires two things: A partner to play with and an empty hand. It can easily be played anywhere and any time, and it purely depends on luck – or does it not? And what use is this game for psychology?
In psychological research, RPS often serves as a game with a simple setup to explore participants’ ability to show rational decision making. For this game two competitors choose between the items Rock, Paper and Scissors and reveal their item of choice at the same time by forming a fist, a flat hand or a victory sign with their hand. Its circular structure, where Rock beats Scissors, Scissors beats Paper and Paper beats Rock, makes the game a real gamble, but what is the best strategy to win – or at least to maximize the number of wins in a series of trials? Is there actually one?
Online you will find a lot of information and a lot of advice on which strategy to choose and below is an example of a summary of strategies:
Many of these strategies are based on statistical analysis of many trials, so this should work, shouldn’t it? Imagine playing RPS against a male opponent and trying out these strategies above. According to 1 in this plan, your male counterpart should play Rock and your best choice is to play paper to win, unless your opponent is aware about this strategy, because then he could simply play Scissors to counter your Paper that would beat his Rock. Therefore, with some experience this ‘I‑know-what-you-do’, could very easily turn into an endless back-and-forth of ‘I-know-that-you-know-that-I-know-that-you-want-to-do’ spiral with EVERY possible strategy applied. Therefore, these strategies are suboptimal, because a player who notices such a strategy in an opponent’s choice can predict the opponent’s move and exploit the situation by responding with a superior strategy and vice versa. Thus, such strategies only work partially and as long as your opponent is not aware of them. Otherwise your opponent might even be able to trick you into applying a strategy, such as No. 4 above, and counter it when you think you got him. So, is there no hope at all?
In fact, there is only one strategy – if we can call it a ‘strategy’ at all – that would actually maximise your wins. Instead of relying on any strategy, why not play every item randomly and with equal probability? According to Game Theory, adopting such a mixed‑strategy works out best for you and you will win 50% of the time. Even though this is not optimal, as your opponent will have the same benefit, but being exploited through strategy playing only decreases your chances. The question now is, are we able to play such a mixt strategy, or will we stick to some kind of strategy and where does psychology come in?
Research in psychology has looked at many of these issues that come along with strategy application as explained above: Research groups studied rational decisional making and the application of stable strategies (e.g. Wang et al., 2014; Xu et al., 2013; Loertsche, 2013), or looked at outcome‑dependent choices participants make for their next move, such as switching (from one item to a different one in the next trial) and staying (choosing the same item again) when playing RPS (Dyson et al., 2015; Forder & Dyson, 2016). Other research groups focused on how participants updated their own strategies, how they recognised patterns in their opponents item choices and how quickly they adapted their own strategy to this. For instance, Stöttinger and colleagues (2013) demonstrated how quickly participants updated their own strategy when an opponent chose to play an item with a higher frequency (frequency bias) or when this opponent’s choice depended on the participant’s previously played item (player-dependent bias). Another study by Dankert et al. (2012) found that right‑brain damaged participants differed from left‑brain damaged participants, as well as the control group. There has also been some research on switching heuristics (e.g. Dyson et al., 2015, 2016; Wang et al., 2014). Previous research indicates that participants do make irrational choices and that they decide on an item by following a certain pattern, for example, by choosing an item that would have beaten (upgrade) or lost against (downgrade) their previous item after a particular outcome.
In general, what we learn from this is that our decision process is not as optimal as it could be and that applying strategies can actually make us vulnerable and expose us to our opponents. Even if this does not seem to do much harm when playing RPS, with similar decisions in other areas of our daily life it can have a huge impact: A goal keeper and a football player at a penalty might find themselves in a very similar position of where to kick the ball or where to jump. Should they be second guessing each other? On a much more complicated level, bankers and investors at the stock market try to second guess what the market (the collective brain of many) does and which strategies to apply to maximise their gains. Politicians during election times, or when they pursue a particular political goal, often apply strategies, wondering what their counterpart might think and how they could outperform them.
Therefore, studying simple decision processes, as whilst playing RPS, can have an impact on a much bigger scale and prove itself important not only at the next game might with friends, but also in many, more complicated situations of our life.
Dyson, B. J., Wilbiks, J. M. P., Sandhu, R., Papanicolaou, G. & Lintag, J. (in press). Negative outcomes evoke cyclic irrational decisions in Rock, Paper, Scissors. Scientific Reports.
Loertscher, S. (2013). Rock-Paper-Scissors and evolutionary stable strategies. Economics Letters, 118: 473-474.
Stöttinger, E.; Filipowicz, A.; Danckert, J. & Anderson, B. (2013). The effects of prior learned strategies on updating an opponent’s strategy in the Rock, Paper, Scissors game. Cognitive Science, 38, 1482-1492.
Wang, Z., Xu, B. & Zhou, H.-J. (2014). Social cycling and conditional responses in the Rock-Paper-Scissors game. Scientific Reports, 4: 5830.
Xu, B., Zhou, H-J. & Wang, Z. (2013). Cycle frequency in standard Rock-Paper-Scissors games: Evidence from experimental economics. Physica A, 392, 4997-5005.
Dyson, B. J., Wilbiks, J. M. P., Sandhu, R. Papanicolaou, G., and Lintag J. (2016). Negative outcomes evoke cyclic irrational decisions in Rock, Paper, Scissors. Scientific Reports, 6, 20479.
Forder, L., & Dyson, B. J. (2016). Behavioural and neural modulation of win-stay but not lose-shift strategies as a function of outcome value in Rock, Paper, Scissors. Scientific Reports, 6.