Let's imagine an experiment. We will tell N normal people that they need to act randomly in the Rock–paper–scissors game (in this game Game Optimal Strategy is to choose an action with uniform probability 1/3). Two question:

  • How close to uniformly randomness can we expect each person to act?

  • More important question. Will this be a stationary distribution or it will change over the time if there will be a lot of trials?

(People in the experiment can't use any kind of external random generators).

  • 1
    $\begingroup$ Anecdotal evidence: loper-os.org/bad-at-entropy/manmach.html $\endgroup$ – Seanny123 Mar 16 '18 at 15:34
  • $\begingroup$ It's even really hard, to some level of precision impossible, to make machines behave at random. Also the optimal strategy is only to use uniform priors if you presume you cannot predict anything of your opponent. $\endgroup$ – Bryan Krause Mar 16 '18 at 20:44
  • $\begingroup$ Depends on your definition of random @BryanKrause. $\endgroup$ – Chris Rogers Mar 17 '18 at 17:58
  • $\begingroup$ @Chris xkcd.com/221 $\endgroup$ – Bryan Krause Mar 17 '18 at 18:14
  • $\begingroup$ People are notoriously bad at being random, especially when asked to do so. I would imagine a google search would be a great starting point, as this is long-established fact. $\endgroup$ – theMayer Mar 23 '18 at 19:23

You might be interested in this paper

Griffiths, T. L., Daniels, D., Austerweil, J. L., & Tenenbaum, J. B. (2018). Subjective randomness as statistical inference. Cognitive psychology, 103, 85-109. http://europepmc.org/abstract/med/29524679


Some events seem more random than others. For example, when tossing a coin, a sequence of eight heads in a row does not seem very random. Where do these intuitions about randomness come from? We argue that subjective randomness can be understood as the result of a statistical inference assessing the evidence that an event provides for having been produced by a random generating process. We show how this account provides a link to previous work relating randomness to algorithmic complexity, in which random events are those that cannot be described by short computer programs. Algorithmic complexity is both incomputable and too general to capture the regularities that people can recognize, but viewing randomness as statistical inference provides two paths to addressing these problems: considering regularities generated by simpler computing machines, and restricting the set of probability distributions that characterize regularity. Building on previous work exploring these different routes to a more restricted notion of randomness, we define strong quantitative models of human randomness judgments that apply not just to binary sequences - which have been the focus of much of the previous work on subjective randomness - but also to binary matrices and spatial clustering.

You'll need to wrangle access to the journal 'Cognitive Psychology' though, I can't find a free-to-air version.

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  • $\begingroup$ When writing an answer you did well to provide a link to an article but it is wise to provide a reason why you thought the article might answer the question. Quoting part or even whole of the article's abstract will be enough. This is just in case the link dies. $\endgroup$ – Chris Rogers Mar 17 '18 at 23:34

A nice psychology article (media article) that provides answers to your question can be found at here. I will try to summarize briefly based on this article.

How close to uniformly randomness can we expect each person to act?

The short answer is no. As explained in the article, on the first round of Rock-Paper-Scissors it is less likely that a randomly selected person will choose paper over scissors or rock. Moreover, as two people play many rounds of Rock-Paper-Scissors together, they tend to not play randomly but adjust their selections based on whether they won or lost.

Will this be a stationary distribution or it will change over the time if there will be a lot of trials?

There are many definitions of stationary, but a paper mentioned in the above article found cyclical behavior which would violate some of the definitions of stationary. However, this might still fit into some definitions of stationarity.

While I'm unaware of a particular article which addresses the question of wide-sense stationary in this game, I would be surprised if this were found in Rock-Paper-Scissors played between humans. There is an interplay of affective (emotional) and rational decision making that tends to be influenced by the actions of human opponents.

I would be less surprised if this were found when a human plays a computer, especially if they knew the computer was playing completely randomly. People play different strategies in games played Human vs. Human as opposed to Human vs. Computer (e.g. the Ultimatum Game)

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