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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).

Zenon
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Brans Ds
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    Anecdotal evidence: http://www.loper-os.org/bad-at-entropy/manmach.html – Seanny123 Mar 16 '18 at 15:34
  • 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. – Bryan Krause Mar 16 '18 at 20:44
  • Depends on your definition of random @BryanKrause. – Chris Rogers Mar 17 '18 at 17:58
  • @Chris https://xkcd.com/221/ – Bryan Krause Mar 17 '18 at 18:14
  • 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. – theMayer Mar 23 '18 at 19:23
  • People individually - http://www.cs.cmu.edu/~jblocki/HumanRandomness.htm – theMayer Mar 23 '18 at 19:30
  • Collectively... look at hypotheses as to the movements of the stock market. There is considerable debate on that subject. – theMayer Mar 23 '18 at 19:30
  • @rmayer06 that would make for a great answer – Seanny123 May 09 '18 at 01:52
  • I've marked this as duplicate as I think they're essentially asking the same question (albeit one uses rock paper scissors and the original uses number sequences); but I think that the intent is the same. If you disagree, let me know. – Jeromy Anglim May 09 '18 at 01:56

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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)

Stat_Programmer
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