Just pick any

what is the question?Randomness, a very basic and simple concept to grasp on abstract terms, has long proven very elusive and difficult to nail down in practice. Although the practical difficulties rose to prominence with problems related to first attempts to produce random numbers on computers, the issue itself has been known already for millennia. Aristotle referred to this as the situation when a choice is to be made which has no logical component by which to determine or make the choice – which later developed into a parable of a donkey and two haystacks. At first glance it is all very simple – if asked to pick a random number it wouldn’t strike any of us as such a difficult task at all. However, as soon as you ask a question “how”, the whole issue suddenly becomes a very thorny one. And – as all the computer scientists know too well – “just pick any” is a lot easier said than actually done.

Randomness by definition lacks structure and meaning and therefore also cannot be created by application of any kind of algorithm or procedure. Anyone even considering this would, in famous words of John von Neumann, be in a state of sin. We humans seem to be extremely good in spotting all kinds of patterns and structures – indeed, this seems to be the way how we make sense of the world  – to the point that we appear to be quite incapable of being random even if we truly wanted to.

If you still think that “just picking any” is an easy thing then read on. Most of us, if not all, have played rock-paper-scissors (also known as roshambo) in our childhoods. Although the game itself is deceptively easy, it is not hard at all to get soundly beaten in it by an experienced opponent. You can take a look at a page of simple pointers to winning in roshambo at the World RPS society website. So, given all this, how does one avoid being beaten?

It doesn’t take much mathematical sophistication to figure out an optimal way to play the game – as there are only three choices available, and both opponents making the same choice results in a draw, the answer is that it doesn’t matter what you do as long it is random. Just pick any: rock, paper or scissors. However, therein lies the catch: if you DON’T pick “any”, if you don’t play randomly, you’re no more playing optimally, and are therefore open to being exploited in ways that were described in the link above.

And as it turns out, humans are remarkably poor in making deliberately random picks – even if we earnestly try, our choices are influenced by the choices we made in the past, in addition to symbolic biases (such as marked preference to pick “rock” as an opening choice and significant underweight of “scissors” in all choices). In a recent study 241 participants played 100 games each against the computer following their biases and adjusting its strategy accordingly (you can find the details in the article “Winning at Rock-Paper-Scissors” by Derek Eyler, Zach Shalla, Andrew Doumaux, and Tim McDevitt, The College Mathematics Journal, Vol. 40, No. 2, March 2009, pp. 125-128). In the end, computer ended up winning 42.1%, losing 27.7% and tying 30.2% of individual games, which is significantly better result than playing random. If you think you’ve got what it takes (after all, you only need to “pick any”), give it a shot.

And, if getting beaten by a silly program starts getting on your nerves, challenge a friend or a colleague and teach them a lesson! Or you can try this to play a round of roshambo with me.

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