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Comment by croutons | Hacker News Reader

I don’t really understand how this is a paradox, but it’s definitely surprising and non intuitive.

It seems like if you have 2 games A and B, the second you start playing them together you’ve effectively created a new game C, which is a game of A and B combined.

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> Is Parrondo's paradox really a "paradox"? This question is sometimes asked by mathematicians, whereas physicists usually don't worry about such things. The first thing to point out is that "Parrondo's paradox" is just a name, just like the "Braess's paradox" or "Simpson's paradox." Secondly, as is the case with most of these named paradoxes they are all really apparent paradoxes. People drop the word "apparent" in these cases as it is a mouthful, and it is obvious anyway. So no one claims these are paradoxes in the strict sense. In the wide sense, a paradox is simply something that is counterintuitive. Parrondo's games certainly are counterintuitive—at least until you have intensively studied them for a few months. The truth is we still keep finding new surprising things to delight us, as we research these games. I have had one mathematician complain that the games always were obvious to him and hence we should not use the word "paradox." He is either a genius or never really understood it in the first place. In either case, it is not worth arguing with people like that.

> I don’t really understand how this is a paradox,

You do:

> but it’s definitely surprising and non intuitive.

That's a common definition of a paradox: "a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true."

Ok I misunderstood what it means to be a paradox, this does seem to apply. The point I was intending to make is that the composition of 2 games entails a new game which creates an entirely new ruleset and therefore new potential outcomes. On the spectrum of paradoxes this one doesn’t feel particularly profound, but perhaps it’s due to the examples being especially contrived.

Exactly. Of course you can rig up a set of game rules that lead to a specified outcome under specified conditions. This paradox just boils down to a game rule that says "Alternately play these two subgames." I don't get it.

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