I'd like to stress a distinction that has been mentioned by James. In the sentence
An inexperienced player attempting to operate under chaos theory may be unable to truely play randomly.
, there is a confusion of terms. Whether referring to Chaos Theory or Chaos Play, actual randomness is not a factor. In fact, one of the core points behind Chaos Theory is that it describes the behaviour of things that are not at all random, despite appearing so. For example, imagine a game of billiards or pool. At the initial "break", when the balls are hit out of their triangle formation by the white ball, the movement of the balls is not at all random. However, neither is the movement of the balls ordered. Instead, their movement lies in the area of chaos. That is, seemingly random behaviour that is instead dependent on initial conditions, which get magnified greatly to seem random.
Imagine now someone uses a pool cue to break. The white ball will hit a particular ball (let's say the "7" ball, which is lying at the front of the triangle) at a particular angle at a particular speed, and this force will then be transferred through the balls, spreading them out in a seemingly random fashion. Let's say the balls are set up in exactly the same way, but the white ball is now hit so it collides with the 7 ball one centimetre further to the left. Chances are, the balls will spread out in a completely different way. This is a simplified version of chaos theory. Slight alterations in initial conditions translates to huge changes at the end of the event.
One cannot play adaptively against a truly random opponent. If one attempts, one will not be playing randomly, but merely playing chaotically to attempt to simulate randomness, or attempting multiple strategies all of which fall apart after a few throws due to the random nature of the player they are being used against. This chaos or list of failed strategies can be predicted by another person far easier than the random play of the random opponent.
I think the answer to your question depends significantly on whether or not you pick up on your friend's chaotic nature. If you don't, and attempt to predict his strategy and outsmart him, you will not play chaotically. If, however, you realise that your friend is playing chaotically and attempt to do the same to almost remove strategy from the match, you will be playing chaotically also. If your friend is using Chaos Play (which, for the record, I believe has its roots in Chaos Theory) and you know this, you may well do the same yourself, while attempting to notice physical or verbal tells that reveal information about coming throws. In this case, you would cease being chaotic whenever you were looking for tells or trying in any way to glean information from your opponent.
A great question, I thought. I found it both thought-provoking and hard to answer.
Just my two cents.