[Jcrew]

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the right strategy against an unknown player is a strategy based on the average playing styles of unknown opponents.

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This is a bit off/incomplete and may be nitpicking. First, playing style distribution should be conditioned on the probability of a player making it to that point with a particular style.

Second, the strategy should not be based off strictly the average playing style of the unknown player, but the max weighted EV of the expected playing style distribution. A simple example: Suppose the distribution of players making it to that point can have two discrete strategies that can be quantitized as A and B distributed at 49/49/2 with 2 being all strategies other than A and B. Counter strategy to A gives an equity edge of +5 and Counter strategy to B gives an equity edge of +6 but the the counter strategy to the average gives you +1. Lets assume that if you pick the wrong strategy, you have have a -1 edge. Clearly it is wrong in this scenario to use the average as the basis of the counter strategy. Generalized, you want the strategy that produces the highest equity when integrated along an equity curve of the expected strategies with a probability weighting.

You may say that those numbers are arbitrary, and that in a poker scenario picking the wrong strategy gives a higher negative edge. That is irrelevant, the point being is that there could be scenarios where you do not want to simply play off the average.

At a poker table, this type of analysis would probably be too excessive, but a case could be made to play as you would play to maximize your edge against the most frequent type of expected strategy rather than the average.