Is a "perfect strategy" possible?

[DarkMagus]

Does anyone think it is possible to come up with a "perfect strategy" that is guaranteed to be at least breakeven (ignoring rake) against all opponents? Could there, theoretically, be a Call%/Raise%/Fold% for every situation that is unexploitable over the long term?

Let me illustrate.

Suppose you're playing heads up NLHE. You're on the Big Blind with KK and your opponent makes a standard raise to 3xBB. Stack sizes don't really matter here.

Against a good, aggressive opponent (opponent A), you'd probably decide to randomize your actions by calling X% and 3betting (100-X)% of the time.

Against a very bad, very loose opponent (opponent B) it might be better to just always raise since he'll put his money in with all sorts of crap.

And against a ridiculously weak-tight opponent (opponent C) who you somehow know will only raise with AA, you should always either fold or call, depending on whether you have set mining odds.

But now let's suppose you are against an unknown opponent, and furthermore suppose that you will only play 1 hand against him so that image is not something to worry about. Would there be an appropriate Raise%/Call%/Fold% to guarantee that you always at least break even no matter what your opponent chooses to do?

If you're playing against opponent C, 3-betting him is obviously very -EV. But the fact that he loses value on other hands by almost never raising should make up for this lost EV, right? And against opponent B, calling is going to be a much worse strategy than raising, but we still probably profit by calling.

Now suppose you are to play a series of these hands against completely random opponents. Each hand might be against different opponents, so you have no ability to track any sort of read, although your opponents have the ability to watch previous hands and get a read on you.

In this situation, it seems reasonable to me that you should, in theory, be able to develop a strategy that should break even against top-notch opponents and profit slightly against opponents who make mistakes. It would be much less profitable than a strategy that exploits our opponents' specific mistakes, but this isn't possible since we never have a read.

Does this make any sense? Comments?