[MarkGritter]

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Everything I'm saying has to do with selecting a strategy facing a closed, totally random hand.

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Yes. The way you do that is by putting your opponent on a range of hands and figuring out what he'd do with them.

In my experiments, there are only 1,000 (or 10,000, or 100,000) hands he could possibly have instead of 52C13 = 365 million. You still don't know which one of those you're actually facing in any given situation. So what I do is pick the one that is best on average, given a complete listing of how my opponent would play those hands.

At some large-enough sample size you should get close enough to the same answer from a randomly chosen sample as from carrying out the same exercise with the entire set of hands.

The differences between real life and the experiment are:

1) In real life your opponent's hand can be one of 52 choose 13 = 365 million. In the experiment he's limited to some "small" random subset of that.

2) In real life you probably don't know your opponent's strategy exactly. (But if, say, somebody published a strategy for playing CP2-7, and your opponent followed it, you _would_ know.)

3) In real life you could not remember a specific play for millions of individual hands, you would have to have a more high-level strategy.

It is not a matter of playing "face up" (though the 2-hand example I gave earlier was--- the hand range was limited to just one hand.) The non-convergent behavior I describe doesn't arise because player A can see player B's cards and adjust, it's because player A knows player B's _strategy_ and adjusts.