Paradox or no?

[piki]

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Ok, continuation from my edit. Let's say opponent opens AA-KK, AKs. What's our equity if we get involved with him with the same range of hands? 50? It is 48,7% because our distribution of hands has changed.

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Our distribution of hands may have changed, but because of our cards, so has our opponent's. If we both play a range of AA,KK, and AKs indiscriminately our equity should still be 50%. PokerStove has it as 50% as well. What am I missing here?

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I am pretty positive I am not mistaken. I am sorry but I do not know a simple explanation for why it is so, though I am sure it exists. I will try with an example:

Let's say only opponent gets his cards first. He takes a look at his cards and acts accordingly. Then the deck is shuffled and you get your cards. I believe you would agree that in that case, our distribution changes and opponent's is independent of our hand. Is it any different if we're dealt cards at the same time?

EDIT: This is so mind boggling. You take a look at the problem from here, it seems logical it changes, you take another look, it seems logical it does not. Thinking about it again, I confused my self and now I do not know right from left. [img]/images/graemlins/smile.gif[/img]

-pix