Re: eg 77vAK
"It's a virtual guarantee that you could not have 5 or 6 of the 6 remaining A's or K's among the 4 hands that were folded since that means someone would be folding KK, AA or AK. Having 4 of the remaining 6 A's or K's among the folded hands seems highly unlikely also."
OK, all this presumes that we know nothing else about the opponents, eg we don't know with what hands they're likely to call early, what kind of players they are, etc.
Under this premise, we cannot have any information about the cards in the folded hands from the number of folded hands! Simply put (and this is very similar to the debunking of card clumping myths in BJ), you can have all 4 Aces and all 4 Kings, for example, being folded: Say you're the SB, in a 10-handed game, and they fold before you, starting from UTG, with ATo/A4s/K9s/A2o/A5o/KTo/K3o/K2o. Now you can dispute the correctness of all those folds, especially the late-position ones, but the fact is that those eight pairs are as likely to be dealt as every other group of eight pairs.
Yes, you think this is unlikely, just as it is unlikely that the winning lotto numbers can be 1,2,3,4,5,6. Well, those six lotto numbers are as likely to come up as any other group of six numbers.
"I was specifically looking at the scenario in which 4 other players folded pre-flop leaving 2 players head to head having gone all-in. There is no real strategy involved here... I am simply disputing the validity of putting the 7's at a 54-46 advantage when in fact they possibly aren't."
If you accept the notion that, having no other info abt our opponents, we do not know what cards our opponents may be folding, then the 77 pair is a 54:46 favorite if the math says so.
"When looked at in this way I wonder if there is any validity in using these ideas in deciding calls where the pot-odds seem to be right on the borderline."
Well, I know there are situations where gambling with the worst of it is absolutely correct/necessary. There are also situations where pot odds are completely irrelevant! But this is getting too general so I must allow others, more experienced and/or knowledgeable about this, to speak up.
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