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Sklansky Fundamental Theorem Of Poker - Limitations
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To continue the thought immediately above, I believe per the Skalansky theorem the "correct" play with 9-9 is to FOLD. Folding, by definition, gives 9-9 an EV of zero.
If 9-9 enters the pot, Qh-Jh has the position to shove all-in pre-flop and Ks-10s can call the all-in. Then 9-9 is faced with either folding and abandoning his dead money (a negative EV) or calling the all-in with a 1-in-3.32 chance (30.16%) to take down a $903 pot (w/blinds and no rake) for a $300 investment, which is also a negative EV play.
So it seems the only way 9-9 can assure a non-negative EV is by folding out preflop on his first action.
Interesting thought question!! In this case, assuming no pre-flop shove. My guess would be that (in the case of how APT would use the theorem in computing an IQ score) there would be an equity calculation on the pre-flop action which would mean that the 99 would have a small -EV pre-flop (a Sklansky "mistake", albeit a small one), and then another equity calculation on the flop action, which would have different EV numbers for each player depending upon the specific flop and action (and thus another IQ computation).
In my opinion your scenario does illustrate the subtleties/limitations of Sklansky's therom and how in most cases there is really not a definitive answer pre-flop and in many cases not until the river. Particularly when you consider that a small -EV pre-flop (when the pot is smaller) can often be more than overcome by the much larger flop-turn-river action.
Going a step further, it would seem than a higher IQ score on the turn and river would be much more valuable and greatly outweigh the pre-flop IQ score.
I generally agree with you summation. My observation would be that the sheer volume of these pre-flop/flop decisions that one has to make over a 500, 1000, etc. hand session which tend to have a "normalizing" tendency to push IQ score towards 100 +/- 10 is part of why I think it is very difficult to imagine IQ scores greater than 115 or so.
FWIW - even on later streets (turn, river) you are seldom at a point of sufficient clarity about your hand vs. the range of holdings your opponent could have (in particular an opponent with an appropriate bluffing frequency) that you are going to make correct "big" decisions much more than, perhaps, 60% of the time.
Another messy question about Poker IQ. How would Poker IQ score this scenario.
You limp in UTG with A-K offsuit and get a raise and reraise behind you. Knowing the way the table plays, you fold A-K expecting one of the two raisers to have A-A or K-K and as the hand plays out you find out that one indeed had K-K. Does Poker IQ:
Give you a demerit for limping in in the first place, since if the cards were being played face up you would have folded because you could see the opponent holding K-K again you.
Give you a modest credit for folding A-K on that street being a 30-70 dog to K-K.
Further how does Poker IQ give you credit for avoiding the damage later if you were to get a K-x-x flop? Against a good player who could lay down K-K with an ace on the board in the right circumstances, presumably your downside on later streets at this point if the king hits is greater than your upside if you catch your ace.
At this point the IQ score is what it is, but your thought questions take this way past what an IQ score can ever hope to reflect. You questions have helped me to deepen my true poker IQ.
The situations you are mentioning are exactly the reason why the PokerIQ is a very long-run statistic, and has a bunch of variance - and also why we never, ever intended it to be anything but for fun. In a single session, it is highly noisy. Overall, it is highly, highly correlated with skill. If I take a long-time user's average PokerIQ score and use it to predict their future performance on the site, it is very statistically significantly related. So it is pretty accurate.
But in the situation you made up there, yes, you will take a hit in the amount of the bet for initially betting with AK vs. KK, because technically you are behind. You will get nothing for folding (because it was the right choice in that situation), and you will not get anything on future streets because you never got there - but by folding you don't take the hit that you probably would have had you continued. Given the game you are playing, your knowledge of your opponents helped you minimize your losses. However, most of the time you aren't up against KK. So in the long run, playing AK more aggressively is better.
I realize this is outside the scope of this topic, but it's worth mentioning - when you have AK, you have taken away half the possibilities that your opponents have AA or KK, so the situation you mention is relatively uncommon. There are only 3 Aces and 3 kings remaining in the deck, so there are only 6 total combinations of AA or KK remaining vs 12 if you didn't have any aces or kings. This is another reason why AK is a great hand to play aggressively in general.
Oh I agree with you observation regarding A-K vs. A-A vs. K-K - except when playing KGB level.
On KGB level, if you hold A-K and there is otherwise a raise/re-raise preflop, you are up against A-A or K-K 100% of the time.
You can just book it. I would have run into it twice today (vs. K-K) with A-K, had I not folded the A-K once pre-flop, and the case king hit on the flop BOTH times, in under 1000 hands.