[StellarWind]

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Good post. One question:

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but it doesn't change my basic point that QQ is not making money off of AK's flop call.

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I understand that QQ would rather AK fold then call. But isn't QQ still making money off of AK's flop call? Isn't this why he should bet instead of check? My understanding was that AK was losing money on this particular street even though his call is +EV. It is +EV because of the pot size but QQ is who is making the money on the flop. Is my thinking misguided?

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You are not misguided. As so often happens this is a matter of perspective.

We are currently at preflop considering the pot equity and implied equity available to QQ versus our AK. He has roughly a 2/3 chance of flopping the best hand. So in a sense 2/3 of the current pot belongs to him and 1/3 belongs to us. That is his pot equity. Implied equity reflect the fact that the flop doesn't end the hand. Whoever gets the worse flop can pay to draw cards. When I say that AK has favorable implied odds I mean that on average these extra bets and cards favor us. We can make +EV peels and whittle away at his 2/3 pot equity when we are behind. When we are ahead he can only lose more money by paying to draw to two outs.

Furthermore there is also the possibility of making Sklansky mistakes postflop. QQ will usually make the terrible mistake of paying for a showdown on an Axx/Kxx flop. The mistakes made by AK on an xxx flop are generally much less serious because we have outs and a better idea that our hand is no good. The difference between Sklansky-correct play postflop and the way it will actually be played is another source of implied odds for AK.

Once we are at the flop our perspective switches. Betting an xxx flop with QQ and being called by AK is more profitable than the only alternative of giving a freecard. But QQ is still losing money compared to the impossible alternative of ending play and scooping up the pot. QQ has the best hand, but his EV is less than the amount of money currently in the pot.

PS: You may have noticed that in my posts in this thread I have discussed the value of possible flops and how the hand might continue. I have not mentioned the roughly 57% hot-and-cold probability of QQ finishing with the best 7-card hand versus AKo. This is because that is not how the game is played and it doesn't matter. The reality is that AK has a worse than 43% chance versus QQ because it folds more hands that it could have won. But it also has favorable implied odds for the converse reason: QQ invests more money in hands that it eventually loses. This is characteristic of battles between pocket pairs and overcards.