I really dislike slowplaying AA... We exactly should want to fold some equity and get value from draws as much as we can, also we shouldn't be bothered that we block top pair as he has many calling draws, some strong made hands.
Which equity do you want to fold exactly? The equity from hands which are drawing dead vs you, or the equity from hands which can outdraw your hand? If you want to fold equity from gutshots, fd, do you think you can really fold those hand with only bet on flop? If you check, do you think that regular checks behind with his draws and that you lose value? Even if he does for some balance purpuse, it is still very small % of his draws, but also he bets some air hands which he would otherwise fold vs your cbet. So I check AA not only to protect my check range but also because it is likely higher EV. You can play c/r on draw heavy board as this one, or c/c flop and turn and c/r river on dry board. This way you reduce EV of his bluffs.
Also why do you think betting hands for 3 streets of value only? I assume we could also bet A6s just on flop and start check calling on turn and river if the board is good
cbet flop with weak top pairs, and c/c down is better vs villians who float flop a lot and fire turn wide, so you punish him for that maximally. We are here discussing how do we play vs good reg who doesnt have leaks in general.
I cbet only hands that can bet 3 streets for value, because if I only cbet one street, I make his range stronger on turn, and turn my hand into bluff catcher on turn vs stronger range, compared to the range which bets flop. Another important disadvantage is that once you cbet flop, and villian raises, your hand is a pure weak bluff catcher and he can raise more effectively vs such a range, compared when you have only 3 streets value range (polarized range).
Advantage of check on flop is that you protect your check range. You will want to check Jx, QQ, KK and there are many combos of that, so you need to protect this range with some Ax hands which can cc down, and you put AA in that range to protect vs large overbets. Also you cant cbet whole range here (if you do, you would be bluff heavy), so it means you would have to c/f decent amount of hands that totally missed, and if you dont put cc hands in your check range, his bluffs will have very nice EV once you c/f.
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