(1) He didn't 3bet.. You did. He 4bet you.
(2) Your 3bet preflop is obviously correct, and if he only 4bets with
KK+, AK, with the
dead money in the pot and your 47%
equity, you are obviously +EV to
shove it in.
(3) This is
blind v
blind, so you should likely have a bit wider of a 3betting
range, and if he realizes this then he should be stacking off lighter, and 4bet bluffing with some frequency. Meaning he is likely surely 4bet/calling
QQ+, AK, and might
bluff some hands.
So getting
KK in here is definately +EV, and correct. On
top of that, your logic for wanting to
flat and see if an Ace drops is wrong. Say he will
stack off preflop with
QQ+, AK, then you have 57%
equity, and he is stacking off with 21
combos. However, postflop if an A/K doesn't
drop he might still
stack off with
QQ+, but is likely not doing anything other than cbetting AK (if he even cbets AK whiffed in a 4bet pot). And on the
flop now you only have 50%
equity against a stackoff
range of
QQ+ (on undercard flops).
So get the money in preflop here if you feel his 4betting
range is strictly value. Now if you knew he was 4b bluffing with a large frequency, then you could think about flatting his 4bet and playing poker postflop, as you expect him to
fold a very large % of his
range to a
shove. In which, you are likely going to be
ahead of most of that
range on most flops. But that's likely not the
case, so just
shove it in preflop.