What do you think of this situation:
1/2, hero has $220 and opens to $12 in MP with KK. Btn calls, SB 3-bets to $40. Both are unknown players.
I elected to 4-bet to $100. I think calling is definitely wrong because that would give Btn very good odds to come along, but I didn’t want to jam because I’m probably only getting called by AA, whereas I can see many 1/2 players 3-betting and calling here with QQ, JJ, or AK; extra high weight on QQ/JJ because I think players don’t 3-bet as much with AK at this level.
Flop comes A-brick-brick rainbow (2 small unconnected cards that I don't remember), and SB checks.
I’m suddenly not loving my pre-flop bet size as much; I have $120 behind in a pot of $200. The clear choice here is to check because an ace is going to call our jam, and we beat pretty much any non-ace hand.
But let’s say villain leads out OTF; it’s obvious from the pre-flop action that I have a big pocket pair, and unless it is specifically AA which is now less likely than either KK or QQ, I’m probably going to have to fold here. Stop-and-go is more tournament strategy, but it seems to work in this spot if used? (Don’t flame me if I’m getting stop-and-go all wrong! I don’t play tournaments at all, just know tidbits of tournament concepts.)
How would you have sized your pre-flop 4-bet? Did my size open me up to mistakes / exploitation post-flop? And any general tips for playing KK with an A on the flop?