I'm putting him on AK, AQ, AJ... something like that. There are 50 of those hands to 12 AA, KK combinations. Or, he may have a pair lower than ours... Again, many more of those than the two over pairs.
Now, the flop comes A.... He bets at us. We can fold because the hands we put him on have us beat.... or at least the hands he should be putting us on would have him beat but he bet anyway. We'd have 2 outs for 9:1 against hitting the trip Q on the next 2 cards. 5:1 pot odds we can get away from.
Flip it around. We raised a standard 4x the big blind. He also has to put us on a big hand. Something like AK, AQ, AJ.... same reason I put him on those hands. They are far more common than AA, KK, QQ. So, the flop comes all ragged. He checks and we bet. There is a likelyhood that we are bluffing or semi-bluffing or have a pair under his cards. How is he going to get away from a pot that contains 2500+ chips when it only costs him 500 to call. Even if he just has two overcards to the board, he's 3:1 to hit a bigger pair and he's getting 5:1 return.
If we are going to re-raise, we should push. There's something to be said about this line IMO.
If we smooth call, we can get away from the hand if an A hits. A bit safer. But we don't get paid off by AK, etc, this way.
If we raise to 1000, we have no FE on a subsequent push, and we cannot fold with more than 2/3 of our chips in.
I'm retired.