I'll echo others sentiments about checking the flop. I'm never checking this flop for the following reasons - which many others have enumerated, but just wanted to add my $0.02.
1) We have a great hand, time to build the pot. Need to get 3 streets of betting here. If it checks thru OTF, we've just lost a street.
2) We have top set. Thus it is unlikely that any villain has top pair or an overpair (as an overpair would probably have re-raised PF (though not always). Thus it will be hard for villain to have something to bet with. 80% of the time they check this. If the flop was A 10 rag or K 10 rag, it is much more likely to connect with them and they may bet their top pair (although I'm still not checking those flops either
). This flop, we have to bet because it is less likely to connect with them to give them top pair.
3) If this flop does connect with them hard for a made hand (i.e. flopped under set or 2 pair, etc), checking here gets less $ in the pot. If we check, they will bet, and we can call or check-raise and get stacks in. But if we bet, they will likely raise us and we can get stacks in. Thus, if they have a strong made hand, stacks are going in regardless, so I would rather bet OTF for all of the other scenarios (where they have a weaker hand).
4) If they have one-pair, they will likely call a c-bet by us since we "raised, and must have AK and must have missed this board." If we check and call, they start to think we don't have AK, or if an A/K/Q comes on turn then we get no more $. Thus c-betting and check-calling probably are pretty similar in terms of how much money we get (we probably get a tiny, tiny bit more by check calling - but it doesn't make up for the times that the flop checks through)
5) This is a super drawy board. Mega-drawy. If we let it check through, and a 9
comes on turn, we're screwed - mostly because we have no idea where we stand in relation to others ranges. If they lead OTT, do they have the nuts or one pair or a draw? How do we play?
6)As others have said check-calling a flop bet and coming out aggro on the turn (or check raising on turn) look super aggressive and get villain to lay down most hands - they might even lay down a set! (prob not) By bet/bet/bet, our range of possible hands remains wide.
In summary, I think that if we play this hand 10 times against a variety of villains, we get more money by bet/bet/bet than by checking and letting them bet for us. In this case, you may have gotten more money by checking - but who knows - perhaps bet/bet/bet would have gotten you even more!