In the 2000s, you very rarely saw check-behinds on the flop in limit holdem by the preflop raiser, in a heads up pot.
The conventional wisdom of the day was always to c-bet a heads-up pot, because you were in position and could easily get your opponent to fold, even if you missed.
The game then evolved, and ranges became applied in limit holdem more than they were before.
This caused people to realize that c-betting a flop which was fairly likely to hit a calling BB hand was a mistake, if you didn't have a piece of it but might want to get to showdown.
Here's a good example:
You're on the button with Ad4h, and raise. The BB calls. Nobody else is in the hand.
Flop: 7c8c9d
This obviously completely missed your hand, but are you necessarily behind? Even a monster draw like Jc6c, while a favorite against you, still needs to hit in order to beat you. Since limit holdem is a game of fixed bets, your opponent cannot put that much pressure on postflop, and thus you simply want to get to showdown as cheaply as possible.
This is where you check behind, and the re-evaluate the turn and river. If you improve, or if the board bricks out, you call down (or possibly even raise, if you improve enough).
The downside here is that it makes it fairly obvious that you missed, so you're almost playing face up poker. Players in position who hit a very wet board are likely to bet their hand in limit holdem, both for value and to charge all the draws chasing them. A lack of a bet indicates, "I have a hand I want to see through, but isn't very good."
Still, the upside is much higher than the downside, and thus you see far more checking back at modern middle and upper stakes limit holdem games than you did in the past.
But what if you have hit the flop in the BB, and your opponent in late position checks back against you? What's the right move? I'll discuss an interesting hand I played in the next post.