One of the more difficult situations you're commonly faced with at the poker table is whether or not to follow through with a continuation bet after you raise pre-flop with big cards, but the flop completely misses you. (A continuation bet is when you show strength pre-flop, most often with overcards, hit nothing on the flop, but continue to show strength, as if you have a real hand.) The decision of whether or not to follow through with a continuation bet is especially tough to handle in limit poker, as you lose much of the ability you might have in no-limit to simply push people off hands with a show of brute strength, even when the flop misses you.
The problem in limit is that you've built a pot via your pre-flop raise and also shown strength, so it'll likely be checked to you on the flop, or, if in early position, you'll be forced to bet out with a continuation bet. You're only able to put your opponents in a position to call 1 SB, which they often have the correct odds to call. You can't apply much pressure and likely still need to improve your hand to win.
That said, it's a clear mistake not to follow through with a continuation bet a majority of the time. Why? For the very simple reason that your pre-flop raise will thin the herd to the point that you're often facing 1-3 opponents, and they often will simply call, indicating they have good but not great hands. With a limited number of people in the hand, it's not uncommon for the flop to miss everyone. If you continue to show strength on the flop, they'll often simply fold. This happens often enough that a continuation bet is correct a majority of the time.
One problem with a continuation bet, however, is that you expose yourself to check-raises from opponents who either have strong made hands or strong drawing hands. Because you show strength, and continue to show strength, your opponents can pretty safely bank on successfully getting in a check-raise on the turn, if they're so inclined. Good players can even make this move on you as a pure bluff, especially if the texture of the board is conducive to it. So a downside to continuation bets is that you expose yourself to occasionally having to make a pretty difficult turn decision when faced with a raise. Do they have a hand? Are they aggressively on a draw, if busted, that your overcards can beat at showdown? If you hit can you improve enough to beat whatever they have, if they have something?
Should you always follow through with a continuation bet? Absolutely not. Should you never follow through with a continuation bet? Absolutely not. The rub, then, is to try to find some basic guidelines that can help us determine when a continuation bet is correct and when it isn't.
There are usually three things I take into account when deciding on whether to make a continuation bet, usually in this order, with percentages for relative importance:
1) The number of opponents (50%)
2) Position (30%)
3) The texture of the board (20%)
The number of opponents is likely the most important consideration when it comes to continuation bets. If you raise pre-flop and only the BB calls, and then checks to you on the flop, you have to bet, 100% of the time. If it's heads up and you're the one showing strength, you have to follow through with a continuation bet. Every single damn time. No excuses.
You also have to fire another bullet on the turn. Every single damn time. Your opponent will fold often enough to make this the correct play no matter what your cards or what the board is showing. You'll also win more pots at showdowns with A high versus a single opponent, especially if they're incorrectly chasing a draw of some sort. If you only have a single opponent, a continuation bet on the flop and turn is always correct, regardless of your position or the texture of the flop.
If you have two opponents, you need to be slightly more careful. But only slightly. Even with two opponents, it's still almost always correct to follow through with a continuation bet on the flop. Ditto for the turn, especially if your flop bet caused it to be heads up. You can still run over two opponents often enough that a continuation bet is correct.
But you do need to consider your position and the texture of the flop, especially when debating whether to continue to fire on the turn. Let's look at a quick example:
You have on the button. The action folds around to you, you raise, and the SB and BB both call.
The flop is
Everyone checks to you on the flop. It's correct to bet here, despite the scary board. Remember, flops miss people more often than not, so even though the board is scary for your hand they may be in exactly the same spot, looking for any excuse to fold. All of the pots you take down when both fold more than make up for the times when someone pops you back with a check-raise. You bet, both SB and BB call.
Turn is , putting on the board.
It checks back to you. Do you continue to bet?
Nay. If it were heads up, yes. But with two opponents, both of whom called looking at the same scary board you are, betting is more often a mistake here than not. One of them has something and a bet isn't likely to drive them both out often enough to be profitable in this situation, especially if someone is waiting to check-raise you. Betting isn't a horrible play but simply checking is better, hoping for a free showdown. Yes, I know, you picked up a gutshot straight draw and you have an overcard but it's hard to find a bet here, even with that in mind, due to the texture of the board.
If you have 3 or more opponents, then you need to slow down even more. It's really hard to plow through 3 or more opponents, even if you have great position, both your cards are overcards to the board, and the board isn't scary. I'm not saying not to ever bet, if it's checked around to you on the flop, as you definitely should a certain percentage of the time, but you shouldn't automatically make a continuation bet in this situation.
Your position, too, becomes much more important. Let's say that you have in the SB. Four limpers, you raise, and everyone calls.
The flop comes
Just check. You're out of position and all you have are two overcards, facing 4 opponents yet to act and a coordinated board. If anyone bets, fold. Someone either has a hand or has a strong draw, so if you bet you'll likely be faced with a raise, which you have to fold to. So just save yourself a bet and check.
What if you have the exact hand above, with the same flop, but are on the button, instead? What do you do if everyone checks to you?
I still have a hard time finding a bet here. The problem is that lots of aggressive players will check-raise here with Ah x, as well as Kh Qx, or QJ, or any set, etc. If you're check-raised, you have to fold. The odds of getting check-raised with that board are greater than the odds of all 4 opponents folding to one bet on the flop. You also can't really improve your hand to one you feel comfortable re-raising with, so even if you hit on the turn or river you're not going to be able to extract full value from it, assuming you have the best hand.
That said, depending on the conditions, a bet on the flop might be correct in the above situation, given the pot size, as long as you're willing to not put any money into the pot if your single flop bet doesn't take it down.
While your position is obviously important, you also need to consider your opponents' position as well. If someone limps from UTG+1, you raise from the button with AhKd, and everyone folds, then you can likely put your opponent on overcards as well, or maybe a low or middle pocket pair. If the flop comes something like 7 5 10, rainbow, then you're going to fire continuation bets all the way to the river, even if you don't improve. Odds are that they're playing overcards as well (which you can outkick) based on their position, so your continuation bets are almost value bets. If you're opponents include the blinds, be more wary of continuing to fire away if the board puts an obvious possible straight out there, as the blinds can sometimes have literally any two cards, whereas opponents in early position (who just limped) are more likely to have overcards/low or middle pairs.
Another issue is what to do if someone wakes up (on the flop, turn, or river) and bets into you before you act. Again, it's too situation-specific to cover all details, but you should be more inclined to respect the bet than to ignore it, especially if players remain to act behind you. Does that mean you should always fold to a bet into your show of strength when you whiff on the flop? Of course not.
If it's heads up and someone bets into you on the flop, you likely want to raise if you have overcards to the board, as you could have the best hand, improve to the best hand, or force them to lay down bottom pair. If someone wakes up and bets and there are four players to act after you, it's usually correct to simply fold.
One additional thing to keep in mind is that the number of players that start the hand should be considered on the turn (if the hand gets to the turn), instead of just focusing on how many opponents you currently face. Against one opponent, fire, fire, fire. Against two, fire, and if it gets heads up, fire again on the turn.
If you start with three or four opponents, though, and your flop bet knocks out all but one of them, you need to be more careful on the turn, especially if the board is threatening. It's a much different situation than if you had one caller pre-flop, who called on the flop as well. If you start with four opponents, the odds are that the flop hit one of them (or that they started with a middle-biggish pair), as they called despite you showing strength. The person the flop hit is likely the one that calls, so you need to give them more credit for a hand and be less inclined to continue firing at them. If you start with one opponent, though, the odds are greater that the flop and turn missed them as well, so you should be more prone to applying further pressure via continuation bets.
That thinking extends to the river, which I've largely ignored so far. Detailing all of the considerations on the river is a bit beyond the scope of this, so we'll just stick to the basics. If someone hangs with you all the way to the river, and you don't improve, you're faced with a tough decision. The problem is obvious: the times you don't follow through with one more bet, when that single bet would win, are really, really costly mistakes. In many cases people incorrectly chase draws to the river and are aching to fold, so as not to showdown what a lemur they are, and one bet from you will cause them to fold, even if they have middle/bottom pair that beats you. Not betting in those situations is a huge mistake.
On the flip side, your single bet can't apply much pressure to someone with a pair of any sort, so if they've called this far, they're calling one more bet. Throwing more money away is hardly ever a good idea if they're going to call, regardless.
So how do you know when to bet and when to check? I really wish I knew.
In general, if its heads up, try to find a reason to bet, when you take position and the board texture into account. If they wake up and bet into you, try to find a reason to fold. Don't always fold, especially if they're prone to bluffing, but you want to fold more often than not if they wake up and bet into you, especially if you have any sort of stats or reads on them as far as being tight and/or reasonably decent. If you get check-raised, fold, unless they're a complete maniac who you've seen them check-raise the river on a complete bluff with a hand that A high beats.
If you have two or more opponents at the river, just check and hope for a free showdown. If faced with a bet and you're closing the action and no one else has called, try to find a call. This is pretty marginal but you should at least break even in the long run based on the small chance that your overcards are good and someone was bluffing with a s busted draw or smaller overcards. If you're faced with a bet and not closing the action, try to find a fold. While your overcards will win enough against one opponent to make finding a call for one more bet on the river correct in general, it's almost never correct to call with two or more opponents going to showdown, as someone almost always has a pair of some sort.
One last thing (I swear) is that you also have to account for situations in which you find yourself playing with complete maniac(s) and/or obvious calling stations. You really don't want to push the continuation bet game with these folks, as most of the value of continuation bets is getting everyone to fold, which they almost never will. There's nothing wrong with passively check-calling a maniac down, if you get it heads up and they don't fold to your flop bet. Let them be a maniac and bet out with nothing, as your goal should shift to always taking it to showdown with overcards, seeing as they're maniacs and can bet with trash the whole way. Ditto for calling stations. If you absolutely know that they fold when the flop misses them but call all the way to the end when they have any pair, then shut it down after the flop bet. Trust your read and don't fall into the trap of automatic continuation bets if they can't accomplish the end result of causing your opponent to fold.
Like many things poker-related, there's really no easy, stock answer, as far as when (or when not) to follow through with a continuation bet. Since aggression is usually rewarded, in general you should be looking for reasons to fire away, instead of looking for reasons to check.
That said, don't fall into the habit of automatically making continuation bets, just because you raised pre-flop. As the number of opponents goes up, be less inclined to follow through with continuation bets. As the scariness of the board increases, be less inclined to follow through with continuation bets.
Be aware of the situation and the potential risk/reward, as it's sometimes correctly to simply jump ship midstream, even after showing strength. Don't be stubborn and keep firing if the conditions aren't right. Successfully employing the continuation bet strategy sometimes involves checking and folding, not just firing away. Pick the spots where conditions are right and try to avoid the dangerous situations where continuation bets are likely to just be setting money afire, with little likelihood of success.