This is an area I often struggle with. For example, I open 67s from the button and get a caller or two (readless opponents for arguments sake). Flop comes a naked flush draw (i.e. no pairs / straight draws), I c-bet, get a caller then the turn bricks (something like a deuce). Now what - bet again or check back? I'd probably bet a scare card like an A (depending on opponent), then give up the river if it bricks.
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Also some opponents are bad to barrel cos they're just complete stations and won't ever fold the turn once they've called the flop, and some are really weak and will just fold loads to continued aggression.
So as always, it depends, but as long as you've got a good logical reason for why you think you should checkback/barrel then you should be alright. If someone questioned why did you X and you don't have any good explanation, that's when you need to worry.
If they're the type to hit a pair and never give it up, especially when there are missed draws on board, then take the free card. Otherwise you're just betting into someone who is likely to have a better hand and is unlikely to fold.
Give them a range. Ask yourself which hands in that range they're going to fold. Then the answer will become clear. There is no single best way to play because some of the time you should take the free card and some of the time you should keep betting. Obviously cards that change the texture of the board are the ones you want to be barrelling on, as you say, but there are opponents we can push around with pure aggression.
You also need to think a lot about your own image. If you've been seen to bet your draws previously, or shown down outright bluffs, then taking a free card may be better. Your opponents are likely to call you down with weaker hands.
The only answer is "It depends".
Just don't get caught in the idea that you're "building the pot for the times you hit". Unless you think your hand is actually a favourite, you should know that you're bluffing.
"don't bluff turns v fish"
depends a lot on your perceived range and villians plus villians tendacies
Should you be barreling on blank turns with a btn range, just depends.
checking is deffo -EV )
Sorry, it was a very open general question - so just doing my best
checking is still -EV, debatable if betting is +EV - depends on how often they fold and how often you get there and also the times you do get there how often you have the winning hand
gg