I mean they're right. The line is bad but, without explaining why the line is bad won't help you grow as a poker player.
Preflop folds to SB (BvB situation)
When SB Limps and you're holding 63o you have two options, Check to see a flop and play very passively or go ahead and 3x pre-flop to represent a stronger BB range. Limping range of SB is very wide and we can usually exploit a limp very easily and not have to see a flop since they should open raise all broadways, all pocket pairs, most mid suited connectors, etc. so most times we can ignore a strong range from such a bad limp.
Villain dependent information based on your HUD and hand history should give you an indicator if they're the type to trap. If they're tight, loose, etc. This information not provided for this hand, as played I'm assuming they have a high VPIP and are a calling station.
Flop: Kd 2h 8h
SB Checks to us. I prefer a check back here as played, sure we have a couple back doors but only the back door straight is of any value to us because the flush would be too weak to call a river bet with anyway. Betting half pot doesn't do anything except inflate the pot and give 4 to 1
odds for villain to call with bottom pair, if our goal is to get villain to fold to a flop bet 1/4 and 1/3 pot works just as effectively. If we had taken the preflop line of 3x villains limp, then there are a lot more strong kings, pocket pairs, broadways, etc in our range. Where a C-bet would make sense for a fold to villain with a lot of kings in our range. With the line that's taken, you will get floated a lot in this spot.
Turn: 5c
SB Checks to us in BB. We have a gut shot now. If we had checked back flop we most likely see SB check this turn as well and we can check behind. I wouldn't necessarily hate a turn bet when it's been checked to us twice in this spot but, as played this pot should really never get so inflated. Instead we bet half-pot again when with the line taken we should check back since they called our flop bet. Their continuing range when they call on the flop crushes our six high. I'm assuming a double barrel/triple barrel half pot line may be a leak in your game, anyone's HUD will show these stats, I don't understand how you get called down here with bottom pair to be honest unless you always bet flop and turn when checked to.
Alternate, scenario if we 3x SB limp and C-bet flop 1/4 or 1/3 pot, we size up a turn C-bet to 2/3 or 3/4 pot, it's really hard for 2nd, 3rd, 4th pair
hands to continue and makes it harder for flush draws to call as you're not giving them correct
pot odds to continue.
River: 8c
SB checks to us again. If SB calls flop and turn c-bets the best case scenario we can hope for here is a busted flush draw when we bet. As played this pot should have never really exceeded the 628 it was on the flop and easy check/fold flop, check/fold turn, check/fold river.
Alternate scenario, Line taken 3x pre, c-bet flop 1/4-1/3, 2/3-3/4 turn bet...pot sized bet on river. If you're going to air ball bluff this line works way better than half-pot bets.
Half pot bets I seldom use unless I'm trying to size up the pot for a turn or river pot sized jam. You don't relay any information and you don't receive any information when you bet half pot or your villains call half pot bets. You get much more information when your sizing down to 1/3 and 1/4 or up to 2/3 3/4. Your villain will polarize their range when you adjust your bet sizing, plus you don't unnecessarily inflate pots without getting more information especially in this scenario.
Hope this makes sense, if you want clarification on anything here let me know.
