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I have showdown value and I might try to check it down rather than turn my hand into (more of) a bluff. In other news bluffing a calling station is not always best. It is possible to bet a calling station for value though. Barrelling is normally used to refer to bluffing.
Other observations:
He has 44/4 stats, but is he limp/calling or limp/folding? Those two stats alone don't tell that story. You suggest he limp/calls a lot, which could suggest as weak a range as 44% of hands that he arrives on the flop with. Then the question becomes which hands he limp/calls with - does he favour connected cards, high cards, suited cards - does he prefer the absolute value of the single high card disregarding the kicker for single high card value, or does he prefer having his lower card being as high as possible for better top pair potential?
Preflop you raise to 5bb with 3 limpers ahead of you. Often people discuss raising to 4bb + 1bb per limper which would suggest a 7bb raise. I don't think your 5bb raise is way too small, but bumping it up to 6 or 7bb would likely be more profitable.
On the flop the cbet is maybe a bit big. The flop is somewhat dry with only a few straight draws possible (JT, which is certainly in his range). Since aside from JT most of his draws (including AJ and similar) have 3-6 outs I could go for something closer to 1/2 PSB. Another side effect of the flop bet is that commitment questions arise - the opponent has a very short stack and once he starts calling bets past the flop he is more likely to be willing to stack off. I think that is another reason for a smaller bet size. (Implied odds questions associated with drawing hands have lesser potential gain, so you don't have to price out draws quite as aggressively)
The other question preflop is - what is your plan playing TT. Are you looking to set up or win unimproved - where is the profit going to be coming from?
When the flop hits and you know which opponent you are up against, what is your plan for the hand? You know his stats, his stack and you have a pretty good idea of his range. If all the money ends up going in, do you think you are a favourite against his range? If not, how much money do you think can go in, with you still going for value rather than bluffing? Since you have two blockers for JT and your opponent is relatively passive and will likely put more money in with worse, you do want to bet for value. But when the money keeps going in, when is it no longer for value and when are you behind? Since you are OOP you don't get the easy pot control lines, so you need to either check one or two streets or bet smaller than normal if you wish to avoid bloating the pot to a point where you know your hand cannot be good.
On one hand I do like checking a somewhat dry flop for pot control - it would keep the weaker parts of the opponents range in play and would let you extract value from those on turn and river - especially if they improve to a second best hand. On the other hand I don't like checking the flop because any 8+ can hit our opponents range and we won't know if we're still good (unless he raises us).
On the larger commitment question I would probably suggest that I am not committed to stacking off, but I am likely profitable if I go for something like $1.5-$2 of value. Being out of position makes this awkward as this is certainly less than 3 pot sized bets.
On the flop I think my plan would be something like bet flop 1/2 PSB ($0.70 for value), check turn, bet river 1/2 PSB ($1.30 for value). Fold if raised on any street. Maybe call turn if bet into depending on if I think the opponent is capable of stealing based on weakness. Alternately I might plan to bet just below 1/2 PSB on the flop ($0.50) - asking the question if he has completely missed and is just looking for an excuse to fold - bet small on the turn ($1) and bet small on the river ($1). These two lines have me betting $2.00 or $2.50 and I think if bets of that size are called by the river we are still ahead of this calling stations calling range and are profitable. The associated questions are - will he ever raise us as a bluff? Or with less than top pair?
Defensively this raises the question - would this line be too easy to read, too indicative of the strength of our hand? Against this particular opponent in this particular hand? If someone else at the table makes a read on us based on our behaviour in this hand and plays back at us in a different hand based on that read he could be very wrong - we might not play an obvious line against that observant opponent the way we would against an opponent we consider an unobservant calling station.
As played the turn is an overcard which completes the rainbow and can easily be seen as a card that it is good to bluff at. But I don't really like bluffing at it for two reasons:
1) TT definitely still has showdown value. 9x, 3x, JT, gutshots and other favourite hands are still in the opponents range.
2) If the opponent has calling station tendencies then you are correct in pointing out that he could have called the flop with any ace - if he does that you could be taking yourself to value town by betting the ace - building a pot that is so big that you can't fold when you check the river and he goes all in.
If you bet the turn and are called, how often do you expect to win a showdown? If you check turn and he bets, are you ever ahead with TT?
I think the most important thing in the hand is pot control, and pot control is hardest when you are out of position.
It is also not invalid to consider that TT might be good enough to stack off with against this opponent due to stack sizes and calling station tendencies. But again that depends on your read of his playing tendencies, lines and ranges - is there a line that you can take that gets all the money in that keeps enough of the weak hands in his range in?
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