CPFR AcJc SvC, ATc3c (using HH as template for discussion)

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CPFR AcJc SvC, ATc3c (using HH as template for discussion)

BN: $25
SB: $25 (Hero)
BB: $25
UTG: $25
HJ: $24.30
CO: $25
Preflop ($0.35) (6 Players)
Hero was dealt A J
UTG folds, HJ folds, CO raises to $0.75, BN folds, Hero calls $0.65, BB folds
I don't think i ever do anything else than call here preflop. Villain has to be opening very wide and calling with worse for me to 3bet strictly for value.
Flop ($1.75) 3 T A (2 Players)
Hero checks, CO bets $1, Hero calls $1
Firstly looking at CO's range pre, he will have plenty of broadway-type hands, all his pairs and the hands that missed will be the medium to low SCs and some bare Kxx Qxx Jxx

He can be cbetting a merged range: all his broadway, top pair+, midpair OR more polar? would he bet with some hands that have very little equity when called?

What are the merits to check-raising for value? or check-calling? how would i favour one or the other? which opponent tendencies should i be highlighting?
Turn ($3.75) 3 T A 7 (2 Players)
Hero checks, CO checks
The turn does check through, had he bet do i call again? merits of check-raising? it would be a merged turn value raise versus worse Ax and protection versus all his semi-bluffs.
River ($3.75) 3 T A 7 K (2 Players)
Hero bets $2.10, CO calls $2.10
Merits of leading or check/calling? Its difficult for me not to have a hand here by the river.
Final Pot
Hero has A J CO has T K CO wins $7.59

Sometimes i think i'm playing too many of my hands on the flop as a check-call. I've taken Ben Sulsky's line of strengthen my calling range when i think it would be more appropriate to develop a check-raising range.

What factors should i consider when deciding whether to protect my calling range AND sometimes miss value with my made hands OR have a check-raising range but be careful to balance it correctly


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