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cbetting "OUR" flops with hands that don't really gain anything from betting | *GTO solution?!*

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cbetting "OUR" flops with hands that don't really gain anything from betting | *GTO solution?!*

Blinds: $0.50/$1.00 (6 Players) BN: $407.00
SB: $63.30
BB: $104.55
UTG: $174.11 (Hero)
MP: $90.94
CO: $162.11
Preflop ($1.50) Hero is UTG with J K
Hero raises to $2.50, MP folds, CO calls $2.50, BN folds, SB calls $2.00, BB folds
Flop ($8.50) Q K A
SB checks, Hero bets $4.20, CO folds, SB calls $4.20
Turn ($16.90) Q K A J
SB checks, Hero checks
River ($16.90) Q K A J 6
SB checks, Hero bets $5.30, SB calls $5.30

Hey,
so this hand made me think about something that I had in the back of my head for quite some time now and that is basically what the title says:

Where basically I have an internal conflict of

pro bet:
-board favours our range
-we block the straight
-we block two pairs
-we can probably barrel villains off of Ax
-we have redraws to AQ/KQ

pro check:
-not many worse hands will call
-nothing better will really fold now (for now)
-we can check/call (IMO with the huge downside that a check call, especially 3way will never be protected enough)

A similar paradox IMO occurs when for example:

HERO opens CO or BU w AJ
BB flats

FLOP: QJT rainbow
SB checks

The board just sort of invites barreling so much but our actual hand doesnt really gain that much by betting, but checking behind caps us pretty hard

I'd be interested in your take on this and wether or not someone has done solver work for these spots :)
cheers

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