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Deep w/ KK: tricky runout

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Deep w/ KK: tricky runout

Blinds: $0.50/$1.00 (6 Players) BB: $118.85
UTG: $205.79
MP: $98.88
CO: $235.66 (Hero)
BN: $112.70
SB: $99.87
Playing on Ignition. After 109 hands (including this one; I don't know how to filter it out in DriveHUD... help welcome!), UTG is looking very TAGgy: 24/20 with an UTG VPIP/PFR of 8.3. Overall 3bet call% of under 15. Villain isn't significantly aggressive or passive in general: just seems solid.
Preflop ($1.50) Hero is CO with K K
UTG raises to $3.00, MP folds, Hero raises to $9.00, 3 folds, UTG calls $6.00
Flop ($19.50) A Q 4
UTG checks, Hero checks
Turn ($19.50) A Q 4 J
UTG checks, Hero bets $11.00, UTG raises to $34.00

When villain check-raises, I don't think I can continue. In that sense, I don't think this hand is super interesting, but I'm happy to be challenged on that conclusion and the line in general.

I'm posting this because I ran the situation through GTO+ and apparently we both played it super goofy: GTO+ wants me to bet virtually my entire range when checked to, but even node-locking the flop to check either my whole range or about a third of it (including KK), villain is supposed to have literally 0 turn check-raises.

So I was just wondering if folks better-versed in theory could help explain what's going on here. I just felt like betting KK here on the flop was total value-cutting (and I thought I'd check AA here too, though I guess with us being so deep that's leaving a lot of money on the table, blockers be damned), but then once the turn came in I thought I should go for thin value and equity denial. I'm not sure how relevant my blockers are here, but I just found the whole situation interesting. Your thoughts are quite welcome.

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