Villain reg 24/18 but showing up with over 40% btn steal on ca. 200 hands sample. How we proceed here, i rarely 3bet those kind of hands oop, and even less often have flop i have no idea what to do like this one. First tought is to bet half or bigger as i would with my overpairs or most of my range in general, but... (spoiler) hand get to turn

PokerStars, Hold'em No Limit - $0.25/$0.50 - 3 players
Hand delivered by Upswing Poker

BU: $53.11 (106 bb)
SB (Hero): $50.00 (100 bb)
BB: $66.61 (133 bb)

Pre-Flop: ($0.75) Hero is SB with 7♦ 8♦
BTN raises to $1.25, Hero 3-bets to $5, 1 fold, BTN calls $3.75

Flop: ($10.50) 3♦ T♦ 5♥ (2 players)
[b][color=#C51F1F]Hero?

Not in my 3b range pre. As played bet halfish sized pot.

Wouldn't 3b this pre as @nonsimplesimon said, but yeah half pot is standard for T high J high textures OOP in 3bp

I used bigger bet, just to remove some more a or k hi flaots, it's proapbly a sizing i would use with jj too, get this turn that in theory is good for me and expected to see river, but villain bets and I chikened without reads, i dont think he is betting 99 or something similar, so what left scared me, but in retrospect, are you guys check shoving here readless, villain never fold nfd vs cr as he gets proper odds to call given i can take this line with worse draw, but what better hand he can fold if we assume 88 or 99 checks?

PokerStars, Hold'em No Limit - $0.25/$0.50 - 3 players
Hand delivered by Upswing Poker

BU: $53.11 (106 bb)
SB (Hero): $50.00 (100 bb)
BB: $66.61 (133 bb)

Pre-Flop: ($0.75) Hero is SB with 7♦ 8♦
BTN raises to $1.25, Hero 3-bets to $5, 1 fold, BTN calls $3.75

Flop: ($10.50) 3♦ T♦ 5♥ (2 players)
Hero bets $7.49, BTN calls $7.49

Turn: ($25.48) J♠ (2 players)
Hero checks, BTN bets $12.61, SB (Hero) folds

You have too much equity to cold turn. You have a gutshot and flush draw. I'd just call.

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I'm not check-folding a 12 out combo-draw to a half pot bet.

i dont think the logic makes much sense for a big flop bet with this hand. id much rather keep his range wider so i can barrel with 8 high as opposed to run into a range i dont think i can bet vs even when i turn a straight draw with a card thats better for my range. i dont think you should 3b pre as he has good stats and you seem very uncomfortable post (i dont mean this in a negative way but you are going to get into marginal situations basically every time you 3b this sort of hand oop and they call). you also can not fold the turn. whether you want to bet or xjam or xcall but you have way too much equity.