PokerStars - 15/30 Ante 4 NL - Holdem - 9 players
Hand converted by PokerTracker 4

SB: 52.7 BB (VPIP: 6.67, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 16)
BB: 50.67 BB (VPIP: 16.93, PFR: 9.13, 3Bet Preflop: 3.13, Hands: 256)
UTG: 64.03 BB (VPIP: 18.98, PFR: 17.16, 3Bet Preflop: 9.09, Hands: 296)
UTG+1: 98.1 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 6)
MP: 38.7 BB (VPIP: 17.58, PFR: 13.14, 3Bet Preflop: 5.65, Hands: 348)
Hero (MP+1): 100 BB
MP+2: 47.93 BB (VPIP: 26.80, PFR: 22.50, 3Bet Preflop: 0.00, Hands: 102)
CO: 100.27 BB (VPIP: 23.96, PFR: 10.04, 3Bet Preflop: 3.96, Hands: 580)
BTN: 97.6 BB (VPIP: 21.05, PFR: 12.37, 3Bet Preflop: 6.67, Hands: 209)

9 players post ante of 0.13 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.7 BB) Hero has 8 8

fold, fold, fold, Hero raises to 2.73 BB, fold, fold, BTN calls 2.73 BB, fold, fold

Flop: (8.17 BB, 2 players) 7 8 K
Hero bets 5 BB, BTN calls 5 BB

Turn: (18.17 BB, 2 players) 2
Hero checks, BTN checks

River: (18.17 BB, 2 players) 9
Hero bets 9.1 BB, BTN raises to 89.73 BB and is all-in, fold

BTN wins 36.37 BB

100% bet the river. He will still call with all his kings.

Actually he has so many more Ks than flushdraws, that I would probably bet the turn for value and protection. It's probably higher EV than checking and going for the occasional home run.

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Barrel turn sometimes but check is fine. As played river we can check again we shouldn't bet-check-bet with air pretty much ever but I guess half pot should be decent and fold is correct vs the ridiculous massive shove.

I would bet the turn again.