I wasn't sure how to play this hand. I honestly don't know how to play boards that run KKK or 777 etc. I thought my A high is kinda strong on such a dry board, so I bet flop and checked x/c turn, hoping he would start to bluff. On the 4 I pair up, and his bet is kinda polarized, so I decided to call it down.

PokerStars - $0.10 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 153.9 BB (VPIP: 28.13, PFR: 25.00, 3Bet Preflop: 12.50, Hands: 34)
SB: 83 BB
BB: 135.6 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 8)
UTG: 133.8 BB (VPIP: 23.88, PFR: 17.91, 3Bet Preflop: 8.00, Hands: 67)
MP: 98 BB (VPIP: 28.57, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 7)
Hero (CO): 223 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 4 A

fold, fold, Hero raises to 3 BB, BTN calls 3 BB, fold, fold

Flop: (7.5 BB, 2 players) K K K
Hero bets 3.8 BB, BTN calls 3.8 BB

Turn: (15.1 BB, 2 players) 2
Hero checks, BTN bets 8 BB, Hero calls 8 BB

River: (31.1 BB, 2 players) 4
Hero checks, BTN bets 20 BB, Hero calls 20 BB

You are right in that your A has plenty of showdown value. I try to get to the river as cheaply as possibly by check/ calling the flop.. Check/ folding the turn.

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I'm not a reg myself, but really don't like the bet on the flop OOP, you're turning what could likely be a best hand into a bluff, he can still float with a pretty wide range and you're just left wondering whether he has a pocket pair a kx type of hand or a random float which all would play the same from his perspective.
As played I think it's just c/f on the turn.

fold pre

I would x/c flop.. he's less likely to have ace highs since he'd 3b a decent % of them pre (BUvCO being a great situation to light 3bet) so we pick off the odd stab.. we can balance our x/c with ace high by x/calling with weak pairs, say 77-22. If he follows up with double barrel on the 2 I'd fold. It's a massive brick so he can't imagine we're folding anything we called flop with.

As played OTF I'd fold turn. As played OTT I'd fold river.

+1

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any pair on preflop have been good for 777 flop. A high not so str

I'd open this pre only with a real donkey in the blinds and a nit on the button, and with a active player on the button I fold it twice as fast.