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NL Holdem 0.25(BB)
HJ ($25.25) [VPIP: 25.9% | PFR: 18% | AGG: 26.5% | Hands: 244]
CO ($27.37) [VPIP: 17.3% | PFR: 14.6% | AGG: 31.2% | Hands: 603]
BTN ($27.35) [VPIP: 29% | PFR: 12.9% | AGG: 30% | Flop Agg: 20% | Turn Agg: 33.3% | River Agg: 50% | 3-Bet: 9.1% | 4-Bet: 50% | Hands: 31]
HERO ($33.59) [VPIP: 25.9% | PFR: 21.2% | AGG: 33% | Flop Agg: 42% | Turn Agg: 27.9% | River Agg: 19.2% | 3-Bet: 5.9% | Fold to 3-Bet: 60.3% | 4-Bet: 9.6% | Hands: 42685]
BB ($18.84) [VPIP: 34.4% | PFR: 12.5% | AGG: 23.1% | Hands: 32]

Dealt to Hero: K♥ A♣

HJ Folds, CO Folds, BTN Raises To $0.67, HERO Raises To $2.51, BB Folds, BTN Calls $1.84

Hero SPR on Flop: [4.71 effective]
Flop ($5.27): 8♠ 3♥ 7♥
HERO Checks, BTN Checks

Turn ($5.27): 8♠ 3♥ 7♥ 5♣
HERO ???

Not very many hands on villain so I don't have a good read. I checked the flop planning to call a bet since I know if I bet, he's likely folding most of the stuff I beat but might be willing to bluff with those hands.

When the flop goes c/c, I might be good at this point but I'm not sure if I should bet here. If I bet turn, what's the plan on the river if it bricks? If I check turn and he bets, what should I do?

Tough spot! I do not know how to play this either....
I think I may check call a reasonable bet and check fold river if not improved.
Some weak A high and K high may check back though they should apply pressure.

I like the check OTF.

OTT...This card is bad. I use to check-call often with Ace high (AK). But not at this board (OTT). I can call a small bet. You know, then you bet, your target is mainly pocket pairs. But OTT some of the pairs have "extra" equity. I mean I can't see how he will fold a pocket pair here. Ofc you can continue OTR, but the problem is the turn, you don't have enough FE. You need at least small FE from your target. Also he will have an option for bluff with some hands. With outs. Pretty connected board.

Just a bard card, just give up imo. On some cards you can check-call, on some you can bet as bluff.

And if you bet OTT, you must often bet OTR. That's the plan. You just don't have enough FE OTT to play with a singe bet very often. But this card is not good for that.

And if you check-call OTT, again, you can give up so easily OTR. You must call on some cards. Yes, Ace high, but what is the point to call only OTT every time!? He know your cards. He expect fold from this hand. OTR...

I would check call turn (but fold against a very large bet like pot), and try to get to showdown. AK is still ahead of his many overcards and has 6 outs to make top pair. On the river, if BU bet again, I would fold AK.