Prima, $0.10/$0.20 No Limit Hold'em Cash, 6 Players
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Seat 1 is the button
Seat 1: Player1 ( €17.13 EUR ) - VPIP: 26, PFR: 13, 3B: 4, AF: 1.7, Hands: 273
Seat 2: Player2 ( €26.89 EUR ) - VPIP: 29, PFR: 10, 3B: 4, AF: 1.1, Hands: 270
Seat 3: Hero ( €21.21 EUR ) - VPIP: 25, PFR: 20, 3B: 10, AF: 2.9, Hands: 5786
Seat 4: Player4 ( €20.00 EUR ) - VPIP: 25, PFR: 13, 3B: 7, AF: 2.0, Hands: 261
Seat 5: Player5 ( €47.54 EUR ) - VPIP: 27, PFR: 20, 3B: 1, AF: 5.4, Hands: 249
Seat 6: Player6 ( €18.32 EUR ) - VPIP: 36, PFR: 12, 3B: 5, AF: 3.4, Hands: 274
Preflop: Hero is BB with K

J

3 folds,
BTN raises to $0.60,
SB folds, Hero calls $0.40
Flop: ($1.30) T

3

Q
(2 players)
Hero checks,
BTN bets $0.60,
Hero raises to $1.80, BTN calls $1.20
Turn: ($4.90) 6
(2 players)
Hero bets $3, BTN calls $3
River: ($10.90) 4
(2 players)
Hero checks, BTN checks
Ok, so I had been at the table for a little while and was playing kind of snug. Button looked like a recreational player but not too much info on him. He probably views me as a regular tag, not too out of line and playing pretty straight forward. I had 3bet him a couple of times when he opened from the button and he folded.
So he raises from the button and I'm happy to take a flop with my hand. I could have raised but I like to mix up calling and raising in these spots. I flop a monster and am happy to play for stacks. I 3x his cbet and he flats, maybe I could have raised to $2.20-$2.50. I lead out on the turn again and he just calls again. I'm putting him on a weak 10x, Qx, maybe a weak flush draw or maybe a stubborn 99, 1010 etc.... My question relates to the river, can I shove here profitably, repping KQ, a set of 3's, Q 10 etc.... or is check fold the best line here? The draws miss and by checking, I kind of turn my hand face up so what do you think? Let me know.
Thanks