$25NL AKs TPTK vs PF 3-bettor

[friskyfleabag]

No reads on villain, I've played about 20 hands on the table and haven't seen this villain 3-bet before. Wasn't expecting to be check-raised on the river, was I right to value bet it having planned to call it if villain had bet?

PokerStars No-Limit Hold'em, $0.25 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Hero ($37.20)
Button ($24.65)
SB ($25)
BB ($33)
UTG ($20.40)
MP ($27.60)

Preflop: Hero is CO with A[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, MP calls $0.25, <font color="#CC3333">Hero raises to $1</font>, <font color="#666666">1 fold</font>, <font color="#CC3333">SB raises to $3.5</font>, <font color="#666666">1 fold</font>, MP folds, Hero calls $2.50.

Flop: ($7.50) K[img]/images/graemlins/club.gif[/img], T[img]/images/graemlins/spade.gif[/img], 5[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">SB bets $3.5</font>, Hero calls $3.50.

Turn: ($14.50) 4[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, Hero checks.

River: ($14.50) 2[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
SB checks, <font color="#CC3333">Hero bets $10</font>, <font color="#CC3333">SB raises to $18</font>, Hero calls $8.

Final Pot: $50.50

[muddydog]

If you put his 3 bet range in a typical small stakes player it would be 10s+ and AK

After this flop you are ahead of JJ and QQ, tied with AK and behind TT and AA. This puts your equity at 58% in the hand. I think either a raise here or a call is fine, if you raise you should find out right here if you're ahead and if you call with position if he doesn't have the goods he probably checks to you but in this case you give him a free card which has a 5% chance of hitting a set for him. So now that I think about it this flop is definitely a raise. I don't see the smaller hands paying you off here as if you bet AK becomes obvious, if you get reraised big you probably have to fold. If you just get called you might want to continue betting for value against someone just looking to get to a showdown.

[muddydog]

Oh here's the pokerstove math if you're curious:

Board: Kc Ts 5h
Dead:

equity win tie pots won pots tied
Hand 0: 58.182% 46.73% 11.45% 11565 2835.00 { AhKh }
Hand 1: 41.818% 30.36% 11.45% 7515 2835.00 { TT+, AKs, AKo }

[resboard]

I think you should raise the flop and find out where you stand. I agree with muddydog about the 3bet range, and you will certainly know if you are up against 1010 or AA. Also, why do you check behind the turn but not the river?