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Sorry - the MP player limped, and the CO raises. I was in the BB and only had to call one raise, not two. Thanks

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Ok that helps me, now on to your hand.

PREFLOP: Looks fine.

FLOP: Standard, If the middle guy has a gutshot or a 5 outer, make him pay to outdraw you.

TURN: Once you bet, and the middle guy raises, theres nothing else you can do but call, so this looks good.

RIVER: Before you can figure out what the best line is, its important to try to figure out want the MP solid guy holds.
Since he open limped from middle, he probably doesnt have AQ,Q5,AA,QQ. His most likely holdings are A5s,A4s, and 55.
I wish I knew the suit of that 4 on the turn since if it is a different suit of the ace on the flop, that would be one less combination of A4s possible. I'll just assume the 4 is a different suit than the ace on the flop when doing my analysis.
So the villains range is A4s,A5s, and 55. Against this range you are exactly 1:1 against him, your not a favorite or an underdog. Since you know the villain will bet all 3 hands on the river, your best move here is to check and call.

In general though, if your OOP against an opponent you have no read on and you bet a one pair hand on the turn and he raises and then you improve to two pair on the river, you should take the bet/call line, since there is a decent probability the villain has a better hand than you, you dont want to checkraise the river and exppose yourself to a 3 bet that you will have to call.

In your example however, since you are against a solid player it is easier to figure out his most likely holdings. When he cold calls your flop checkraise when hes not even closing the action that is the first clue that he has something, and then he pops the turn, given his flop action he will almost always have 2 pair or better when he raises the turn. So when you combine his postflop play with his preflop play, the only logical hands are A5s,A4s,and 55. Since you are neutral agaisnt this range and you know he will bet if you check, checking and calling is the best line.