Can you tell us what Villain looks like? Young, old, what clothes he was wearing etc?
For arguments sake, I've assumed that he will call with this range on the flop. Its pretty wide, but that's what makes fish fish.
JJ-99, 55, AJs, A5s, AdQd, AdTd-Ad6d, Ad4d-Ad2d, KJs, K5s, QJs, QdTd-Qd9d, J7s+, Td6d+, 9d6d+, 85s, 8d6d+, 75s, 7d6d, 7d4d, 65s, 6d4d-6d3d, 53s+, 4d3d, 3d2d, AJo, A5o, KJo, QJo, J9o+, 85o, 75o, 65o
On the flop your hand is 62% to win against this range. So maybe you want to bet more, to get value from a Jack, and to force draws into making a mistake.
The turn Q
is a bad card for you, but you do have the K
blocking a lot of flush draw hands, plus you have a redraw yourself.
Your equity against the above range is now 58%
Assume that he called with a tighter range pre-flop
JJ, 55, AJs, A5s, AdQd, AdTd-Ad6d, Ad4d-Ad2d, KJs, QJs, QdTd-Qd9d, J9s+, Td8d+, 9d7d+, 8d6d+, 7d6d, 65s, 54s, AJo, JTo
Then you have 67% equity on the flop, and 58% on the turn.
A very tight range would be
JJ, 55, AJs, A5s, AdQd, AdTd-Ad6d, Ad4d-Ad2d, KJs, QJs, QdTd, J9s+, Td9d, 9d8d, 8d7d, 7d6d, 65s
You're 60% on the flop, and 46% versus this on the turn.
So the right move depends on how loose you think this player is. Its a hard one, if this is the first hand of the table. The sigh and the eye-roll could mean anything. Its probably a hand that is ok, but that he lost a lot of money with at some point in the past.
If anything, that tell would indicate that villain is a recreational player. Why emote in such an obvious way, when you are just calling on the button in a multiway pot? I don't think he is being deceptive/acting here, its an honest reaction to a memory he has of playing the same hand in the past.
This would lean me towards thinking that this guy has a looser range of hands than is appropriate.
Go for the check raise, AI on the turn. Allow hands with a jack in them to think they are ahead, and bet. Protect your equity. Its not a super awesome spot, though, and you will get called by better a lot of the time.
AP the J
on the river is a terrible card for you, whatever his range.
Against the tightest range your equity is exactly 0%
Against the moderately tight range.... your equity is 0%
Against the loosest range we assumed, your equity is still a piddling 10%
Its a clear check fold here