A#41: Wow. This is a tough one. You've got a flush, but it's only the 4th-nut flush on the flop. Worse, the board paired. You're a long way from having the best hand.... but you're getting fairly good odds to call. What to do, what to do....? Let's employ REDi and see what she says.
Reads: The problem stated that the "player limps about 40% of his hands and raises about 10% preflop." This is kind of weirdly worded. Does it mean that he's playing 50% of his hands dealt to him, including EP? Or does it mean that he's limping 40% of the the hands that he does play, and raising the rest? I'm going to assume that at a $5/$10NL cash game, the players are fairly competent, and therefore let's go with the latter. Further, I'll assume that he's playing a typical 8-10% VPIP UTG, but because he limped we're going to discount the upper end of that range. Per 'stove, 10% VPIP is something like 88+,A9s+,KTs+,QTs+,AJo+,KQo. If we remove the top 20% of these hands, we're left with TT-88,AQs-ATs,KTs+,QJs,AQo+
Now, the fact that he check-called the flop and turn means that he had at least a part of the board, so I think we can remove most of the QJ, AQ, AJ, and AT from his range, except those that have a nut flush draw (i.e., those that have the Ac). We can probably also remove TT, 99, and 88 because of the high probability of overpairs in a MW pot. This leave just KTs, KJs, KQs, AKs, and AK. Further, if I think we can rule out hands that don't contain at least one club in them (e.g., AKs would only be Ac-type hands.)
He has to know that we have a good hand, as we reraised on the monotone flop into a 5-way hand. He also knows that we probably don't have the nut flush, as this means we'd have a hand like AJs+, and we probably would have raised it up PF to thin the heard. Maybe we have a lower AcXc hand, but this is less probable. Therefore his check-raise on the turn is fairly polarized between missed nut flush draw bluffs, and near-nut hands.
Estimate. Against this range, we have somewhere between 20 and 30% equity, depending on how we weight his range to include Ac-high type hands (i.e., missed draws) or not. I think I'm leaning toward the 20% end of things as he has to now we're strong, yet he's cold-calling the flop and turn, and then X/R'ing on the river.
The pot is $1590, it's going to cost you $610 more to call. This means you're getting 1590/610 = 2.6:1 on your money in direct pot odds. This means you have to be right ~28% of the time to break even.
We've put about half our stack into the middle thus far, so we're pretty close to being pot committed, but we're not quite there yet.
Decide. Yikes. This is a close one, and, frankly, I'm unsure of what to do. We're almost pot committed (but not quite). We're also getting nearly enough odds to call, but that depends strongly on our assumptions of how bluffy the villain is. The problem didn't state he was particularly aggressive or bluff-minded, so again I'm leaning toward him more likely having a strong hand than a weak one. So, what to do?
In poker, a good rule of thumb that I believe strongly in (but sometimes fail to heed) is that you should fold if you're unsure where you are in the hand (and you're not pot committed).
Implement. Try to get the villain to show you his hand if you fold....
All-in for now...