Alright, here it goes. This only applies to sets in position of course, as oop you get it in every time.
Bdon, the standard line as you I'm sure know is to still bet/call the turn when the flush card comes, even if you're oop. In other words, if you had to choose between bet/calling the turn, bet/folding the turn, and checking behind the turn, you would pick bet/calling and it's not close. There are however, some times when you should check behind the turn because it's unlikely your opponent will put more money in the pot when he's behind and his range consists of a ton of flushes.
For example, lets say you opened the CO with
[Qh] and the sb and the bb called. The flop comes
[7s][5d]. The blinds check to you, you bet 85% of the pot and only the SB calls. Turn comes
and the SB checks to you...
This is a check behind almost always. There is only one queen left in the deck, and there aren't many queens in a small blind calling range to begin with. The fact that it's 3 to the flop makes it more likely your opponent is folding hands like
[8s] and less likely they'll CR with a draw, as your CB looks stronger so they want the BB to come along as they draw. If you do fire a double barrel here, you're almost always folding out hands like 7x and 55-99 as you yourself could have turned the flush or have AsQx and have them drawing to one out. You're losing almost no value by checking behind, and other than hands like
[8s] your opponent has almost no spades in his range. If you do check behind, you give yourself another chance to get value out of hands like 88 on the river and more importantly you give yourself a chance to fill up and stack your opponent if he has a flush. About the only hands it's really horrible to check against here are 55 and 77, and with your opponent calling on a drawy flop 3-ways oop that's unlikely.
On the other hand, lets say we have
[2h] and the flop comes
[9c][Ac] flop and the turn comes
. It's pretty obvious we absolutely have to get it in here. We can't check the turn because there are a ton of aces in his range which we can both get value out of and we don't want to let spike a free club, and the board just turned a very likely two pair for both T9 and AT. So this is an easy bet/call as there's a ton more value in a turn bet here, there's a much greater chance we'll be outdrawn if we check, and there's several two pair hands which are going to try to get it in against us on the turn here.
Anyways, I tried to choose two extreme examples and your hand obviously falls somewhere in between. My default would be to bet/call against a total unknown here, but if I knew my opponent was a regular who folded to 80%+ flop bets I would be checking behind here always.
The better player should win the race. Always.