[Eratosthenes]

I think button's preflop calling range is likely to be:

1) pairs, with medium pairs more likely. Usually reraise with big pairs, usually fold the little guys.

2) big suited cards.

3) a few big unsuited cards. These are the "just call AK in position" hands.

4) a few misc. suited connectors. JTs, T9s, etc. He folds a lot of these hands, so they are unlikely.

With this range, I think that the button will call the flop with more than just sets and flush draws (he should be raising sets, but who knows). Certainly hands like 99-QQ are still going to be hanging around, and maybe some AQo type hands that are putting you on two big cards.

If he has made a flush on the turn, you still have 7 outs to the 2nd nut flush, which might lose all your chips.

I hate checking because that is just yelling "Steal this pot.", unless he might think you have a flush and are going for the check raise.

The one good read we have on villian is that he is happy to slow play a big hand, so if we bet the turn and he calls we have not gained much information.

I want to get this hand to showdown and would call a modest turn bet if I checked. So I'm betting half the pot.