[W. Deranged]

Let's do a comparative exercise:

-In hand #1, there is an obvious draw possible on the flop. In hand #2, there is not. The general board texture in hand #2 is such that it suggests to me that the betting will be generally more representative of hand strength than in hand #1.

-In hand #1, villain raised the flop, whereas in hand #2 villain only continued to bet as would be expected of the pre-flop raiser.

-In hand #1, villain has not really done anything to indicate he has a hand he must showdown. In hand #2, when villain calls your turn check-raise, he almost certainly indicates that he has a hand that he is intending to showdown.

With all these factors, I think it is pretty clear to me that hand #2 is a check-fold. Villain pretty clearly has a hand that at least contains an A or K, as a seemingly rational, somewhat tightish/passive villain likely could find a fold with a hand like QQ here.

Hand #1 is harder, particularly against an unknown. I am certain that betting is not correct, as once villain calls the turn I don't think we're ever folding out a better hand on a seemingly innocuous river card (any J or good T is showing down), and the running pair means that any kind of heart or straight draw could not have picked up a weaker hand with which he'd make a crying call. So I basically think we're never getting called by a worse hand if we bet, and we're never folding a better one.

The real question then is whether hand #1 is check-fold or check-call. Since the board is so draw heavy and no draw hit, there are many opponents against whom checking here makes great sense to induce a bluff from a missed draw. Getting 8-1 on a river call I might try to snap off a bluff, and again, it's the board texture that would motivate that decision.