[Luke]

I haven't looked at either of these books in over a year but my basic understanding of the "check with outs on the turn" concept is that you generally want to check hands with 4ish outs (gutshots, 2 pair when flush or straight is likely).

But when you have a flush draw or say middle pair + flush draw, you may want to continue betting because you have might have the best hand and you have enough equity to justify calling a raise if it comes from a better hand.

Luke