Depending on my pocket cards... say I have the ace and no possible straight flush on the board, I am check/calling until the river. I am hoping to see another card of that same suit on the turn giving another player an inferior flush. If not, then lets hope they have top pair or trips. If I am first to act on the river I would probably place a medium size bet hoping to get raised or at least called. If I check, then my opponent could be afraid to bet, but if I place a medium size bet (smaller than the last bet my opponent made), and he actually has a hand, then he will at least call, but he will probably raise or push all in thinking I am trying to steal. If he pushes, I instacall. If he raises, I re-raise hoping he goes all in so I can call him. If he goes this far, then he deserves what he gets. He should have already figured out exactly what he was up against!!