This is rare, but I have seen it happen. How do you react when you're playing the board?

Let's say the board has a J high straight (and for simplicity's sake you're heads up by the river). Do you represent a Q and bet into it hoping your opponent folds? If he calls, even if he doesn't have the Q you'll split the pot but probably lose money to the rake. What if you're opponent is first to act and he bets out, or you check and he bets?

Is is different for a tournament where there's no rake to be concerned about?