This very obvious situation points toward the key distinction between play in the final round of betting and in earlier rounds. With one card to come, you would most certainly bet the four jacks to avoid giving your opponent a free card to outdraw you. Your bet forces him either to fold and thus give up any chance to outdraw you or to call and pay for that slim chance. However, when all the cards are out, betting to avoid giving a free card no longer applies.
So if you now still decide to bet your hand, you no longer ask what your chances are of having the best hand but rather what the chances are of winning the last bet when you are called. This distinction may seem like hair-splitting, but it is most assuredly not. In fact, it is crucial to successful play — that is, to winning or saving extra bets — when you are heads-up on the end. To take a very common situation, let’s say you have three- of-a-kind in seven-card stud, and you know your opponent is drawing to a flush and has nothing else.
The odds against that opponent’s making the flush on the last card are, we’ll assume, 4- to-1, which means you are an 80 percent favorite to have the best hand. If opponent checks, you certainly should not bet because, as in the case of the four open jacks, a bet has no positive expectation. Your opponent will fold if he didn’t make the flush, and he will call or possibly raise if he did. So even though you are an 80 percent favorite to have the best hand, you become an underdog if you bet and get called.