This is something that's annoyed me for a while, so I thought I'd be a jerk and make a post about it. Your goal on any street of poker, or in any gambling game for that matter, is to make the play that maximizes expectation, not to simply make any play that happens to have positive expectation, or to avoid a play that has negative expectation. In fact, whether or not a play has positive expectation means literally nothing in itself. The best play may in fact have negative expectation, or the worst play may have positive expectation.

Consider this game: you choose one of three options, a profit of $10, a profit of $100, or a profit of $1,000. All choices have positive expectation, but obviously only one is correct. Similarly, you could play a game where you choose either a loss of $10, a loss of $100, or a loss of $1,000. Here your best decision has negative expectation. Simply pointing out that a play is "+EV" or "-EV" here is in itself meaningless.

Another interesting thing is that the apparent "expectation" of a play can be arbitrarily distorted by the particular accounting rules that happen to be used in the game. In poker, you make several transactions during a hand, where money is transferred from the players to the casino, and then at the end there's typically one transaction from the casino to a single player. This leads to a situation where calling with the worst hand is seen as a "+EV" play if you're getting the appropriate pot odds since, purely as a matter of convention, money in the pot is no longer considered yours. If instead you were to keep all your bets in your stack until the end of the hand, and then the loser transfer all this money to the winner, calling with the worst hand becomes a "-EV" play since there are now no "pot odds" to speak of (instead, winning the pot is now equivalent to *not losing* past bets), and you will win less than half the time. In this situation, both plays are "-EV", but folding and transferring all your past bets to your opponent may cost more over the long run, making it the inferior play. This is the case in backgammon money games where players typically only make transactions at the end of each game, rather than incrementally throughout the game. If you simply don't think in terms of "+EV" and "-EV", and instead recognize that it's a question of maximizing expectation regardless of whether the numbers happen to be positive or negative, the confusion disappears altogether.