Would you ever make a -EV play in equilibrium?

There are essentially two (not necessarily mutually exclusive) ways of thinking about poker. One is to try and play exploitively, attempting to maximize your earnings by best-responding to your opponent's play (for a review of concepts and vocab, see here). The other is to try and play a Nash equilibrium strategy, which means that you cannot be exploited, so that if your opponent is playing any non-Nash equilibrium strategy, you make money.

The first method by definition is more +EV than the second, given that your opponents are making some mistakes. However it requires accurate knowledge of your opponent's strategies, and small errors in your beliefs about their strategy can lead to you being exploited in turn. Sometimes this can lead to large mistakes on your part. The beauty of the second strategy is that it requires zero knowledge about your opponent. No matter how he chooses to play, he cannot beat you. Unless he plays perfectly himself, he will lose over time.

This leads me to a couple of recent posts by gnome. The question is, "is it ever a good idea to make a -EV play?" If you're trying to play exploitively, the answer is potentially yes. For instance, raising small pocket pairs in early position maybe lose money, but opponents in late position may over-react to your high raise % in early position by giving you a lot of action when you have a monster hand.

If you're trying to play an equilibrium strategy, however, the answer is no. Recall that equilibrium means that neither player can improve his payout by changing his strategy, keeping his opponent's strategy fixed. In order for your -EV in a given hand to good, you have to be able to induce some more +EV spot in the future. Since poker is a zero-sum game, a more +EV spot for you means a more -EV spot for your opponent. But this could not be an equilibrium, because your opponent could deviate to the less -EV play*. The basic intuition is, your -EV play being +EV in the metagame requires that your small mistake in the current hand induces a big mistake from your opponent later. But in equilibrium there are no "mistakes", so this is impossible.

-BRUECHIPS

*Really arcane side note for those that know something about repeated game theory or are interested in learning more: I think it might be possible that you could get an equilibrium with -EV plays in given hands if the two players had different discount factors. Basically, you could keep trading your current small mistakes for his big mistakes in the future because you care about future payoffs a lot more than he does. If this were the case, the repeated game would no longer be zero-sum. In poker, this doesn't seem to apply since usually you're hoping to incur a big mistake within the same session or at least at a different session in the near future, so discount rates shouldn't be high for either player.