blitzing on third and long and the problem with poker forum advice

[pete fabrizio]

A friend and I once had an argument about blitzing on third and long. As an avid reader of TMQ, he was convinced that this is usually a bad idea, and instead you should play cover. He cited all kinds of statistics about average gains, frequency of sacks and interceptions, etc: If you put all of this together, blitzing is -E.V. relative to covering. I agreed with all that. And of course my friend is not stupid, so he understood that you have to blitz sometimes to keep your opponent from exploiting your overall strategy. Fine. So where was our disagreement? He insisted that covering is the "better" play.

This is exactly the kind of thing that happens in poker forums: Someone posts a hand, and after a certain amount of discussion there is frequently some kind of consensus as to what the "best" play is, as a matter of e.v. The majority of posters will just regard this as the "answer," but a significant minority understand the idea that sometimes you may have to play differently in order to keep your play varied and to keep your opponents from being able to exploit your predictability. But most of these people still think that the consensus play is the "best" play, and that other plays should just be thrown in to mix things up, usually at some small interval.

My friend and all of these forum posters are wrong. For every difficult situation against even slightly observant opponents, the "best" play is the optimal mixed strategy, not any one of the plays that it contains, no matter how much more +e.v. they may be than others.

While this may seem like a mere semantic distinction, it has very specific consequences. E.g., in the optimal mixed strategy, the most +e.v. play may not be the play you should make most often, or even often at all. A very simple example of this is trick plays in football. Many of them have enormously high e.v. compared to run-of-the-mill passing and rushing plays, but only when they are used very very sparingly. Undoubtedly, if various football situations were posted as hands on 2+2, the responses would always say that you should run a half-back pass (or the statue of liberty). An example in Omaha might be the lone-ace bluff. The times that you run it, it should be a very profitable play. But if you do it every opportunity (or even a majority of opportunities), it will lose its value and create some very profitable situations for observant opponents.

While posters make this kind of mistake in all of the forums around here, I think it is a bigger problem in PLO since very game-theoretically complicated situations come up more often. Finding the proper solutions to these situations can be very difficult, and is not as clear-cut as analyzing hand-ranges and finding the "best" move.