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

[pete fabrizio]

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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.

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The sentiment of your post is excellent, but the quoted text is 100% wrong. By definition, all strategic branches in an optimal mixed strategy must have the same EV. Otherwise you could improve on your supposed "optimal" strategy by replacing the lower EV branches with the higher EV branch.


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I think I just addressed this briefly in another post. I'm certain that your bolded text here is wrong, especially so when your opponent isn't playing game-theoretically perfect poker.

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Lol, I'm certain I'm right because I'm simply giving a definition, not an opinion.

From this thread in the Special Sklansky Forum, Jerrod Ankenman says

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It's probably true that there is a little bit of blurring near the threshold hands, to prevent the opponent from exploiting cards that come on future streets. This is probably limited to just a few hands. But my opinion is that the bulk of hands throughout the tree are pure. The reason is that if a hand is mixed, then playing it both ways has to have equal equity, and I just don't think that broad swaths of hands are indifferent between two actions.

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Trust me, read Mathematics of Poker. You'll find it thoroughly enjoyable (and educational [img]/images/graemlins/tongue.gif[/img].)

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While I haven't read the book, I understand the game theory involved, and if Ankenman endorsed that principle too strongly, he would be wrong. I'm sure Ankenmen and Chen understand this, but you can't define yourself into a box. Either a mixed strategy in which some of the elements have different expected value from the others is maximally profitable or not. There are some situations where you can prove this is the case (see my example about dry-sidepot bluffing). There are other situations you can construct very easily, *especially* if your opponent is playing non-game-theoretically-perfect poker. E.g., limping in EP occassionally with small suited connectors in limit hold'em b/c it keeps your opponent completely confused about what you're holding -- this is especially effective if your opponent will exaggerate how often he thinks that you have those type of cards, and it doesn't matter if you lose money on them the times you do play them.

Again, I doubt Chen and Ankenman would make such a huge mistake in their book, so I suspect you are misinterpreting what they are saying.