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.

[pete fabrizio]

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btw, Pete, law school does suck. Get out while you can.

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I'm working on it, the end is nigh. Just hoping I "get out" the right way.

[Troll_Inc]

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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.

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"that" principle
"this"

Pete, you do not always write very clearly. Sometimes there is a little bit of guessing as to what you mean exactly. I think, although I'm not sure, that is part of the problem with the Poker Math parrot.

[Subfallen]

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I think what you meant to say is that message board analysis often arrives at the best play assuming the metagame induced by overall near-optimal play.

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Exactly.

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could someone elaborate as to what this means plz?

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I think what you meant to say is that message board analysis often arrives at the best play assuming the metagame induced by overall near-optimal play.

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Exactly.

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could someone elaborate as to what this means plz?

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Imagine your friend John Q. asks you for advice on a PLO hand where his top two pair are facing an all-in raise on the flop. Unfortunately Mr. Q. doesn't have any reads, so he's just asking for your default play.

Consciously and subconsciously, you will call upon your own experience to answer John. If you are a nitty-ish TAG, you may recommend folding because you intuitively expect your opponents to respect your bets. Or, if you have played 100k's of hands as a super-LAG, your instincts may be to snap-call.

My point is that you, like everyone else, have subconscious assumptions about metagame that are based on your overall poker strategy. If John Q. plays an overall strategy similar to yours, your advice will probably help him out. However, if John plays much less (or much more) aggressively than you do, taking your advice could be disastrous.

When you post a hand in a forum full of players better than you, their underlying metagame assumptions will be different from yours. Specifically, their advice implicitly assumes you are already playing an overall strategy that is near-optimal.

Thus the sentiment expressed in the OP.

[Subfallen]

Pete, you're clueless bro. An "optimal strategy" in game theory is a strategy that yields the best EV versus a MAXIMALLY EXPLOITIVE OPPONENT. Not a human opponent who makes mistakes and can be manipulated into making exploitable adjustments.

Thus, in practice, a game theory "optimal" strategy is usually NOT the strategy that optimally exploits a specific opponent in a specific situation---which is what you're talking about.

You're confusing categories badly here.

[RoundTower]

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There are some situations where you can prove this is the case (see my example about dry-sidepot bluffing).

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I disagree, I don't think you have proved this. For a start you failed to consider the case where sometimes you value bet light into the dry sidepot on the river. I would like to see a better example (doesn't have to be a poker example, a contrived game might be even better). I'm not 100% sure if this is possible, a year ago I could have worked it out.

[Subfallen]

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There are some situations where you can prove this is the case (see my example about dry-sidepot bluffing).

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I disagree, I don't think you have proved this. For a start you failed to consider the case where sometimes you value bet light into the dry sidepot on the river. I would like to see a better example (doesn't have to be a poker example, a contrived game might be even better). I'm not 100% sure if this is possible, a year ago I could have worked it out.

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WTF GUYS THIS IS NOT A POINT UP FOR DEBATE THIS IS A MOTHERF'ING DEFINITION WE'RE TALKING ABOUT HERE. MAYBE I SHOULD START A THREAD ARGUING THAT 6 IS A PRIME NUMBER. HUH? PROVOKE SOME GOOD DISCUSSION THERE, YES?

[Truthiness24]

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Pete, you do not always write very clearly. Sometimes there is a little bit of guessing as to what you mean exactly. I think, although I'm not sure, that is part of the problem with the Poker Math parrot.

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Once you quit or get out of law school, you'll learn to write again. [img]/images/graemlins/ooo.gif[/img]

[pete fabrizio]

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Pete, you're clueless bro. An "optimal strategy" in game theory is a strategy that yields the best EV versus a MAXIMALLY EXPLOITIVE OPPONENT. Not a human opponent who makes mistakes and can be manipulated into making exploitable adjustments.

Thus, in practice, a game theory "optimal" strategy is usually NOT the strategy that optimally exploits a specific opponent in a specific situation---which is what you're talking about.

You're confusing categories badly here.

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I think you have this confusion exactly backwards. First, I am not necessarily talking about facing "maximally exploitive opponents" when I am talking about using mixed strategies in the OP or elsewhere in this thread. Second, even when playing "maximally exploitive opponents", I'm saying I believe that there are times a mixed strategy is called for even when the various parts of the mix have different expected values. In your earlier post you denied this assertion, and then claim that it all flows from a DEFINITION, of all things. And then you call me clueless.

I'm not going to get into a flame war with you, and maybe I'm wrong in my second assertion (though I doubt it), but you are showing an incredible lack of reading comprehension.

[pete fabrizio]

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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.

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"that" principle
"this"

Pete, you do not always write very clearly. Sometimes there is a little bit of guessing as to what you mean exactly. I think, although I'm not sure, that is part of the problem with the Poker Math parrot.

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While I'm not a great writer, I think most of the breakdowns in this thread (and others) stem from poor reading and/or poor reasoning.