HU Theory - outplay vs. force coinflip?

I've been thinking about the HU strategy discussed here, of pushing almost any two cards (when the blinds are > X% of your stack). W/o getting into all the details of whether or not the strategy really is optimal, here's what I've been wondering:

If I understand it correctly, and as stated by some posters on this board, there is really no couter-measure that can reduce this strategy to anything less than neutral eV. And that counter is obviously just to do the same thing. So heads-up we have achieved a Nash equilibrium-type optimal strategy that cannot be countered. Again, if I understand the assertion correctly, then let's just assume the conclusion is correct. I'm not bringing this up to debate the actual theory.

So here is the question. If you are playing against a passive, weak-tight player who you know you can chip away at with min or 3xBB raises, and won't fight back unless he has a premium hand, would you really want to employ this strategy? Why reduce yourself to 60% eV when you can get almost 90% by outplaying the person? I really can't see an argument for the "all-in" HU strategy against a mouse. Seems to me like this cannot possibly be the best strategy if you know you have a decent edge in HU skill.

So let's take it one step further. Phil Helmuth and Mike Matusow are HU for the WSOP title. Even though our all-in strategy is the absolute optimal (again assuming) strategy, if either one of these guys starts playing this way, he basically admits that he doesn't think he has a skill edge over the other. Of course if one of them does adopt this strategy, the other one absolutely has to adopt it as as well or lose (and they both know this being the poker geniuses are)--thus forcing it to a coinflip.

So I may not be getting the clunky words out of me so good-like, but do you see what I'm getting at? Basically either guy has the option of forcing it to a coinflip, or laying back and trying to outplay the other. Very interesting conundrum, sort of a two-way Spanish Prisoner kind of thing. Or not.

(Forgive me if this topic has already been discussed ad-infinitum. I searched but couldn't find anything, or figure out which keywords I should even be looking for. If it has can someone please point me to the thread?)

thx,
Matt

Note: I originally posted this on the poker theory board, but the only response I got told me I should come post it over here.

[tewall]

Say you're at 10xBB. Basically you're looking to be the first one in the pot. The situation you're talking may be OK if you're lucky enough to have it folded all the way to you, and you're in the small blind, and you know the mouse is as likely to fold to your smaller raise than all-in, but that's not likely to happen. Usually there will be more than one person to act, and you won't have enough information to be sure how they'll act (and if you guess wrong, and they do call your smaller raise when the would have folded to the all-in, that's very bad). So going all-in is likely to be higher EV than a smaller raise.

Also the Nash equilibrium assumes perfect play by the opposition. Usually they will be folding more hands than the Nash equilibrium would suggest, and not pushing enough, which means you should push more and call less than what the Nash equilibrium would suggest. Doing this, of itself, gives you a big edge.

I think it was at a higher level than that.

suzzer: What we talk about on these forums is about a specific situation in which our stack is low compared to the blinds. When pros are sitting at a tournament, the blinds to not increase to that level like they do online. The "poker" skill is removed by the structure and the "Nash Equalibrium" becomes important because your chip stack is too low not to be pot comitted if you play at all.

If you can beat the guy 90% of the time playing a different way, why the hell wouldn't you?

The way I understand it, the Nash Equilibrium jazz is basically the "optimal" strategy, in that it cannot be made -EV no matter how your opponent plays. It is not necessarily the most +EV option in every situation, and if a different strategy is more +EV because of your opponent's incorrect play then you should use it.

[wuwei]

The player you describe is not playing optimally, so yes, you can adjust your play to take advantage of his weaknesses.

Right, but I'm thinking more in the abstract here. My point is: let's say Hellmuth and Matusow are both aware of this optimal strategy, but they also both know that if either one starts using it, the game becomes a coinflip. And further, if one of them starts using it, the other one has to. However with both of their egos, they wouldn't ever be able to accept that their opponent was playing "optimally" (IE - as well as them) and therefore wouldn't want to push it to a coinflip, as each would still think he has an obvious skill edge over the other. You see what I'm saying? I think it makes an interesting decision in either player's mind.

Again, I'm just reiterating what's been asserted here: that there is an "optimal" strategy which when pursued by both sides turns the game into a coinflip, and a "better" strategy which will give you a better chance to win if you're opponent is not playing "optimally". I'm not debating whether either of those is true for this post. I'm just saying that if they are, I think it creates an interesting conundrum.

[jb9]

If stacks are deep enough (I don't know... 15+ big blinds maybe, 25+ would be better), I generally prefer to see some flops and "play some poker".

I still raise or fold preflop, but unless my opponent wants to make it a push or fold competition, I won't necessarily do it unless it seems to me that my opponent is better postflop than me, then I'll push or fold.

Basically, and maybe this is what you are asking, if I think I can outplay my opponent postflop and we have enough chips to play postflop poker, I would rather play that way because I think I'll win more often than coin flipping.

If I think my opponent can outplay me or that we are fairly evenly matched, then I'll be more inclined to push or fold preflop.

Of course, in most SNGs, by the time things are heads up, the blinds usually are pretty large compared to stack sizes, so there is often little chance for heads up postflop play.

I don't play many heads up tournaments, but I have played a few at Stars, and I must admit I find it a bit boring and, for lack of a better word, disappointing when I find out my opponent is only going to push or fold preflop even though we start with over 70 big bets.

[tewall]

If the stacks are large, the Nash equilibrium doesn't apply because whatever that strategy would be is too complicated for anyone to know what it is. It works well when the stacks are smaller and you can prove mathematically with what hands you should push, but with larger stacks any pushing only strategy can be countered (although the edge one gets by doing so is less than one might think intuitively; e.g. three was a post showing with stacks at 50xBB, which is pretty big, the best counter strategy would produce an edge of 61%, meaning that by a pushing only strategy anyone could win almost two fifths of the time against a world class opponent with stacks as large as 50xBB).

Once the flop enters into the equation, the math becomes very difficult.

[lacky]

it basically depends on the stack sized in realation to the blinds, and how meek he really is. At some point the blinds are big enough you can never coreectly fold to a reraise, so you might as well push and make him fold his borderline hands he might have called with. If the blinds leave you room to fold to his push, and he folds much too often, then yes, constant small moves is best IMHO. Problem is making those kinds of reads on a player is an in exact science/art at best, and alot/most players here are playing multiple tables. In that case using a stratagy that is close to optimal regardless of your opponent makes alot of sense.

[eastbay]

[ QUOTE ]
Right, but I'm thinking more in the abstract here. My point is: let's say Hellmuth and Matusow are both aware of this optimal strategy, but they also both know that if either one starts using it, the game becomes a coinflip. And further, if one of them starts using it, the other one has to. However with both of their egos, they wouldn't ever be able to accept that their opponent was playing "optimally" (IE - as well as them) and therefore wouldn't want to push it to a coinflip, as each would still think he has an obvious skill edge over the other. You see what I'm saying? I think it makes an interesting decision in either player's mind.

Again, I'm just reiterating what's been asserted here: that there is an "optimal" strategy which when pursued by both sides turns the game into a coinflip, and a "better" strategy which will give you a better chance to win if you're opponent is not playing "optimally". I'm not debating whether either of those is true for this post. I'm just saying that if they are, I think it creates an interesting conundrum.

[/ QUOTE ]

I think you're neglecting the fact that at the optimal point, your opponent is getting outplayed unless he also plays optimally. Most opponents don't do that, so you are not a "coin flip" with them.

But in the end, if you have knowledge of an opponent's strategy, you want to play the maximal counter-strategy, not the equilibrium. I don't think anybody has ever claimed otherwise. It's just that equilibrium is a good default when you don't have much information, say, while you're 10-tabling. You are outplaying the vast majority of opponents and not giving anything up to the rest. That's a pretty good place to be.

What's dangerous about your so-called "better" strategy is that you open yourself up to the possibility that your opponent is better at determining your strategy than vice-versa. At which point you get spanked.

eastbay