What to do when Villian is going all in too much...

[ravensfan]

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in fact the further he digresses from Nash Equilibrium himself the greater your edge gets. You can then modify your game depending upon how he plays to increase your edge. Meaning that if he calls too infrequently push more, if he pushes too much call more, etc.

Check out the STT forum. Buy SNGPT and check out the headsup tutorial with all of the Nash Equilibrium charts in it.

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In this case i agree that if "he's pushing too much you call with A7o" with 10-15x bb. Also, i agree that as his pushing range gets wider, so must your calling range to enhance your EV.

Maybe it's semantics based on the latter part, but i want to clarify for myself too... I thought the whole point of game theory was that you were equal to/inferior to your opponent and wanted to reduce the skill edge. When you determine that your opponent isn't as good as you and is making fundamental errors, aren't you chunking off some EV by following the formula given that you're better. Generally, if I feel that my opponent has too tight of a calling range, and sometimes makes fundamental mistakes post flop, i won't call with marginal holdings as I feel my edge is larger by folding and outplaying later.

STT theory is great, and the SNGPT is the best investment I've ever made.

[EvilSteve]

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I thought the whole point of game theory was that you were equal to/inferior to your opponent and wanted to reduce the skill edge. When you determine that your opponent isn't as good as you and is making fundamental errors, aren't you chunking off some EV by following the formula given that you're better. Generally, if I feel that my opponent has too tight of a calling range, and sometimes makes fundamental mistakes post flop, i won't call with marginal holdings as I feel my edge is larger by folding and outplaying later.

STT theory is great, and the SNGPT is the best investment I've ever made.

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You're understanding this correctly I think, what you're getting at is the difference between maximal and optimal strategies. The Nash equilibrium describes an optimal strategy for both players such that neither player can improve their EV by changing their strategy. So if I'm playing my equilibrium strategy, you don't want to play anything other than your equilibrium strategy against me. But maybe later I switch to a new strategy which has exploitable flaws. You could stick with the equilibrium strategy and still do at least as well as you were doing before (likely better), but you probably aren't exploiting my specific flaws maximally. So now you switch to a strategy designed to counter mine which does even better than the equilibrium, this new strategy is maximal but not optimal. That is, your new strategy is the best you could play against my new strategy, but you could get in trouble if you ever use it against someone else, because your new strategy also has exploitable flaws.

This is obvious but I'll state it: Nobody knows the equilibrium strategy for headsup NL holdem. It exists but solving for it would be a huge intractable computation. What is known is the equilibrium strategy to the subgame where the button is restricted to only 2 options, all-in or fold. The reason this is useful is that for small stack/blind ratios, the small blind doesn't lose much equity by being restricted to those options, so the subgame equilibrium strategy approximates the full game equilibrium. Its a very good approximation up to an effective stack size of around 8bb, and above that it becomes progressively less useful. My preference against any halfway competent opponent is to just play the equilibrium push/fold strategy when we're below 8bb. I'm never going to play significantly better than that, and I could easily play worse.

But what if the big blind is 400 and the smallest stack is 4000, so effective stack size is 10bb? If you were on the button you could choose to play push/fold but you certainly don't have to, and if you think you're the better player you would probably want to see some flops. So the subgame equilibrium becomes irrelevant, you aren't playing push/fold.

However when you're in the big blind, if your opponent is playing push/fold, you're automatically playing the other side of the push/fold strategy and I think it would be useful to at least know what the push/fold subgame equilibrium looks like, as a guide. Then like you said, if your opponent seems to push too often or not often enough, you adjust your calling requirements accordingly. The equilibrium strategy gives you a good default baseline to work from, although against a weaker opponent you would probably tend to fold the most marginal of the calling hands, especially if you can use your advantage in later hands playing flops from the button. Pretty much what you said I guess, hope this helps.