Re: Heads up Theory
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That's a nice interpretaion, although still very very obscure (BTW, in a sense it is not very different from some of Gigabet's ideas, that were presented here in the past).
However, there's one simple problem: that's NOT what Jman was claiming on this thread (except for maybe in one of his very last posts).
This is the idea that was repeated again and again, from the beginning of this discussion: (I quote from an earlier post by Jman, titled "CONCLUSION OF MY THEORY IN PLAIN ENGLISH" (the capitals by Jman)):
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When the EV difference between pushing and folding are minimal, and you are heads up, err on the side that will decrease the size of the smallest stack (increase stack disparity).
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That is ALL. That is the theory, and as presented in this thread again and again IT DOESN'T MAKE SENSE, period. It is pure and absolute nonsense.
Of course you can "modify" it and word it differently (As Jman started doing as a reply to one of my last posts) and then come up with an explanation for why in fact you gain more the times you win chips than the times you lose, or why in fact it's only relevant when you are big stack or whatever, etc etc etc etc, but this calls for a whole new discussion (in the spirit of Giga's posts, maybe), in which you will discover that you need a completely new model for the EV of HU play, a thing that is way beyond what was suggested on this thread.
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I suppose I should just let the thread die but I find theoretical crap like this interesting and liked thinking through the arguments people were making. Anyway, I agree that through most of the thread J-Man is saying something stronger than my interpretation, basically that it is a good idea to try to manipulate your opponent's future calling range by making a -EV push even when outside the extreme push any 2 threshold. I think he's wrong to think that this is the case because an optimal strategy will exist each of the new possible stack scenarios. As explained in my last postin the 23 example, I think you can make an exception in the case where you are nearing the push any two threshold. So, I think he might be on to something, albeit something that is more theoretical than practical, if he restricts himself to the case I talked about.
Also, although I do see the superficial similarities to the Gigabet blocks theory, I am pretty sure what Gigabet was saying wouldn't apply in a heads up setting. My understanding was that the advantages of gaining a block come via the dynamics of multihanded play. In other words, being chip leader with roughly 4:2:2:2:1:1:1 ratios is more valuable the a linear model would indicate partly because of the way the other stacks interact with each other and with the big stack. Not applicable to headsup play, which is why I think any J-Man theory has to be extremely restricted. (There may be an analogy to the three-body gravity problem in physics here, or it may be too late for me to be trying to think.)
Regardless, an interesting thread. Hope I contributed something.
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