Good questions. Thanks for joining the discussion.
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So, if you are going to be better than someone HU, that is have your $Equity>Chip Equity, you must have to do it when the stacks are more equal in size.
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John Paul, I'm either not understanding what you're saying or I think you may be mistaken.
If the hero is more skilled than the villian, then the equity of the hero's chips is greater than the hero's chips as a percentage of all chips in play for all levels of the hero's stack between 0 and 100%. In other words, the hero's skill advantage will manifest itself at any stack size and may be more powerful at smaller stack sizes.
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Even if the blinds do not put the short stack all in, it sems to be the 2+2 dogma that you can have a stack so short that you have to push any 2 cards, and the big stack should always call. In this case neither player can play better, just worse than pushing. Can this stack size be determined analytically in terms of stack sizes and blind sizes?
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If you haven't done so already, take a look at the heads up and hand ranking threads in the
favorite threads list. A lot of work already has been done to calculate push top x% and call with top y% of hands at different blind levels. poincaraux also has posted some similar
analysis on the poker stove website.
The Shadow