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  1. #19
    daviddem's Avatar
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    One thing to be wary of here is the idea of "worse hand in your unexploitable shoving range".

    For example take the following game:
    - starting stacks of 1000
    - blinds 0.5 and 1
    - you are SB and button
    - you can shove or fold, then villain can call or fold

    It can be shown that your unexploitable strategy is to shove only AA, and the unexploitable strategy of villain is to call with only AA.

    However as the starting stacks decrease relative to the blinds, it will become optimal (unexploitable) for you to start shoving wider than just AA, against villain who still only calls with AA at this stage. You might think that the next hand you will add to your shoving range is KK? Not so. It can be shown that the first hand to add to your shoving range is ATs. With stack sizes of 833.25, you will find that the EV of shoving AA only is the same as the EV of shoving {AA,ATs}, whereas the EV of shoving {AA,X} (with X=any hand other than AA or ATs) is worse. One of the reasons for this is that your fold equity is better with ATs than with hands that do not contain an A because there are only 3 AA combos left for villain to have, whereas there are 6 otherwise. Another reason is that AT offers more straight possibilities than for example AK. If you stove {AA,ATs} vs AA, you will get slightly better equity than with {AA,AKs}.

    Again it is very much worth reading the corresponding chapter of MoP. Very insightful once you get past the math.
    Last edited by daviddem; 05-20-2011 at 04:48 AM.
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