AA-rag OOP vs. deep stack and short stacks

[RoundTower]

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These kinds of numbers always confuse me. How is it possible that your EV is less than somebody else's in the main pot, but more in the side pot despite the dead cards? Maths guys, please explain.

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Using a different example from the one above:

Suppose you have the nut flush draw with one card to come. Player A is all in with top set, Player B is all in in the side pot with you. To make it even simpler, suppose you also have the card that middle set needs for quads.

Now you have some EV in the side pot, but it is less than Player B's. You also have some EV in the main pot -- this time more than Player B's. Where did his EV go? It went to Player A -- the times he wins the side pot, Player A wins the main pot.

That's how what you describe is possible. What is not possible is that the % of time you win the side pot is less than the % you win the main pot.

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These kinds of numbers always confuse me. How is it possible that your EV is less than somebody else's in the main pot, but more in the side pot despite the dead cards? Maths guys, please explain.

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It has to do with the fact that most of hero's "outs" in the side pot are cards that miss the 66xx. In the main pot though, these are mostly splitting cards with he other AA - so they only count half as much. Remove the other AA and these cards get full value thus greatly increasing Hero's EV.

To illustrate this, look at the win and tie columns for the AA88 hand. They're each about 27%. These main pot wins and losses get split among hero and 66xx in the side pot.

All the ties count as wins for hero in the side pot. This adds about 0.135 to hero's equity, bringing him to about 0.42. As for the AA88's wins, many of them occur when he spikes an 8. Most of these also go to hero.

When two AA hands face off against a third, completely different hand, most of the time the third hand either beats both or neither and so his equity 3 way is only slightly worse than his equity 2 way.

[BluffTHIS!]

Joe, you are right that stack size, position and the bad sidecards with your AA are important considerations in this hand, but you have not properly interpreted them as to how to play. The 2 shorties are real short, so they should be no consideration at all. Then since you can get almost 70% of your stack in by a reraise versus the LAG who covers you, that is what you should do, followed by betting allin no matter what comes if he doesn't set you in preflop. If he folds to that reraise and 1 of the shorties calls and beats you, you can't lose much.

If the other 2 players had stacks similar to yours and were loose enough to call your reraise with mediocre hands, which means you cannot get it headsup, then that would argue for calling only. But it is still reasonable in those cases to get a little more than 10% of your stack in by calling because of the times you flop a set and can double off of him when your hand will be disguised by not playing it hard preflop.

I have said in the past here that I have occasionally folded AA rag hands with a big stack in an aggro game facing other multiple big stacks, but this is not one of those situations.