The First Problem
I have been experimenting a bit lately with pokerstove. If you don't have it, it is free to download and is pretty useful. What it does is calculate odds/equity for hand range match-ups. For example if one player has a top 20% hand and the other has a top 40% hand, it will tell you how often the top 20% hand will win (no, its not twice as often). I used it to do a limp/call range calculation for a hand I had with Hoy a few posts back. That problem did not fully consider the BB in the hand. So I thought I would attempt a slightly more complicated calculation that considers the actions of the button, SB and BB completely. This is for the semi-common situation late in an MTT when it folds to the button or the SB and everyone has similar stacks that are pretty short relative to the BB. What range should the button be stealing with and what range should the blinds be defending with? Using game theory you can calculate it based on a few simplifying assumptions. I will will lean on pokerstove, and trial and error to nail down the ranges for everyone involved. If this is somewhat easy, I may try to throw the cut-off in as a follow up calc.
So below is the set-up, and I will not calculate it till later in the week. You may guess at the ranges if you would like, or try to answer one of the questions if you want.
Blinds 1k/2k, ante 250.
Button, SB, and BB all have 10k in chips to start.
Action folds to the button.
1) The button may not limp, and can only push or fold.
2) If the button folds, the SB may not limp and can only push or fold.
What range does the button push with?
What range does the SB call the push with?
What range does the SB push with when the Button folds?
What range does the BB call the button and SB push with?
What range does the BB call just the SB push with?
What range does the BB call just the button push with?
What is the Expectation Value for each player in this situation?
All of this assumes that each player is maximizing their own EV for the situation.