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Old 05-29-2004, 03:22 AM
Aisthesis Aisthesis is offline
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Join Date: Nov 2003
Posts: 5
Default Re: Median Best Hand Part II

Nice summary of the discussion until now!

I decided to go ahead and figure it through at a 9-player table for UTG, basically just following the calculation in the Sklansky article and using the K-S rankings, which give A9s as median best hand.

The result was actually pretty shocking to me! Even under the given assumptions (which may actually favor the all-in a little bit), you need to be VERY desperate to move in UTG. Assuming all worse hands will fold (not necessarily the case for BB) and all better hands will play, the move is plus EV only if your stack is 1.53 times the total amount in the pot up to that point (blinds plus antes). I expected it to be WAY higher than that! So, anyhow, it looks to me like from a mathematical standpoint, you're going to be much better off moving in in the small stack from LP with a lesser hand than you are in EP with a fairly decent one.

Here was my methodology: I figured that 50% of the time, you win the blinds plus antes with the all-in (I just set this value to 1 for simplicity). The other 50% of the time, you see the flop against a superior hand.

Taking all the superior hands according to the K-S ranking, weighting them according to frequency of occurrence, and then running them through pokerstove individually, I get that the superior hands will win on average 66.38% of the time. Then if you calculate a break-even in terms of stack size, that yields that your stack can only be at most 1.53 times the amount of the pot for a positive EV on this move!!!

Of course, it can still be a valid play even with bigger stack-sizes if you consider that some superior hands may fold (like ATo, 66, 77 maybe). But purely in terms of cards, you need to be pretty desperate to move in with A9s UTG.

In light of Sklansky's results on the SB version of the problem, where the stack-sizes allowing an all-in are surprizingly large, the curve as you move toward the later positions is going to have to be very steep indeed.
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