Any two from the button (Game Theoretic Analysis)

[Jdanz]

Pokerstove has 68s as 38% against pretty much any hand that might call from the BB for like 5x the BB. So some assumptions.
SB will play top 10%
BB will play 20%

so

If you have 10 chips the sb is 1 and the bb is 2.....
You steal (1-[(.1+) + (.9*.2)])or .72
You play the sb (.8*.1) or .08
You play the bb (.9*.2) or .18
you play both (1*.1*.2) or .02

say you win 25% when you play both (roughly right by poker stove)

your EV =
times you steal + times you play sb and win + times you play sb and lose + times you play bb and win + times you play bb and win + times you play both and win + times you play both and lose

more simply =
(.72*.3)+ (.08)*(.35*12-.65*-10)+ (.18)*(.38*11-.62*-10) + (.02)*(.25*20-.75*-10)

or 2.16 -.184 - .3636 - .05 = 1.5624

so on your 10 chip investment you can expect a +1.5624 return if my assumptions are accurate.

The results would seem to indicate that if the blinds are reasonably tight you should at this stack size (5BB) be correct to push everytime, with any two, and it's not even close.

Further while i'm sure my assumptions are off (and i'd really like some response as to what assumptions and in which direction) The evidence is SO overwhelming plus EV that it leads me to believe i should be pushing with any two more, and probably calling pushes more often from the BB.

This is really important stuff, help me refine the numbers.

Comments and critisisms.

-JDanz

[bmxreed36]

Very interesting and in fact, I often do push with almost any in this situation but not always.
You use 68s for your calculations but then apply the results to be the same for all hands such as 24o, 37o, etc.
That estimate of how many hands the blinds will call with is a big if--I think it would be a rare situation to have it set up this way.
Although, the calcualtions do show a positive EV, the one in four times that you get called (appox.) and the 2 out of 3 times that you lose that hand ends your tournament and your chance to make any more EV+ plays. Even if the same situation arises many times in one tournament and you are successful the first few times, it's always the last one that makes the other ones worthless.
You definitely show that it may be better to push with more hands with this setup and also call more from the blinds, but I still have to make my decisions based on what exactly I have and how the blinds are playing. I might push 70% against a certain two in the blinds but only 20% against another two.

[Jdanz]

sure, but what i'm looking to show is that even if you get called about 30% of the time, you're still making a very positive EV play. I picked 68s as its a crap heads up hand but not absoluite trash, the results are still positive for 32o just not as much.

-JDanz

[woodguy]

Read DS's article about this from last month's magazine here. (http://www.twoplustwo.com/magazine/issue2/Sklansky0205.html)

Lots of good stuff about what you are talking about.

Regards,
Woodguy

[Jdanz]

Thanks very much.