Re: The Math behind a push...
 

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Case 1: Villian calls a push about 10% of the time {AA-77, ATs+, AJo+, KQs} Hero is 28/71 vs villian's range.

cEV(fold) = 410,000
cEV(push) = .9(steals blinds) + .1(villian calls and hand plays out)
= .9(440,000) + .1[ (.28*615,000 )+ (.71*225,000) ]
= 429,195



Case 2: Villian calls a push about 25% of the time {AA-22, any ace, KTs+, KJo+, QJs, JTs} Hero is 35/65 vs range

cEV(fold) = 410,000
cEV(push) = .75(steals blinds) + .25(villian calls and hand plays out)
= .75(440,000) + .25[ (.35*615,000 )+ (.65*225,000) ]
= 420,375




So...

Definitely +cEV, but only marginally (+1BB when your stack is 20BB) and it gets worse as your opponent's range loosens.

IMO, risking too much for too little given your stack and ability to use it.

I think this is a perfect example of passing up a marginally +EV bet now if losing it will cost you the opportunity of making an even greater +EV wager down the road.


That being said, many times I limp here and bet any flop.


[i]Edit: in case it's not evident from my post, I think raising the calling a push is bad, bad, bad. I'm either pushing (which I wouldn't have done at the time, and I think the math justifies that decision), limping, or folding. The limp/fold decision is based upon how active villian has been preflop.

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This is what I was trying to get at Betgo. I didnt explain or prove it as well, but this is it. And one more time, the A9o push was with the button and blinds still to act, 4 handed.

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FWIW, the A9o hand is an autopush. Do the math and you'll see.

Re: from chipleader to out in the stars 45k rebuy
 

I think you raised too much.

You asked villain to play for all his chips, you got it, with no ability to get away from the hand.

Calling A2 is slightly CEV- if hero is loose and CEV+ if hero is any two. It's a gutsy call, but probably $EV+ as 20XBB will get you close to the final table.

Re: The Math behind a push...
 

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That being said, many times I limp here and bet any flop.

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Against typical opponents, I believe that line is most profitable in this situation.

Re: from chipleader to out in the stars 45k rebuy
 

If you're going to raise to 100k in the first hand you might as well just put the BB all in. You're obviously not folding so why even give him the chance to reraise.

If he's pushing with A2o then I don't think you've been paying enough attention to who is weak/tight and your table and who is willing to gamble. Try to pay more attention to who isn't defending their blinds and pick on them.


With the A9o and only 3 players left to act and your stack at only 9.5BB you have to make the push.