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#1
12-22-2005, 04:15 PM
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The Math behind a push...
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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#2
12-22-2005, 04:55 PM
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Re: The Math behind a push...
[ QUOTE ]
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. [/ QUOTE ] 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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#3
12-22-2005, 05:58 PM
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Re: The Math behind a push...
[ QUOTE ]
[ QUOTE ] 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. [/ QUOTE ] 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. [/ QUOTE ] FWIW, the A9o hand is an autopush. Do the math and you'll see.
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