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hero raises to .35, villain calls .2, with remaining stack = 4.77
so hes calling .2 to win 4.77, giving him implied odds of about 23.5:1, which is plenty for most opps.
to figure out the amount to raise preflop, just figure
(4.97-B)/B = (probability youre going to stack flop) / (1/9)
this means, if youre never folding the flop, you need to be raising to .15+.53 = .68 for him to not be making a +ev decision to setmine a lower pair here.
imo, giving opp a range of jj+ here, doing a little bit of combo counting..jj(6), qq(6), kk(12), aa(1), youre basically even money in this spot. gg
on the other hand, if dudeman wanted to mine you, say he flats your pre raise with any pair, flop comes same
22-66,88-tt (12*8), he folds to your 47% pot bet (in this case, .34 into a pot of .72)
77,qq,jj (6*3), he raises you, and you two stack off, he wins
kk (12), he raises you, and you two stack off, you win
ignore aa for now because its going to make a small difference.
so we get 126 total hands
96/128 = 75% of the time, you win .72, he loses nothing
18/126 = 14.3% of the time, you lose 4.77
12/126 = 9.5% of the time, you win 4.77
soooo...
your ev from this situation is = .75*.72 - .143*4.77 +.095*4.77 = +.311
and his is = .75*0 + .143*4.77 -.095*4.77 = +.228
basically, this shows that because of your preflop sizing, youre putting him into a position where he basically cant make a mistake once the flop comes. The moral of this story is, if youre going to stack AA no matter what, at least dont make it +ev/correct for your opps to call you, so its important that you 3bet him much bigger.
I also appreciate feedback if anyone wants to look at this. I know i didnt include hands like scs or such, but it was just kinda a simpler way of looking at a particular sort of situation.
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