Re: Common situation w/ midpair and an 18bb stack
lol you beat me to it kurtkatt, anyhow here's my attempt.
(It's been awhile since I actually crunched the numbers so please look for possible errors).
I'm only going to do it for my actual hand, 77, and this is also not taking into consideration that someone behind me might call.
I think in this situation MP2 raising range is actually slightly wider than what Cheburashka suggested.
At this buy-in, assuming that MP2 is standard decent TAG that's capable of mixing it up preflop,I'd say it's more like: 22+, A8s+, ATo+, QJs+, KQo, plus a few random SC's, let's say JTs, T9s, 76s.
So he's raising w/ 14% of his hands from this position, as reasonable presumption imo.
When I push for he has to call another 4,436 to win 6,911....5336(my stack)+900(his raise)+675(blinds/antes).
So he's getting about 1.7-1, not quite 2-1 on his money to call.
I think his calling range is 77+, AJs+, AQo+, or about half the hands he'll raise w/ (6.3%).
To simplify let's say he'll call w/ exactly 50% of the hands he's raising with.
50% of the time I win 1,575= +1,575
My equity vs his calling range is 35%.
equity win tie pots won pots tied
Hand 0: 35.247% 34.42% 00.83% 279382800 6697068.00 { 77 }
Hand 1: 64.753% 63.93% 00.83% 518855160 6697068.00 { 77+, AJs+, AQo+ }
So, the other half of the time I'll:
Lose 5,536 65% of the time= -3,598
Win 6,211 35% of the time= +2,174
So if my ranges are correct pushing w/ 77 here is actually slightly +EV to the tune of +151.
Before doing the math I actually thought it would be +EV to push here, even if only slightly so.
Once again, someone please check my math, I'm kind of rusty.
edit: noticed and fixed an error already (i think). That error actually changed it from being slightly -EV to +EV, which is what I orginally thought pushing here would be.
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