So he needs to call at least 50% of the time on the river with a worse hand for a push to be correct? (self-obvious)
Anyway back to the turn, you really think this is a fold? Someone bets 1/2 pot into you on 2 streets and you fold TPTK?(specially since we underepped our hand) I really think we see worse aces, or AK here a lot of the time.
Here is my thinking on possible hands by the river:
22-55, these hands all have either a straight or a set. They are quite possible but pf makes them iffy.
99-KK, very opponent dependant, aggro opponent might try betting them both streets, but would usually check the river.
AJ-AK, Very possible, hands trying to get value the whole way with value bets on all streets.
Note: I didn't even include air here, as I would have noticed if Villian had done crazy stuff prior to this (I hope)
This was my thinking in general, I just felt that top pair type hands were the most likely hands(60-70%). And if we narrow it down to the river, The river will be bet by sets and straights all the time, and by AJ-AK most of the time. I don't really do hand distribution math, but basically
IF
# of combination of 22-66) < (river bet frequency)(# of combination of (AK(most likely)+AQ(fairly likely)+AJ(rarely))
So if the above statement is true I shove, if its false I call(or fold if it is really small (less than 30:81).
Note: I assume that all hands that bet call a shove (20 into 111)
I haven't plugged numbers in, and I would like to say that after looking at hundreds of posts on 2p2 i've never done this much math/logic.
This post came off pretty snoty reading it over, but I'm no good with grammar. I would appreciate some thoughts on this, I don't usually go into this much detail.