GTO aside, even the most expertise live players are not thinking on an extremely high level on every single hand (That's not to say I don't thoroughly enjoy reading and discussing the deeper, theoretical levels too
). If BB is a semi-expert then I think there are few ways this hand can typically go down once flop goes check/check. This represents more of what I personally find in practice and what I think is the most likely outcome for the hand.
1) Preflop: Most players I encounter do not have a wide 3! range from BB v BTNo (a different discussion) and I think it can often be safe to assume that many BBs may never even have a 3! range in this spot.
2) Flop: On a 964 board, if I were Villain in BB, I would assume that Hero's check back frequency is not optimal. He is most likely overweight in Ace His, underweight in pairs, and underweight in 8 Hi-Khi as well.
3) Turn: As the BTN, I would assume that when BB checks he is repping no pairs as he should expect me to check back again since the 3 rarely hits our semi-unbalanced range. If BB is well-balanced in his turn xR frequency then I would check AT; however, I personally would try to exploit BBs turn check and bet the turn for value/prevent free river cards.
4) River: If I'm the BB here, I am almost never betting this river with any hand. If I have two pair or better I would usually go for a xR as most people would likely just call with a large majority of their Aces here as well as pay off to the xR but not a potential third bet. The A is a card the BTN will almost never fold and we should not be bluffing our Qhis or worse imo. Given that BB should rarely be bluffing on this river, when he does bet I think the best two options for hero are 1) to call and 2) raise and fold to a 3!. Personally, if we really narrow down ranges and put BB on Ax then we only beat A2,A5,A7,A8 (Also I think BB may bet A5 on turn). We lose to A4,A6,AJ,AQ,AK but I also think that BB may bet some AJ-AK for value on turn.
With all that said if Villain is capable of folding any Ace then I believe it is a call. If Villain is capable of 3! bluffing (which seems rare if it would even ever happen) then it is a call as well. If Villain isn't playing his A game, is SDB, and I could live with myself for folding to his three bet, I would raise. All in all, I lean toward calling.
Last edited by NedSchneebly; 02-23-2018 at 02:51 AM.