EDIT: You may as well ignore all this. It's twisted and wrong. Just skip to my next post.
Okay, so I went away and thought about this a bit more.
I'll illustrate this with a different hand; one that is a little simpler and more clear cut. I understand it's quite unrealistic, and contrived.
Hero is folded to on the button, holding AKo, and raises. SB folds, BB calls.
Flop is Qc 5d 2s.
The BB checks with 100% of his range.
51.013% { AKo }
48.987% { JJ-22, AQs-A2s, KTs+, QTs+, J9s+, T8s+, 97s+, 86s+, 76s, 65s, 54s, AQo-ATo, KJo+ }
If Hero cbets the BB will fold 100% of the hands that hero is ahead of, and call with 100% of the hands that hero is behind. He will never raise.
If hero checks behind, hero is 100% certain the BB will bet the turn if he makes/already has a hand better than hero's. Hero knows the same is true for the river. Hero knows the BB will never bluff. Knowing that the BB will check fold later streets where he doesn't have a hand, hero plans to check behind the turn if he improves, in order to bet the river. Hero has no intention of barreling as a bluff, or anything like that. (I understand this is all very contrived, but bare with me).
So lets split the BB's range up into sections. The hands that we beat, and the hands that we don't.
1. Hands that have us beat: JJ-22,AQs,A5s,A2s,KQs,QTs+,65s,54s,AQo,KQo
About half his range.
He will not fold to a cbet, and he will not raise. All of these hands beat us, many crush us.
Best course of action: Check behind, hope to catch, and keep the pot small, in case we catch and are still behind.
2. The hands that we beat, but don't dominate: J9s+,T8s+,97s+,86s+,76s
Much less than a quarter of his range.
He folds all of these if we bet. Each of these hands has clean outs, and will only put more money in the pot when they have us beat. The only implied odds we have are if running cards come off. We catch an ace or a king on the turn, and check behind, then he spikes a pair on the river, bets, and we raise, and get called. Hell of a lot of ifs and maybes. Far more likely that he outdraws us when he puts more money in.
Best course of action: kill the hand off. Cbet. There's negative expectation in seeing another card.
3. The hands that we beat, and dominate: AJs-A6s,A4s-A3s,KJs-KTs,AJo-ATo,KJo
More than a quarter of his range.
He folds all of these hands if we bet. Each of these hands has outs that would improve us both, and leave us ahead. If we both made a pair of aces, for example, we'd have villain dominated, and could win an even bigger pot. The problem is though, we don't want the chips to start flying too hard against alot of villains. Sure, we might have him outkicked, we might also be behind. If villain has a hand in this range, and we both improve, we'll want to create a medium sized pot, for fear of hand that dominates us, from range 1.
There's also the issue that while each hand in this range has dominated outs, most of the outs are not dominated. There's no expectation in villain catching a jack with AJ, for example (baring running card situations).
Best course of action: I'm not so sure. I like the implied odds of his tainted outs, but most of his outs are untainted. I don't really know whether I'd like to win the pot here and now or not.
So for about half his range, we should check behind, and try and draw (range 1). For small amount of his range, we should protect our hand (range 2). And then there's range 3, where I'm not really sure. There are implied odds in seeing another card, but there is also the risk of being drawn out on. Let's just call it 50/50, and say that for the majority of his range, the best play is a check behind.
I'm less concerned with whether I'm right in this situation, and more concerned with whether my methodology for analysising the situation is correct. You see, I'll be examing my hands when make this play, and I need to know I'm analysing them right.
Massively appreciate anyone who bothered reading this far, and doubt you even exist.
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