Corsakh,
I think the first hand's really not close. If we ignore the chance that he checks back a 7 (
)), then I just don't really see the downside. He never has a set and he's almost never calling a bet with two pair, and there are only 11 2 pair combos possible anyway. He's prob more likely to bet 9T than to call a bet with it. There are plenty of hands to bluff with in his range... A2cc-A5cc,ATcc, KQcc, QJcc,QTcc,34cc, A6s, 55,56, A8. Obviously plenty of those hands are discounted, but they're all quite possible and all pretty likely to bluff.
Plus, even if he never bluffs, I now get a bet and a raise out of 7x instead of just one bet. So I think it's really not close at all.
The nanonoko hand is much more debatable.
Let's say he bets river when checked to with Qx 80% of the time and calls a river c/shove with Qx 20% of those times, and let's use betting 180 as the alternative to c/shoving and assume he always calls with Qx. Then, when he has Qx, and I c/shove, I make .8*(142+.2*363) = 171.68. If I just bet, I make $180 of course. So, when he has Qx it costs me $9.
Since that's essentially break-even, IMHO that makes it pretty clear that checking is better, since I think he definitely will get here with TJ/78 and bluff more often than he'll get here with 9x/88/77 and will call a bet. Lemme know if you're not convinced and I'll finish up the math.
(You're wrong that he's never calling the turn with a bare straight draw. He is and he should be because my range on the turn includes a ton of air that c/fs most rivers and the rest is made hands that he has good implied odds against. Sure, sometimes I have a boat and sometimes I have a FD, but those are small concerns.)
nemee,
Glad you like the series.
I think you're wrong that he's calling a turn 3-bet there with any draw unless he somehow manages to get to the turn with a flush draw + straight draw... which is obv incredibly unlikely. All his other draws here are to 1-card straights, so he has no implied odds.
So what we have to weigh here is the money we lose when he sucks out on us vs. the money we gain when he continues. He probably averages like 10% equity here when we're ahead, so I think that makes it a pretty clear check.