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ok my self-imposed 3 hour ban is over. i think i am thinking clearer about this hand now
all of this assumes that of villain's "continuing range" to our riverbets, he always shoves full houses and always smooths with one pair hands (the ones in his designated continuing range), and he never bluffs FDs if we lead into him. because of these assumptions, we obviously never call when shoved over.
if villains continuing range for our chosen betsize is AQ,KQ,56s,55,66,88,79s then we beat 18 combos and lose to 13. if he only bets the "we lose to" hands from my last post when we check to him, then he needs 14 combos of bricked FD's (roughly 52% of his range) in order for c/calling to be preferable to leading.
if villains continuing range is same as above, but we ADD the 6 combos of AQ to his vbet range, he only needs 8 combos of bricked FDs (30% of his range) for his betting range to be weaker than his calling range, which would thus make c/c > bet
if villain calls a river bet with the same range minus the 12 combos of KQ, then we only beat 6 combos and lose to 13. so betting becomes -EV. in which case we have to determine if villain bets enough hands we beat in order to call when we check to him, based on pot odds, equity etc etc. if villain happened to use the same betsizing, we need 8/29.85 = 0.26 = 26% equity, which requires between 4 and 5 combinations of missed FDs for a call to be +EV.
obviously thats all speculative - he may have 1 of 3 combos of QQ (if he 3bets it 66% of the time preflop), or he may never float the flop with 66 or 56s, or never call pre with 79s, or sometimes jam bricked FDs after we lead the river. he may or may not raise the flop or turn with sets. there are plenty of variables. but i think the analysis of each scenario is correct based on the assumptions provided about villain's range and how he will play it. if not please correct me so i can stop being a fish.
edit: when i say he needs x amount of air in his betting range to make this option>that one or whatever, im assuming he bets the same amount with the given range as CBAT chose to bet in the actual hand. in reality it probably wouldnt be the same, but probably close.
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