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His definite calling range (no combos discounted):
AQ (6)
77 (1)
A7s (1)
A9s (1)
total of 9 combos
His probably calling range:
AJ (8)
AT (6) {I'm having him fold or 4-bet ATo some of the time so we discount AT 25%}
total of 14 combos
His maybe calling range:
A8s (1)
A6s-A2s (8) {I'm discounting these combos 20% as well because they sometimes 4-bet or fold}
total of 9 combos
His always folding range:
KQ (12)
QJs QTs (4) {I'm really not sure he calls turn with this many queens so I'm discounting QJo entirely and QJs/QTs by 33%}
Qc9c (1)
KcJc (1)
KcTc (1)
JcTc (1)
KJ (2) {Seems reasonable to expect this hand to get stubborn and call turn from time to time}
total of 22 combos
grand total of 54 combos
So, worst case scenario he will call his maybes every time:
EV(shove 60.4) = (22/54)*(80.26) - (9/54)*(60.4) - (14/54)*(60.4) - (9/54)*(60.4) = -3.09bb
And, best case scenario he will fold his maybes every time:
EV(shove 60.4) = (22/54)*(80.26) - (9/54)*(60.4) - (14/54)*(60.4) + (9/54)*(80.26) = 20.35bb
how often does he need to fold his maybes?
0 = (22/54)*(80.26) - (9/54)*(60.4) - (14/54)*(60.4) + (9*x/54)*(80.26) - (9*(1-x)/54)*(60.4), x = 13.2%
So this seems definitely like a spot where you should be bluffing quite a bit. The question is what are the best hands to choose for this bluff?
As you said, blocking KQ is pretty bad. It seems quite clear to me that your best bluff by far is JT with no club. This blocks almost none of his always folding range but much of his AJ/AT that is almost certainly calling. A lot of people 3-bet JTo with high frequency in SB vs BU, but I'm not sure how often you have that hand.
JT with one or two clubs is still quite reasonable for bluffing, probably better than 87 on the river, and DEFINITELY better than 87 if you consider the compound turn-river play. 87 is a horrific semibluff on the turn, as it draws to a bluff catcher, and betting the turn strengthens his range to such a degree that I'm almost certain you wouldn't be able to c/c a river 7. The only function betting turn has with 87 is that you block A7/77, and in a GT sense you fold out lower equity hands that would make you fold your best hand, such as KJ/KT. You also fold out chop sevens and 88-JJ which may have peeled the flop.
I think all your low club hands such as 5c4c 8c6c etc are reasonable bluffs on the river. Not quite as good as 87, but they had much higher EV building the pot up to this point. Not only do you need to justify betting river with 87, you need to own the turn play as well.
Anyway, sorry about the epic-length post. I'm okay with the flop cbet. I think there are some runouts that will be very profitable for your hand, but I think the board pairing turn is a pretty thick give-up. It is possible that without betting hands like 87, you will not have enough bluffs, but I am not so sure. You have KT/KJ and high clubs that make leveraged turn bets but give up on the river, and you have JT and low clubs to follow up on that leverage. Remember that his indifferent bluff catchers will block half of your value range, so its pretty easy to bluff too much even when you have all the big Ax to bet.
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