I broke this down into 4 groupings of hands just because I was curious. The 4th is basically irrelevant because it's significantly discounted b/c of turn action.
Combonator Output combonator.com
Board: As Kh 8s Jh Ac
Vs Hero Cards: Ks Js
Combinations in complete range: 117 [Hero Eq: 29.06%]
Grouped: 117 combos, 100.0% [Hero Eq: 29.06%]
Ungrouped: 0 combos, 0.0% [Hero Eq: 0.0%]
Group 1: 40 combos, 34.2% (34.2% total) [Hero Eq: 0.00%]
Group 2: 20 combos, 17.1% (17.1% total) [Hero Eq: 30.00%]
Group 3: 28 combos, 23.9% (23.9% total) [Hero Eq: 100.00%]
Group 4: 29 combos, 24.8% (24.8% total) [Hero Eq: 0.00%]
Group 1: Trips only, added A8s, A8o, removed A9s
AQs, ATs, A8s-A2s, AQo, ATo-A8o
Group 2: Second pair, added KQs, KQo
Group 3: Third pair+, added TT, Qh9h, Qs9s, T9s
QQ, TT, QJs, Q9s (2), QJo, JTs, T9s
Group 4: Manual selection
KK+, JJ, AKs, AJs, A9s, AKo, AJo, QTs, QTo
If we check-call, we need him to be bluffing about 10.8% of the time. This is slightly complicated because he can bluff with a hand that chops with ours (or pips us), but since so much of his "bluffing" handrange is made hands, he may not be capable of bluffing here a ton. I'm going to assume that he's going to check-back with KQ and KJ-KT most of the time, and that he won't bluff super often.
40 ways we lose 1BB (Ax, A8) = (40BB)
8 ways we lose 1BB (KQ) = 8BB x 20% = (1.6BB)
28 ways we win 9.25BB (QQ/QJ/JTs/TT/T9s/Q9s) = 259 * 10% = 25.9BB
12 ways we win 4.625BB (KT-KJ) = 55.5BB x 20% = 11BB
It's been a while since I've done this, so I'd definitely appreciate someone double checking. Specifically of note are when we win half the pot (or the whole pot), I can't remember if you're supposed to include your bet in the total calculation - since we're weighing it against the 1BB we spend in the other calcs I think you're supposed to, but can't remember for sure.
Anyway, with those assumptions, we lose about 4.7BB over 88 hands. If there's any chance he doesn't 3-bet the turn with 88, JJ, KK, AJ, or AK, it's looking even worse for us, because we need to add them to his value betting range. If we can narrow down his Ax range a bit more on the turn, however, it becomes a little closer, and if he is good enough to turn made hands into a bluff frequently, it's going to get closer and closer to breakeven.
This one is a bit easier, I think.
Let's assume he calls with QQ, QJo+, 80% of the time and KTs+ 90% of the time. I removed JTs and TT just to be fair to the fact that he won't always call with the bottom of his known range given how strong your hand looks. I'm just weighting this because I don't have a certainty that he always calls or always folds the second-pair-ish range of his hands.
We lose 1BB 40 ways from Ax = (40BB)
With KQ, we lose another 1BB * 8 ways * .9 = (7.2BB).
With QQ/QJ+, we win 1BB * 14 ways * .8 = 11.2BB.
With KT-KJ, we win 4.625BB * 12 ways * .1 = 5.5BB.
With KQ, we win 9.25BB * 8 ways * .1 = 7.4BB.
Total, we lose 23.1BB over 74 hands, for a loss of about (.31BB/hand).
The more I look at it the less gross a check-fold feels. We need him to be willing to fold KT+ a LOT (30%) for this to be a good bet.
Of course, this is all just a model and I'm sure lots of my assumptions could be way off. I mostly posted this to get people talking more about what we expect him to do with various parts of his range (and how likely he is to have that range, given previous streets). If you're betting, why? If you're check-folding, why?