AJo

Summary of the below:

Under certain assumptions (PS charts +your post):

1. Bet-fold turn with almost all 66,77. Check-fold turn with 88.
2. The villains turn raising range can best be "calculated" using Equilab.

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I don't know if there is a standard 3-betting range. Here, if you take the ps.com charts, you have

PS.com 3-betting vs HJ open: AA-66, A9s+, AT+, KQ, KQs. (113)

Assume you c-bet 100% on the flop. Assume too that you bet a pair of jacks with ace kicker or better for value (because that is what you did). Not at all sure I'd agree with this, but that is another matter.

Turn value range: TT+, AJ+, KQ (73)

Your value range is 66.6% = 73 combos of your total range. Your opponent is getting 6:1 to call on the turn -> 14% bluffs in total turn betting range for 1-street balance. Your bluffing range should be something like 12-13 combos. This should include both hands that you should fire again with on the river and hands that you fire only once with (at least in theory). On the river you will be giving your opponent 9:1 for a call. You need then (assuming he calls on turn) 7 bluff combos on the river. These 7 combos should be the rock bottom of your turn bluffing range.

Suggested turn bluff range with intention to bluff twice if called: 77 except 1 combo + A :heart:9 (6).

Six more bluffs needed on turn to stay 1-street balanced.

Suggested turn bluff range with intention to check river if called: 66 (6).

Resulting turn checking range: AT + 3 combos of A9s + 99 + 88 (28).

Of course, the river card will alter what is value and what is bluff, but that is a later problem.

You will be given 7:1 to call if you check on turn. You should fold some 14% according to 1-street balance. check-fold the 88, you will have 14% folds. Sure, you have equity with 88 for trips and straights, but that equity sucks versus his raising range. (The only problem is what to do with the left over 77 Fold it! Face it, this flop hit the opponents range hard.)

Now you get raised. You get 10:1 to call. Most people would say that you should fold 1:10 = 9.11% of your range. If you now fold all pocket pairs you bluffed with that will be 12 combos = 16%. Too much? No, not really, because your opponents raise cost him 2 bets, giving himself immediate odds of 9:2, so he needs this (from a 1-street perspective) to work 18.22% of the time.

Given the premises of the OP, and the assumptions that ps.com ranges are "standard" and that we bet jacks with A kicker (like OP) or better on turn for value, then a reasonable folding range when raised on the turn is 66+77. The single bluff combo A :heart:9 can be turned into a re-bluff.

This is fairly "balanced" given the premises. Also, the rest of your range has a bunch of outs to improve, so I see little else to fold turn with. But like I said, I'm not too sure AJ is a value bet on this board. Strictly speaking, it is not assuming that the opponent is playing according to the ps.com charts.

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To compute the villains turn raising range, you can use Equilab: Tools->Handrange Calculator. First chose a range for someone 3-betting preflop + firing twice on that board. Say then that you want 55% equity versus that range. Take the result and intersect it with your opening + call flop range.

Add to that a suitable number of bluffs. This is the tricky part because when raising, you are investing 2 bets and the opponent needs to call only 1 bet. This results in practice in that you raise too little GTO-wise (as a bluff), but this is compensated for by that the opponent is calling too much (most opponents see only the pot odds, not your investment). In effect, you exploit his calling tendencies by under-bluffing here.

It's pretty tough for UTG to have many semibluffs on this board since he mostly has got a pair himself and he should just raise with some single Ax flushdraw hands although i would not recommend that against some unknown guy as your 3bet range and bet flop + bet turn contains not a single hand thats going to fold on the Turn. 88 99 you should and you would check, same with small PP's like 66 77 etc. Hands you should be check/folding the Turn with so you always have a pair with Ax included.

This is also a hand you can check/call on the Turn, as well as you should check/call AT. AsYohan suggested, you may follow through for another 2 barells with 66 as your worst hand but on the lowstakes against unknown players, balancing is to be neglected over taking focus on exploitive play.

As played a Call is mandatory and you should just check/call the River or Checkraise. He may have K9s 89s AK or maybe QJ JT TT QQ etc. It's not terrible to donk out since he might be shy with valuebetting KQ AQ, though he shouldn't raise those hands on the Turn and also KK and AA, which most players on the lowstakes would valuebet once again. Since check/raise River and fold to a 3bet is no option for me against an unknown, i would probably just check/call.

You find this too weak, you'd assume he caps AK TT and QQ Preflop? Might be the case, might be not. We don't know.

Suggestions?

I obviously made a blunder when calculating EV for 88 I used the villain's turn raising range, not his bet when checked to range. If the villain is balanced, then 88 is a check-call, but marginally so (partly because the villain is balanced, and partly because hitting a 9 might be a disaster).

@firsttsunami
You wrote "...as your 3bet range and bet flop + bet turn contains not a single hand that's going to fold on the turn".

Wouldn't that be unbalanced?

If we actually have a bet-folding range on the turn, this would automatically exploit an opponent incorrectly assuming that we don't have such a range.

I'm not arguing, only asking

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If we check all pocket pairs, as you primarily suggest, then, (assuming ps.com ranges) we don't have a single bluff in our turn betting range. But here I'm not asking, just stating a fact ♦

EDIT: This is almost decidedly unbalanced. After all, the OP asked for balanced ranges. I can see that on this particular board we should cut down a bit on bluffing, but not all together. Also, if this happens to be correct, then there is something fundamentally wrong with our 3-betting range to begin with (ps.com chart).

you are right that gto-wise it might not be the correct play to just have strong hands in our betting range and never bet/fold and this would be the case if we'd check all PP's < TT. Of course you can construct a range , containing hands that we can bet/fold with on the Turn. Hands such as small pocketpairs or you might sometimes 3betting with 67 87 /suited in general to mix up your range with some connectors and deception hands.

A9 A8 you could also take intoaccount as semibluffing hands but not bet/folding hands. GTO-wise you should certainly have a hand like 66 and/or 77 in your Range but on these stakes i wouldt take gto plays too much into consideration since players don't think as reasonable and as analytic about range distribution and divide ranges and assign hands to its categories etc.

That doesn't mean that learning GTO and thinking about balancing isn'T a mistake or bad at all. It's necessary to get an idea where people have leaks and where they are unbalanced and where you can attack them but in an isolated manner i'd prefer to be unbalanced myself to play the max-ev play and not the most and best balanced play since most people don'T recognize and pay attention on it.