Stakes: $2/$4 online private club

Hero (BB): $517
Villain (HJ): $490

I'll skip the reads because I'm going to assign a range to villain at the end of the post, and my question is how to determine what my turn line should be based on such a range.

Preflop
Villain (HJ) opens to $12
Folds to SB
SB (huge aggro fish) flats
Hero has AK and 3bets to $38
Villain (HJ) & SB both call

Flop (Pot: $114)
JK5
SB checks, Hero bet $90, Villain snap calls, SB folds

Turn (Pot: $294, effective stacks $340)
JK5 6
Hero ??????


My read has villain's range at the following. Let's just assume this is true:
AKs,KTs+,QTs,AKo,KJo+,QQ-JJ,55,AdQd,AdJd,AdTd,Ad9d,Ad8d,QdJd

Given this range, how do I evaluate what my turn line should look like?

This is a very complicated question but I'll give it a shot.

First of all, review the purposes of betting:
1) To get more money in the pot when you are ahead.
Are you ahead? Yes, right now you are ahead of 11 hands, losing to 4 and tied with a 2.
2) To offer opponents insufficient odds to draw.
3) To get opponents to fold.

I doubt that any of the hands you describe are going to fold, but maybe. I probably wouldn't fold them. At least we could offer them insufficient odds.

AKs, AKo - tied. (BTW, I think he would have raised w that hand).
KJs/o and JJ and 55 = losing.
(When we are talking about these suited hands, I assume we are talking diamonds.)
KQs - he's drawing to 12 outs (9d and 3Q)
KTs - he's drawing to 12 outs (9d and 3T)
QTs - he's drawing to 17 outs (9d and 2 Aces [you have 1] and 3 9's)
QQ - he's drawing to 2 outs (2Q)
AQs - he's drawing to 13 outs (9d+4T)
AJs - he's drawing to 11 outs (9d and 2J)
ATs-A8s - they are drawing at 9 diamonds.
QJs - he's drawing to 11 outs 9d+2J.

Only the Queens might/should fold.
So, I think they can all reasonably draw if they are offered odds even as low as 4-1 actual odds, a couple of them can draw with 3-1 odds.
They will probably all be thinking of their implied odds, of course, $$$, so they will probably draw with odds as low as 2-1.

Therefore, if you are going to bet, what are you going to bet? Even a pot sized bet offers them 2-1 odds.
If you bet 1/2 pot, then you offer 3-1.

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Maybe you should shove all in to deny them odds. Of course then you lose the whole stack when you are up against KJs or one of those hands that beat you and also when your opp outdraws you.

But, shoving may also get some folds. If I were your opponent I would probably fold all of the 9 out draws and many if not most of the other draws.

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Since your question asked about math, I'll stop here. But there is also poker psychology and pot commit stuff to talk consider.

I would also point out that for me at least, this sort of thinking is almost impossible to do at the poker table in real time (especially online of course. haha).

I hope that there are no glaring errors in what I said and that you find it helpful.

GL out there.

Magnum