Facing a tough, stubborn opponent. I have Jc-10c and have limped.
The flop is K-10-x with one club. It goes check-check.
The turn brings in the club flush draw.
The tough, stubborn (but not unaware) opponent bets $20 into an $18 pot.
I know she has a king with a decent kicker.

I can call, hope to hit the flush, J or 10 (13 outs?). She might pay off a middling value bet if I hit.
But ... Can I raise, say to $50 or $60.
She would have to think about what I have. I think she might fold say 25 percent of the time.
And if she calls I have my 25 percent equity or so on the river.
Thoughts?

Not the right area. Sent to beginners.

Simple math. LetÂ’s assume your estimate of fold equity and your river equity are right. If you raise you will win a $38 pot 1/4 of the time. 3/4 of the time your opponent will call. Of these times you win $88 1/4 of the time and lose $50 3/4 of the time. You therefore lose 3/4 x 3/4 = 9/16 of the time and win $88 3/16 of the time. Your EV for a raise is (1/4 x 38) + (3/16 x 88) - (9/16 x 50) which comes out to -$2.13. EV for the raise is negative so you should not raise.

Update - I originally used 25% as your river equity. It actually is 13/46 (assuming clean outs) which is more like 28%. A small difference but significant. If your 25-% fold equity is right then your EV is 1/4x38 + 3/4x(0.28x88 - 0.72x50) which comes out to +$0.98. A raise actually is profitable. Be careful though; it is close and a lower fold equity would probably push it back down to -EV.

This does not mean you should raise though. There are two reasons: calling might be better and raising gives your opponent the chance to reraise and kill your implied odds, likely forcing you to fold. Assuming she will not reraise consider a call. You win 28% of the time and lose 72%. You lose $20 on the call when you lose so that contributes -20 x 0.72 = -$14.40 to your EV. When you win you must win $x such that 0.28(x + 38) = 15.38 to make calling equal to raising. A little algebra gives x = $16.92. Therefore if your opponent will call for about $17 or more when you hit an out, you should call rather than raise.

Stremba took the math right out of my mouth.

I think there is a small issue with hero’s raise amount. Op wrote “Can I raise, say to $50 or $60.” I take that to mean the total amount hero has to invest is the 20 call plus a raise-of 30. In that case, the amount hero wins on the turn is 18+20+30 = 68 as opposed to the 88 Stremba used. This results in a turn EV of -3.22 which will not be a significant change.

I read it the same way as you; I just messed up and added the full 50 when villain calls instead of 30 more. It is close but it means folding beats raising, and if villain will not pay off when we hit an out then folding is correct

Fold. Assuming you have a good enough read to "know she has a king with a decent kicker" rather than knowing that is in the range of holdings she can have you should get much better spots to use that knowledge. Especially if knowing this is her holding you equally know her calling percentage is high enough so you shouldn't fire two bullets as she will call you down too often.

Preflop action is unclear. Position? Stack sizes? Did you limp in EP and did she raise?

Hard to discern how she'd respond to your turn raise without that info to put her on a range.

Would say, that in these spots in general, we should generally avoid raising, when we're quite sure our opponent likes their hand.
We generally have about 30% equity or so on the call, good thing is that the draw IS a backdoor, so we're more likely to get paid off. Also, how likely will it be that we can get paid off with a river bet ?