Okay here we go. Dude's got like $2 behind so if you decide to play you'll be spending another $3.20 or so to win about $7.30 since he's not folding. That's like 2:1, so let's decide if we have 33% equity here.

First, let's understand how we fare against the most probable hands. Thinking in terms of equity stops any need to think about redraws, so here we go. Against an ace or a queen with no K, we're drawing to 11 outs twice, so we have about 44% (against AQ that would drop us to like 40%, but that's not going to happen often). Against the bare K with no ace or queen, we're dodging 11 outs twice (8 clubs and three kings), so we're about 56%. Against an ace or queen with the K, we're fucked at about 7-8% or so. Finally, against a set we're around 30-32% (a number I just *know*).

So he 3-bet us preflop, which could probably indicate JJ+, AK, and maybe AQ. He raises our flop lead, which drops his range to something like AK, AQ, AA, QQ, 88, KK. This is how I would think about it using the idea I outlined in this post.

There are nine combos of AK w/o the K and three that have the K; so that's 4 for us, 5 for him and then another 3 for him.

There are nine combos of AQ and suits don't matter. I think AQ is less likely, so I'm going to discount this to 3 for him.

There are three combinations of AA/QQ/88 each for a total of nine. I don't think we're seeing 88 very often here, so I'll discount this to six total with about 2 for us and 4 for him.

There are three combinations of KK, so we'll give us 2 and him 1.

This brings us to a total of 8 for us and 16 for him, or dead on about 33%.

PokerStove agrees with our evaluation against this range:
equity win tie pots won pots tied
Hand 0: 32.828% 32.83% 00.00% 9750 0.00 { JcJs }
Hand 1: 67.172% 67.17% 00.00% 19950 0.00 { AA, KcKd, KcKh, KcKs, QQ, AQs+, AQo+ }
So it really comes down to reads, if you want to fold in marginal spots, and if the range we put villain on is a good one. All of these are really skills that are outside of the scope of this post in a lot of ways.


Edit: The point I forgot to make was that most of the time you can make a normal calculation based on your own outs and then adjust for redraws by raising or lowering that percentage a few points for whatever is necessary. If you play around with PokerStove you can get a feel for this fairly quickly. Backdoor flush draws, for example, usually give about 3-4% equity to the person that has it.