The board was down last night, so this never got posted... here it is today, gotta run... let me know thoughts and where I'm sorely lacking...

22+, At, A6, A5, Kt : C-bet this flop to build pot
Ax, KJ, QJ: C-bet this flop probably 60% - 70% of the time

Ok, that was my answer from part #1, #2 above.

Let's see... now on to part# 3.
1. Are you vulnerable to a flop pot-sized raise against your flop c-betting range from Exercise 2 if Villain has KQ? Since I know he has KQ (your parameters to the question) I am only vulnerable if I hold QJ in my range so far. Even that hand has outs, but is currently beaten. Thus, if I KNOW he has KQ, no, I'm not very vulnerable. I don't know that this is what you were asking for though, as there isn't a lot of math present here. My impression is you want to know how many hands out of my range are already beat, vs. my odds of improving to be able to catch the lead in the hand...

2. Are you vulnerable to Villain calling the flop with KQ and betting 2/3 pot whenever you check the turn? Let's see, since I know villian has KQ and is c-betting with a non-made hand at this point, the same holds true for both question 1 and 2. No, not vulnerable unless I hold QJ.

3. What is your flop c-betting range trying to exploit in Villain's play? Well, the obvious answer is my c-betting range is trying to build value in pots where I'm currently ahead and also entice villian into continuing in the hand with a poor holding. Also, my c-bet if I'm holding air is to represent strength and force out a better hand... all standard C-bet answers which I don't think is what you are looking for here.

So I'm going to go back, re-read the questions again, see if I can figure out what math part we're talking about and how to apply it, and then hopefully, work hours permitting (lunch is over) figure it out... or figure it out tonight when I get home... either way, I'll check back in as soon as possible.[/quote]

Ok, I'm back... and with a little encouragement from Spoon, I'm going to try to figure this out in a logical fashion now.

From the first exercise I am c-betting nearly my entire range, for the sake of this exercise, let's say I'd c-bet everything but 22, 33, 44, A2 - A4. Thus in my original range of 22+, AXs, ATo+, KJ+, QJ, I have a total of 297 Hands, a pretty wide range here. Thus, my c-bet range consist of 66 Hands. This leaves me with 231 Hand combinations I'd continue with post flop, our of 297, which is 77% of my pre-flop range, which is about right for my original estimate of 80%.

Now back to the questions:
1. Are you vulnerable to a flop pot-sized raise against your flop c-betting range from Exercise 2? (I got focused on knowing the cards, and we assume he is fit/fold, so he has decent holdings). (Also, I read Spoons example reply to me, and I'm doing this not knowing what he holds). Now, we put in 5 into 7.5 bb, making it 12.5 bb. He has to call 5 bb then raise making it 22.5 as the correction point out. This is where I get lost in the math. It seems to me that a pot sized bet, would be 12.5 in the pot, 5 to call, making pot 17.5 and if he raises pot-size, it would be 35 in the pot. I'm fuzzy on that one, going to have to research it more.

Ok, using spoons numbers, pot is 12.5, he raises to 17.5 Spoon states:

He's betting 17.5bb when the pot is 12.5bb, so he would need us to fold about 58% for his bluff to be +EV, not counting his equity when we call. So let's see how often we're folding to a raise.

Which I am trying to figure out where the 58% comes from... 12.5/17.5 = 71%, 17.5/(17.5+12.5)=58% but why? so, let's just run with that... I have no idea why we use those numbers, and spoon wants honest opportunities to teach here, so I'm missing something basic. Anyway, villian needs me to fold 58% of the time. According to my figures above, and answers to exercise 2, I c-bet 80% of my hands, but I'd only continue further with a smaller range, 55, 66, TT, AT, JJ+, for a total of 45 hands now out of the original 297, for a percentage of 15%, making me vulnerable to his re-raise.

2. Are you vulnerable to Villain calling the flop with KQ and betting 2/3 pot whenever you check the turn?

Ok, so I'm checking only about 20% of the hands I opened that flop with, 22, 33, 44, A2-4, A7-9 (though not all of the time in this range, but for the sake of the exercise, let's run with it). This is 114/297 hands or about 38%. If I check, pot is to him at 7.5 bb, he bets 2/3 pot, or 5bb, thus pot is now 12bb. To figure out his percentage, I think you take 12.5/(12.5+5) = 71%. Thus he needs me to fold 71% of my range pre-flop to make this profitable. Since my pre-flop checking range is 38% (62% of hands I bet with) and he needs me to fold 71% of the time, (29% of my hands go check-fold) I am still somewhat vulnerable, though not completely.

3. What is your flop c-betting range trying to exploit in Villain's play?
My c-betting range is trying to exploit his fit/fold policy by forcing him to dump hands that have middle/bottom pairs, or miss the flop completely, regardless of what I hold. While vulnerable to his response, if BU has my range a bit tighter than I'm playing, he'll be more exploitable, feeling I hit. If he knows I'm loose, he has a better feeling I might be bluffing at the pot (which I am a lot of my range) and will continue.

(Note: many of the answers in this post are probably laden with errors, as I don't know a lot of the poker math. I am also pretty weak on strategy, so take that into account. Spoon is trying to teach us willing to learn players out here something valuable, and I thank him for it... even if I get totally lost in the process...