Hi again,
Bogdan, I have a really important question for you, and I can't sleep at night because of it 
It's just about the topic we discussed here, but it's from one of the articles. I thought that you are pretty much the only person that could clarify it to me, and this will be the thread that you are likely to see the fastest 
Instead of guessing what I don't understand, I'll just give you a quote. It's huge, I know, I'm sorry. I highlighted two numbers that I cannot understand. (link here, or see the quote below)
Spoiler
100BB Stacks
Preflop:
6 folds, CO raises 4BB, BU calls 4BB, 2 folds
Flop: 3 :spade:, 9 :club:, T 
(Pot 9.5BB)
CO bets 6BB
An obvious continuation bet. Most players will make this bet. The question is, whether it's exploitable or not. The answer is: it depends. Very often it is exploitable. A small calculation to illustrate the point: assume CO is more or less tight-aggressive and doesn't know the Button. His preflop range is likely to be something like this:
22+,A6s+,KTs+,Q9s+,J9s+,T9s,98s,87s,76s,65s,54s,ATo+,KTo+,QTo+,J9o+,T9o,98o,87o
This is roughly 25% of all hands and 334 hand combinations. Against a raise from BU, CO is likely to play top pair+ and strong straight draws (T9 – AT, JJ+, 33, 99, TT, QJ). That leaves us with 4*6 (pairs) + 4*12 (top pairs) + 6 (2 pairs) + 9 (sets) +16 (draws), which equals 103 possible combinations.
Now we need to determine the continuation betting range of the CO. For the given range that CO will stay in the hand with, this is the factor to determine whether or not you can exploit the continuation bet.
Assume BU raises 18BB. He is investing 18BB to win 15.5BB. According to the EV formula, he needs a fold roughly 54% of the time to make the bluff profitable. CO will continue to play with 103/334 = 30% of his preflop range.
If he bets more than 68% of his range, BU can make a 100% profitable raise regardless of what hand he has. It should be noted that the range that CO will continue to play against a raise is quite loose. Frequently this range will be tighter.
The range that CO raises preflop is quite tight and will frequently be looser. If CO were to open raise 30% and on the flop not to play all combinations of QJ and only continue with TPTK+, the result would be the following:
CO plays about 400 combinations preflop. Against a raise he might play 12x AT, 6x T9, 8x QJ, 9x sets, 4x6 overpairs = 59 combinations which equals 59/400 = 15% of his range. This would result in a continuation betting frequency of only 33%. In the first example, his range isn't as strong. Some opponents might bet 100% and become exploitable. However, in the second example it's much more obvious.
The situation isn't perfect but a frequency of 75%+ is no exception despite anything over 33% being immediately exploitable.
What I DO understand:
First example:
- CO's preflop range is 25%
- he will continue after a raise with 30% of his initial range
- BU needs to make CO fold in 54% of the cases for his raise to be profitable (raise-sizing dependent value)
Second example:
- CO's preflop range is 30%
- he will continue with 15%
It's all good, just what you told me. In the first case he will continue with 30% hands, thus our FE is 70%. In second example he will continue with 15% hands, thus our FE is 85%.
What I don't understand is the value of 68%+ for the first example, and the value of 33%+ for the second example. Apparently, it is the minimum value of CO's c-bet stat needed for BU's raise to be profitable. How this value was calculated, and how do we use it?
Finally, what this 75% value at the very end is all about?
Thanks so much. I wasted like the whole day reading this bit over and over again. I tried to do any possible mathematical action with these numbers. I already know it by heart....still I can't get these 68% and 33% 
PS: in the first sentence that I made bold, originally it was said that CO has a 100% profitable raise, not BU. I thought that it's a typo and corrected it.
A
7
(4 players)
