[quote]

*Originally posted by VorpalF2F*
**Part 1:**
In the article "

*Mathematical Concepts for No-Limit Holdem (3)*" is the following:

As bluffs and semi-bluffs play an important role in this article, it is important to introduce the possibility of an opponent's fold to the EV calculation. This formula:

*EV = Equity * (Win + Investment) - Investment*

will not be sufficient. There is no variable for an opponent's fold in this formula. We therefore need a more general formula to calculate the EV:

*EV = Pfold * Pot + (1 - Pfold) * (Equity * (Win + Investment) - Investment)*

The **probability that you win the pot is Pfold**; if you don't win the pot immediately we use the EV. **Pfold is the probability that your opponent will fold**. Under the assumption Equity = 0 the formula can be simplified to this:

*EV=Pfold * Pot - (1 - Pfold) * Investment*

Loss in this case is your continuation bet. This is the case for all pure bluffs. Given the definition of a pure bluff, you can only win if your opponent gives up.

Both bolded parts seem like they are saying the same thing, they just worded it kind of weird which makes it a little confusing. If your opponent folds then your equity does not matter because the hand is over, but if your opponent does not fold then you need to calculate equity since it is very rare that you are getting your money in drawing dead, and this part of the equation accounts for the times that you suck out on your opponent.

For part 2, what exactly do you mean by bluff raise? My interpretation is that you want to bluff raise a continuation bet or something of that nature.

So lets just do a quick example and show how I would calculate this. I am going to make the assumption that your raise is a pure bluff and that your equity is 0.

Since equity does not matter, the best equation to use is

*EV=Pfold * Pot - (1 - Pfold) * Investment* and we are going to let

x = Pfold just so it looks a little nicer.

So if the pot is 6bbs, and your opponent cbets 5bbs and you raise to 15bbs the eqaution looks like this

Ev = 0 Pot = 11 Investment = 15 Pfold =x

0 = 11*x - (1-x)(15)

0 = 11x - (15-15x)

0 =11x -15 +15x

15 = 26x

(15/26) = x = 0.5769 = 57.69% = Pfold

So in this example you would need your opponent to fold 57.69% of the time for your bluff raise to be break even. Considering your hand probably has some equity, this is most likely a high estimate but trying to calculate your equity when it is not an all-in situation is rather difficult. If you had a flush draw with 9 outs, you would have about 36% equity IF you got to see the river, but only about a 18% equity to improve by next card. And then you can always try to bluff the turn again so the calculation gets even more complex.