Quote Originally Posted by acg123 View Post
first let me say, wow. lol I had to write it out on paper to fully understand what you were saying.
im still a little confused about why we are setting EV(3bet) to zero. what is that percentage? I mean I understand how why you need to know it to fully solve my original question, but what does that number represent? our break-even equity on the flop? our equity by the river? or is that how often I will win regardless of my holdings? thanks for taking the time to go through this with me btw.
EV(3-bet) is the expected value of your strategic option of 3-betting with a given hand. It is what you ultimately want to solve for. I set it equal to zero because I want to discover the minimum hand necessary for 3-betting here. Thus, I'll know that this hand and all stronger hands will be +EV to 3-bet.

You could set EV(3-bet) to any value you want and solve for R to find the minimum necessary postflop value (R value) hand to 3-bet and have an EV of at least that. This is sometimes useful, as in the case BB vs BU facing a raise you have a third option: you can call.

If you face a 4bb open BB vs BU, you have three EV values:

1) EV(3-bet to 12), the expected value of 3-betting your hand to 12bb
2) EV(fold pre), this is always zero.
3) EV(flat pre), this is the EV of flatting

In order to maximize your value, you're going to VPIP with all hands that have a EV(3-bet to 12) or EV(flat pre) of greater than zero. Additionally, you're going to 3-bet to 12 with all hands that have an EV(3-bet to 12) of greater than EV(flat pre) or EV(fold). This will typically have you 3-betting your strongest hands for value in addition to some marginal hands as semibluffs. The semibluffs will have a lower EV(flat pre) or might be minus EV to flat at all.

So really, instead of solving for EV(3-bet pre) = 0, you might want to solve for EV(3-bet pre) > EV(flat pre), but this gets complicated. I'd stick to using zero for a while until you get the hang of this.