Ok, here it is:

As hero is committing himself to play with his stack in every flop, there are two possible outcomes. Either villain folds the flop or not.

Let's look at the EV when villain folds the flop:

Hero is 4betting with 32 more, and he is going to win a pot of 72. So the EV is +$40.

That was easy.

The trickier part is to determine

a) how often the villain hits the board

b) what is his average equity when he hits

In order to play with his stack villain needs 32% equity on flop (pot odds). Now as we know both player's ranges, we can use propokertools to calculate it. You can play with that PQL stuff, but the easier way is to use Oracle. Here is the thing.

To get top 25% range, we simply type 25%. To exclude aces, we add ! AA** (these commands/syntax can be found at the website). So villain's range is 25% ! AA**. Hero's range was AA**.

That shows how easy it is to calculate that for 35% equity. In Oracle you can't calculate for 32%, so I clicked on that "show PQL", copied the text, pasted it to PQL section in propokertools.com and changed the value to 32.

It gives the answer, 44,5% of time.

**So now we know that hero will win the pot on flop 55,5% of times. 44,5% of times villain will call the shove.**
Now villain will not have 32% equity on flop usually. He has a lot more. So we need to figure out what would be his average equity, when he hits the flop for at least that 32% equity.

Sounds complicated, but with Oracle and propokertools it's pretty simple.

Again we have to copy that PQL commands to

http://www.propokertools.com/pql and see what the result is.

The result is average equity of 58%.

**So now we know that those times that hero is called on flop, he has 42% equity.**
Now we need to calculate hero's EV for those situations. Hero 4bets preflop 32, and 64 on flop to win a pot of 200. Now hero's equity share of that pot is 200 x 42% which is 84. Hero bets 96 to win 84. EV is actually -$12.

So here is the conclusion:

55,5% of times hero's EV is +$40.

44,5% of times hero's EV is -$12.

**That gives the total EV of +$16,9.**
**Now is this important at all?**
Well, in my opinion it is. Lots of players are wondering in 3bet/4bet pots what to do. Yeah, it is easy to play that QJT9ds when someone 4bets, but what about some more marginal spots? What is the needed SPR to justify a call with KKQT?

When player calculates that stuff himself, he begins to understand how the game works. Like in this, how many of you would have thought that to 4bet aces that way is actually just +17bb in the long run. I am sure that most of you thought that it would make bigger winnings in the long run. Now comes the question, why are we 4betting aces and risk our stack for such a small winnings? I know it, do you?

**Should I be able to do all this kungfu in the middle of the hand?**
Well, if you can it would be awesome. Although I don't think there are many people in the world who can do it. Let alone some of those freaks would actually play poker. But if you roll these situations and numbers around for a while, you will begin to understand how different hands work in different situations. And how the stack sizes affect the outcome etc. It's like with pot odds and equities. They seem superhard in the beginning. I struggled 6 months with simple pot odds and equities. I tried to learn it from the books, and they all explained it with mathematical terms and formulas. And I thought that I would never understand them. But now, couple of years later, they just pop to my head. Don't even need to calculate and think them that much in most common situations.

Same thing here. When you do the calculations for different types of hands, you will realize what hands are better in calling and what hands should be folded. And you will see what the SPR should be for certain types of hands to justify preflop call etc.

And last, but not least. This is pure and boring math. Even if you calculate this sh*t for years, you won't be a good poker player. Sit&go's, tournaments and shallow holdem are coming to a point where it is all about math. 1 table sit&go's are pure math for serious players. They just tune their ranges against other regulars all day long, to get that tiny edge. Like one German pro, he used to play for 3 hours a day and use 6 hours a day to study other players and adjust his ranges. In my mind that is sick stuff.

PLO is such a game that it won't be mathematically "cracked". So many variables that it's very hard to play game theory optimal in plo. So it's a lot more than math. But still, the game is purely based on math. Even your reads, intuition, feng shui and stuff has mathematical value in your head. When you think "hmm, is he bluffing or not" your mind is comparing the odds in your head. You might just not know it. So the more you understand about math, the better foundation you have.

I mean, there are winning players in PLO1K that don't really know the math behind situation described here. I have seen them wondering "that guy 4bet me, he has aces. Hmm... Should I call with this hand or not? I don't know if it's profitable or not, maybe I should learn it someday". And this is true story. There are very talented players, who might be even better if they learned the basic math stuff needed in PLO.

UGH.

P.S. Another way to get the average equity for villain is to use the graphs in propokertools. But that's too complicated for me