Poker math question

[Python49]

I've never been too great at the mathematical aspect of the game but am looking to figure out something that may have a simple solution i'm overlooking.

I'm basically trying to figure out if a play is +EV or not given a certain range. The situation is:

A player that I know is capable of 3 betting a pretty decent range 3 bets from the big blind after I raise AQo from the button. I raise A [img]/images/graemlins/club.gif[/img]Q [img]/images/graemlins/diamond.gif[/img] to $18 pf and am 3 bet by villain to $50 straight.

I call the 3 bet intending to shove a good flop.

Flop($100): K [img]/images/graemlins/spade.gif[/img]2 [img]/images/graemlins/diamond.gif[/img]2 [img]/images/graemlins/heart.gif[/img]

He bets out $70 into the $100 pot and I move all in for a total of $338.

I realize that i'm risking $338 of mine to win $170 so I would need to win this 2/3 of the time to at least break even but i'm unsure how to figure out if this play is +EV using a pokerstove range of hands.

If I assume he folds out all hands but AA/KK/AK and his raising range is AA-88, AJo+, ATs+, KQ, suited connectors and occasional random steals... then how do I find out if i'm actually going to be winning this 66%+ of the time? Kind of confused on how to go about this.

[tarheeljks]

www.pokerstove.com

when he calls you are usually smoked, but you should have a good amount of FE, granted this is pretty spewy.

[jay_shark]

A)Fold equity : 179*x where x is the percentage of time he folds .

B)Calls and you win : 438*(1-x)*(0.33)

Use poker stove and it's easy to see you'll win close to 33% of the time against his range .

C)Calls and you lose : 338*(1-x)*(0.66)

We want A+B-C >=0

solve for x and we get 179x +146(1-x) - 225.33*(1-x) >=0
258.33x-79.33 >=0

x>=30.70%

So if villain folds more than 30.7% , then your play will show a profit .

[DarkMagus]

OP assumes that villian folds everything except AA,KK,AK on the flop, so we're almost never winning the pot when called.

I don't think pokerstove can really help you answer this. You'd need to manually tabulate the hands yourself.

There's 3 ways to deal AA, 3 KK, and 9 ways to deal AK, given the cards that we can already see.

For 88-JJ, there are 6 ways to deal each, for a total of 24. QQ has 3 ways to deal. AJ has 12 ways to deal, AQ has 9 ways to deal, ATs has 3 ways to deal, KQ has 9 ways to deal. Throw in maybe an extra 20 hands to account for random suited connectors and stuff.

So he calls 15 times and folds 80 times. Assuming both your reads are correct (his 3-bet range, and that he will fold KQ and worse) then this is a profitable bluff since he will be calling about 16% of the time.

[jay_shark]

Correct . You have to count manually all the hands that he would call you with give his range of cards , and then compare the new range with your hand using pokerstove .

In this case , you already know what x would be and you can compute your fold equity .

ie A) FE=179*65/80
B) 438*(15/80)*0.0175
C) 338*(15/80)*0.9825

It's easy to check that A+B-C is positive EV .

[Python49]

Makes sense, thanks guys!

[tarheeljks]

i don't think its reasonable to assume that he's folding kq here as your line looks to be fos. in fact you will probably get looked up by any K he 3bet w/unless he 3bets w/like K4suited. unless you have history that lets the opponent know you will shove w/ monsters on dry flops, you can also expect to get called by tons of pp's and you haven't even accounted for the times he shows up w/a random 2 (prob A2suited).

edit: i realize this was just a thought excercise, but its important to take into account how applicable this excercise is.