If you hit the out, what % of time you win

[Luke Montgomery]

I have read a few of sklansky's books and have a quick question for anyone with a math head on their shoulders.

I understand you got outs and you have pots odds, and all the details/exceptions around it, but I was curious if there is a mathematical formula to help you determine what % of the time a hand rank will win a specific hand.

I mean, if I am figuring out my outs to see if I have pot odds to call, I need to be figuring out my outs to specific hand rank. So is there a formula (even if it's too complex to do in your head while at the table as I am just curious) that will show what % of the time a hand rank will win a specific situation hand.

Lets say I am holding Ks Qs:

Flop comes Ad Qh 4c

There are 6 people in the hand.
How do I calculate what % of the time I will win if the turn is the King for 2 pairs. Or if a Q comes of on the turn for 3 of a kind. Is there anyway to calculate or estimate the % of times I will win as oppose to lose when an out I want hits.

Luke

There isn't a formula. Each situation is far too specific with too many variables. The best you can do is estimate your opponent's likely hand range given the flop, which is mostly a matter of experience. The texture of the flop is enourmously important in this. For example,

A/images/graemlins/diamond.gif Q/images/graemlins/heart.gif 4/images/graemlins/club.gif is very different to
J/images/graemlins/diamond.gif Q/images/graemlins/heart.gif 4/images/graemlins/club.gif which is very different to
A/images/graemlins/diamond.gif Q/images/graemlins/heart.gif T/images/graemlins/club.gif which is very different to
A/images/graemlins/diamond.gif Q/images/graemlins/heart.gif J/images/graemlins/diamond.gif and so on

The number of people in the pot, the looseness of the table, whether it was raised preflop, and the flop action, all factor in here far more than any equation. You also have to factor in redraws for once you actually make your hand.

So you can see why there isn't a formula of any kind. You have to read the texture of the flop relative to your opponent's likely hand range. After a while you get a feel for what to draw to and what not to.

[Luke Montgomery]

Hi,

Thanks for your reply, that makes sense, I figured it was pretty difficult, but though I'd ask anyway.

How does PokerStove do all this then? does it use a formula/equation of some sort? Any ideas ?

It runs hundreds of millions of simulations each second. Take KQ vs AJ on AQ4 flop, it will run through every possible turn and river:

2c3c
2s3c
2d3c
....
9d 5s
9d 5h
....
AhAd

and add up the number of times each hand wins or loses. For preflop against a couple of random hands, this can be a trillion or more possiblities. The good thing about PokerStove is that it's optimized to eliminate certain cards which are blanks or equivalent, which makes it run much faster than traditional simulations. It still looks at billions of possibilities though.

[Luke Montgomery]

And yet, it really just shows the EV of the hand with a specific board and specific opponent (or randon opponent) hands. It doesn't really show the win % of a hand rank if you were to hit your outs for that rank.

Is there anyway to estimate or come up with anything remotely in the range of showing how strong your hand is.

Like if I was to write software to show how strong or weak your 3 of a kind is on the specific board, is there any formula you can think of that would at least give an idea of it. Maybe a formula which takes into consideration scare cards of higher ranks, etc..