Poker math. AA vs KK HU. sbrugby hand

[pokerroomace]

http://www.cardrunners.com/fusetalk/...9834&catid=156

this is sbrugby's post:

Analysis of a hand
Yesterday I put in a late ngiht session after getting back from Vegas. I started off playing Ivey HU at 300/600 and did quite well. I ended up about 100K from Ivey if I recall correctly. It felt good to put in a win against him since my last three sessions had been losers against him. He always leaves after losing a big pot so once he dropped the 100 he left. I think this is a very good strategy for him and I admire his disipline to stick with it. I don't think it would be best for me, so I don't intent to implement it into my game, but it defenitly appears to work for him.

After playing Ivey I played some 100/200 plo on stars and played Gift of Gab at 150/300 deep table. I began to tilt and dropped all my prevous winnings. I was not playing my best and should have quit sooner. I ended the night on this hand which I thought about all day.

KK vs. AA (link: http://www.pokerhand.org/?1029172)

After the hand I was very angry at myself since I had been tilting he was playing very passively. I stormed off to take a shower and go to bed being mad because I "knew" he had aces. So all day I thought about the hand and once I cooled off I realized my push was closer than I thought. I intuitively knew that kings were extremely strong HU. Then I asked the question how deep would I have to make folding kings correct. I went through all the math and realized you have to be exteremly deep to fold KK HU. I won't bore you with it but its not even close at 300BB. I was shocked and realized the hand was just a cooler.

sbrugby is arguably the best online player in the world. how did he do the math for this?

[pocketfours]

sbrugby is arguably the best online player in the world. how did he do the math for this?

I'm a member at cardrunners so I posted this there:
http://www.cardrunners.com/fusetalk/...&enterthread=y

[moronest]

It would be good if your site allowed the forum to be viewed without having to pay.

Seems pointless putting the link here.

[pocketfours]

It would be good if your site allowed the forum to be viewed without having to pay.

Seems pointless putting the link here.

Sorry about that, I actually didn't know that the forum is for members only. Here is the post:

There are several ways to approach this problem, but one way to do it is to calculate if Brian committed himself to the pot when he raised to three times the big blind from the small blind.

In order to calculate if he was committed to the pot, we need to simplify the problem. We assume that after Brian made the initial raise, he showed villain his pocket kings and called in the dark. The correct play by villain now becomes to move all in with AA and fold everything else. If Brian still has a positive expectation we can conclude that he is committed.

We need to find out if Brian has a positive expectation even if he shows his hand and calls in the dark:

EV = P(fold)*EV(fold) + P(aa)*(P(win)*EV(win) - P(loose)*EV(loose)) > 0

EV = 0 gives:

P(fold)*EV(fold) + P(aa)*(P(win)*EV(win) - P(loose)*EV(loose)) = 0

Stack size = X

EV(win) = 3BB + X //The amount we win if our KK beats the aces

EV(loose) = X - 3BB //The amount we loose if the aces hold up

P(fold)*EV(fold) + P(aa)*(P(win)*(3BB + X) - P(loose)*(X - 3BB)) = 0

P(fold)*EV(fold) + P(aa)*P(win)*3BB + P(aa)*P(win)*X - P(aa)*P(loose)*X - P(aa)*P(loose)*3BB = 0

P(aa)*P(win)*X - P(aa)*P(loose)*X = P(aa)*P(loose)*3BB - P(aa)*P(win)*3BB - P(fold)*EV(fold)

X*(P(aa)*P(win) - P(aa)*P(loose)) = P(aa)*P(loose)*3BB - P(aa)*P(win)*3BB - P(fold)*EV(fold)

X = P(aa)*P(loose)*3BB - P(aa)*P(win)*3BB - P(fold)*EV(fold)) / (P(aa)*P(win) - P(aa)*P(loose))

X = P(aa)*P(loose)*3BB - P(aa)*P(win)*3BB - P(fold)*EV(fold)) / (P(aa)*P(win) - P(aa)*P(loose))

The probability that villain has AA:

P(aa) = 4!*48!/2!*50! = 0.004898
P(fold) = 1-P(aa) = 0.995102
EV(fold) = 1BB

The probability that KK beats AA is on average approximately (varies depending on suits):

P(win) = 0.18
P(loose) = 0.82

X = 0.004898*0.82*3BB - 0.004898*0.18*3BB - 0.995102*1BB) / (0.004898*0.18 - 0.004898*0.82)

X = -0.99373056 / -0.00313472 = 317.0BB

So if the stacks are less than 317.0 big blinds deep, we really cannot fold KK even if we show our hand to our opponent. Against an unknowing opponent, the stacks certainly need to be a lot deeper still. We can conclude (as Brian did) that he was pot committed and compliment him for a flawless play. A cooler, pure and simple.

[moronest]

Many thanks,

You are a gent.