Chris Ferguson (Game theory problem)

I recently read a book which had a game theory related problem originatly presentet by Chris Ferguson...

NL HE 1$/2$

Everyone folds to SB (50.000$) who makes it 5$ to go.
Before BB (50.000$) looks at his hand SB accidently reveals two black aces...

Well apparently game theory somehow dictates that BB can call with any hand and then bet any flop that gives a random hand 15% or higher of winning and the aces will have to fold...
If you know this problem and the reasoning behind the solution then plz try to explain it to me in a way I can understand [img]/images/graemlins/confused.gif[/img]

I think it would be because now that he knows you'll be making a move X% of the time and actually have a hand that beats him X% of the time (since he knows you have two red Aces), but whether he calls or folds doesn't change your EV from the hand and he can do nothing better than guess if you're ahead of him.

I'm not sure on how to do the math on this (even though I understand it as I read in TOP) but I believe the 15% is just the number thats needed so that he can bluff in such a way that makes what I stated above true (that mathmatically the SB can not change the BB's EV on the hand without a total guess)

[AaronBrown]

I have not seen this problem before, but it doesn't add up the way you describe it. I'm assuming you mean there is $10 in the pot preflop if BB calls, and SB and BB each have $50 left after the preflop betting.

If BB calls preflop and goes all in postflop, SB has to put up $50 to win $60. He'll do this if he thinks his chance of winning is $50/($50+$60) = 5/11 or better. He'll always better than 5/11 chance against a random hand. So if BB goes all-in all the time on any flop, SB calls him all the time. The worst flop for black AA is triple red suited connectors between 6 and 9, AA is 60% to win against a random hand. Even with a perfect flop, BB loses money with this strategy.

To make this work, BB must consider not only the chance of AA against a random hand, but the chance of AA against the hand BB actually holds. Let's say he goes all in on any hand for which he has a 30% chance of winning, and his average chance of winning on these hands is 46% (I just made these numbers up). If he does this, then SB will fold whenever he goes all in. So he makes $7 when this happens. If he folds with less than a 30% chance of winning, he loses $3 on those hands. If there is 1 of the first for two of the second (again, I made those numbers up), he has positive expected value in calling.

While it's possible to compute the numbrs in the last paragraph, you'd need a computer to go through all the calculations. It's not a simple game theory example. I think there must be something you left out.

It was Matt Matros's Book right? I don't remember the explanation exactly but I think it was included in the book.

It's actually a much simpler problem than it first appears. The answer is:you can call with any hand.
The reason?
Because after the flop, if you bet out at it, the guy with the Aces has to fold. He has no idea if you are bluffing or have the goods, whereas you have complete information. It's hard to play poker against someone who knows what cards you hold.

Tommi

[sweetjazz]

[ QUOTE ]
It's actually a much simpler problem than it first appears. The answer is:you can call with any hand.
The reason?
Because after the flop, if you bet out at it, the guy with the Aces has to fold. He has no idea if you are bluffing or have the goods, whereas you have complete information. It's hard to play poker against someone who knows what cards you hold.

Tommi

[/ QUOTE ]

It's not that simple. You have to use that the stacks are both $50,000, while the pot is only $10 (if BB calls).

The complete information is more valuable than the preflop nuts only because the stacks are deep enough.

Thank you all for the response!

[ QUOTE ]
I think it would be because now that he knows you'll be making a move X% of the time and actually have a hand that beats him X% of the time (since he knows you have two red Aces), but whether he calls or folds doesn't change your EV from the hand and he can do nothing better than guess if you're ahead of him.

I'm not sure on how to do the math on this (even though I understand it as I read in TOP) but I believe the 15% is just the number thats needed so that he can bluff in such a way that makes what I stated above true (that mathmatically the SB can not change the BB's EV on the hand without a total guess)

[/ QUOTE ]

Well I can follow this far, but I don´t see how it adds up to giving BB a positive EV... Or at least better than EV -2$ per hand. Otherwise it would be a better play to just fold preflop.

a 15% hand, (which a random hand according to the book should be) can make a large bet offering close to 1-1 odds for SB, a little less than 30% of the time, and that bet would, no matter what the choice, have EV 0 for both players.
Well what about the last 70%??? Somehow big bets on the later streets are part of the answer, but I don´t see how... [img]/images/graemlins/confused.gif[/img]

Question about the hypo- does the SB know that the BB saw his hand?

[housenuts]

i think there's some confusion. if they are left with $50,000 stacks, then he should fold because there's no sense in calling to win $10.
however if they only have $50 stacks, then $10 is a significant percentage of that so he should call.

If I'm the SB, and the stacks are both $50, I'm going all-in in the dark, on any flop.