Difficult (I think) Q I posted over in the poker theory forum

[eastbay]

I'm not even sure I have the right answer, but I do have an answer.

NL, HU game theory Q

[lorinda]

My first instinct is that I feel like the house has the edge in this game as they have position ever hand. I want a decent size stack compared to the house and small compared to the blinds.

Lori

[lorinda]

Argh.

I think that if the blinds are small enough that the house has no other strategy than to call, then we can have an edge as we are the only ones who have a decision to make.

I'm going to guess that with equal stacks of around 500 chips each (or whatever the correct stack is to make folding 23o correct) then we can have an edge.

Lori

[lorinda]

My range of stacks where I believe I could have an edge is therefore <Whatever range is required so that the house always have to call if we play, but that we sometimes are able to fold>

Lori

[eastbay]

[ QUOTE ]
My range of stacks where I believe I could have an edge is therefore <Whatever range is required so that the house always have to call if we play, but that we sometimes are able to fold>

Lori

[/ QUOTE ]

Your intuition about wanting a stack which is some smallish multiple of the blinds is correct according to my solution.

However, in my solution, at the point where the game is a wash, both players have hands that they will play and pass on.

eastbay

[lorinda]

Please excuse the thinking out loud.

I believe it's possible to have bigger stacks than my initial range, but I'm not sure how to quantify that and suspect I will now be slowing down my post rate [img]/images/graemlins/wink.gif[/img]

Lori

[bawcerelli]

if the house is playing "ICM" perfect, how can you have an edge? seems like stack sizes and blinds don't matter other than affecting what's pushed. then again i'm probably missing something.

[lorinda]

That was my first thought, but if we have (and I'm not sure of the exact numbers) a 32% equity of winning with 23o, then with stacks of 550, 550 we are better off saving our 350 (to return 1100 which is only 31.4% I think).

However, even if BB knows we are only ever folding 23o, he should still call with everything.

We therefore have more control over the game than the BB, so logically we have an edge at that point.

At some point, the BB has more correct options than we do because he has enough chips and enough information to be able to do better things than us. There is a range however where we can remove all options from him (my above range) and there is another range where we can remove enough options from him that we still have an edge... that's the tough bit [img]/images/graemlins/frown.gif[/img]

Edit: Sigh... those numbers are backwards, you would need a hand that has 31.4% equity to push there, and you have 32% , so you would push. Please assume the stacks were 600 each there, so to push you would need a hand with 33% equity (400 to return 1200)

Lori

[eastbay]

[ QUOTE ]
if the house is playing "ICM" perfect, how can you have an edge? seems like stack sizes and blinds don't matter other than affecting what's pushed. then again i'm probably missing something.

[/ QUOTE ]

Note that the house doesn't know what strategy we're going to play, so the house chooses the strategy that minimizes our maximum edge we can get over all the strategies we could possibly play.

This is far different from guessing what strategy we might play, and trying to maximize its edge against us.

In other words, the house plays as defensively as possible.

eastbay

[Jman28]

This would take a lot of work to figure out. My intuition though is that there definitely is a stack size where the player has an edge.