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

[eastbay]

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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.

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Confession: this took several evenings with a computer and the latest papers on computational AI to get the answer I arrived at.

I'm wondering if someone smarter than me can arrive at a similar answer in a more intuitive way.

I'm also not 100% sure my answer is correct, so if some other computer geek wants to duplicate it using the full blown analysis I did, that would be cool too. [img]/images/graemlins/wink.gif[/img]

eastbay

[Jman28]

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I'm wondering if someone smarter than me can arrive at a similar answer in a more intuitive way.

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Man, I gotta wake up tomorrow and go to a wedding. This sounds like a challenge though. Damnit. I may or may not try and figure this out tonight.

EDIT: 2k posts even. Hmm. Yay?

[eastbay]

[ QUOTE ]
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I'm wondering if someone smarter than me can arrive at a similar answer in a more intuitive way.

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Man, I gotta wake up tomorrow and go to a wedding. This sounds like a challenge though. Damnit. I may or may not try and figure this out tonight.

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Nothing personal. I just wonder if there's a hand-wavy way to get at the basic answer. There may not be, it may be intrinsically in the details. I'm not sure.

eastbay

[Deuce2High]

Eastbay, you are needed over here!

http://forumserver.twoplustwo.com/sh...;o=14&vc=1

Consider your time taken to answer that question my only customer service request as a proud customer of SnG-Analyzer!

[lorinda]

Please note that in my assumptions every % chance of winning a pot from 0.001 to 99.999 are possible. The fact that this is not the case WILL have a bearing on the results, but I have windows calculator as my only ally, so I am basically trying to just use logic here.

Fact 1: There is a point where the stacks are so small that we have an edge because we have more control over the game than our opponent.

I am happy that I have shown the above to be true.

Now I'm going to try to create another fact. (Assuming my logic in the first fact makes sense)

If we push less than half of the time, we cannot be favorite against someone who copies our strategy

We start with x chips each.
We push 50% of the time
Our opponent calls 50% of the time
Every time we fold, we lose 200 chips.
Every time we push and our opponent folds, we win 400 chips
Every time we push and our opponent calls, we break even.

Half of the time we lose 200 (-100 EV)
1/4 of the time we win 400 (+100 EV)
The rest of the time we break even (0 EV)

At this point, the game is even, so our opponent definitely has an effective counter to our play if we push 50% of the time or less.

Therefore, our next fact is "We must push over half of the time"

If we push 30% of the time, the house again just copies us.

We fold 70% and lose 200 (-140 EV)
We push and steal 21% and win 400 (+84 EV)
We push and get called 9% and break level (0 EV)

If we push 70% of the time and the house copies us..

We fold 30% and lose 200 (-60 EV)
We push and steal 21% and win 400 (+84EV)
We push and chop 49% and break level (0EV)

Clearly at this point, the house can no longer copy our play.

Lori

[lorinda]

If we push less than half of the time, we cannot be favorite against someone who copies our strategy

I believe that the above means that the bank can get away with calling at least 50% of the time.

Edit: I also feel that there are some dodgy concepts in what I have tried to show so far. I think I've got as far as I dare, and I'm not even sure these simple facts are right, and that's before even factoring in chips properly.

Maybe leaving up this route of thinking will help someone else attack the problem without computing it.


Lori

[Gigabet]

Intuition tells me 6000. I will give my reasoning after I find out if I am close to your answer or not.

[eastbay]

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Intuition tells me 6000. I will give my reasoning after I find out if I am close to your answer or not.

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Each player has 6k chips? Not terribly close.

eastbay

[microbet]

I'll just guess. 10.

If the stacks are too deep, your push or fold only strategy will be bad. If the stacks are very short, you will be pushing any two and they will be calling any two. (So, if there were no profitable stack size 1 BB would be optimal)

Edit: I mean 10 Big blinds.

[lorinda]

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Edit: I mean 10 Big blinds.

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I think this is still too large.

Edit: I think we're pushing a lot here and the BB is calling a lot. I can see that it's over the original 1100 or so that I thought in my first case, but I think we get to the heart of the main strategy pretty quickly when we get past the 23o=fold point.

I'm going for 2400 chips each.

Lori