Collusive Entanglement

[Zeno]

A thought experiment for a three-handed hold’em game:

X, Y, and Z have equal stacks, limit game.

You are Z.

Give X & Y various degrees of skill level and playing style (graded say between 1 (novice) through 10 (expert)).

At what degree of skill level would you start looking at your cards in order to beat the game?

At what level are you, Mr. Z, guaranteed a wining strategy?


Now progressively add players A, B, and C with the same various degrees of skill and style. At what opponent skill level do you start looking at your cards in order to beat the game?

Does the above thought experiment seem silly?

-Zeno

[Ikke]

I don't have a clue how your rating system will work in Hold'em. If with a novice (1) you mean incredibly weak tight and fold every hand then, no, I don't have to look at my cards. If he plays in such way that he will call any bet till showdown with any hand, then, yes, I have to look at my hand.

Also, I'm not sure you can be sure about a guaranteed winning strategy. That was my whole question about the existince of an optimal play. And, due to the possibility of entanglement, it might be so that 2 individuale inferior strategies might beat "a higher rated" strategy.

At first sight I just don't see how with this thought experiment I can find the answer to my questions. The experiment seems a bit flawed to me if you relate it to optimal strategy. Just like Achilles WILL eventually catch up with the turtle, Zeno. [img]/images/graemlins/wink.gif[/img]

Regards

[SA125]

As I'm sure you knew from reading my initail response, I'm not sure what the poker end of this post meant or setteled for me. But it looks like it's still up in the air for you too.

But as far as the Zep goes, that alone the post was worth it. The lights were beating down upon Jimmy's face as he played the 12 string in Kashmir. Then halfway thru the show they set up a few straight back wooden chairs, grabbed some small acoustics, a few beers and sang some songs.

SV reminds me of Robert in this thread when, after sitting down and taking a sip of beer he sang

"Ride a white mare in the footsteps of dawn
Tryin' to find a woman who's never, never, never been born."

Steve A.

[Sredni Vashtar]

[ QUOTE ]
What is your definition of an optimal strategy in a n-player game (n>2)? From your last sentence I gather that it is a non-exploitable strategy. You say it can't be beaten, even by entangled strategies. But doesn't the example given in Jerrod Ankenman's post just prove that even an "optimal" strategy can be beaten by entangled strategies (assuming what he says is correct; haven't verified it)?

If we are looking at HU games than it's pretty clear what the definition is of "optimal strategy". Trouble (at least for me) arises when it is applied to a multi-player game.


[/ QUOTE ]

Ikke, I was sloppy writing that post.I was thinking of the H2H definition of optimal. I am going to stay away from traditional game theory and stay within my own area where I know I am certain. I was defining, and still define that an optimal play would be one that you could employ, it wouldn't matter what your opponents did, and you could not lose. So due to collusiveness, you can't have a general all encompassing optimal strategy mulitway.

Ill make these statements with confidence:

In holdem, there can exist collusive entanglement to such a degree that the game is not worth playing while those conditions exist. This is rare.

It is not that rare in that hands will occasionally pop up that are CE and knowing this is an advantage.

You can beat holdem for a little more by understanding CE and by working it in your favor. At some point CE would just be plain old strategic entanglement. Good players already do this whether they realize it or not.

You can demonstrate the above using thought experiments and examples.

Thinking about this yourself will be more worthwhile then being spoon fed it.

I have four pints of Guiness that need to get drank.

I'll probably start some threads eventually and show how this works in practice. (Although there's plenty of info in this thread to come up with situations oneself.)

SV.


PS While I did not verify the Bill Chen proof, since I had come to a similar conclusion with my work , and Chen/Ankenman's previous work has been highly credible, I posted it without reservation.

[Zeno]

The rating (skill level) system is flawed but can be modified. But you have to start the race. I wanted to push out the turtle just to get someone off the starting line. Continual modification and change is a given.

[ QUOTE ]
Also, I'm not sure you can be sure about a guaranteed winning strategy. That was my whole question about the existince of an optimal play.

[/ QUOTE ]

That's why I wanted to dream up something.

From Mr. Ferret’s last post:


[ QUOTE ]
I was defining, and still define that an optimal play would be one that you could employ, it wouldn't matter what your opponents did, and you could not lose. So due to collusiveness, you can't have a general all encompassing optimal strategy mulitway.


[/ QUOTE ]

See - Achilles can't catch up or overtake the turtle. [img]/images/graemlins/smirk.gif[/img]

This is all getting to me - I wanted to quite thinking about poker and then Mr. Ferret has to start something interesting and I am over here babbling.

-Zeno

[turnipmonster]

I must be a tad confused then. it seems to me like in the cases presented thus far, what may be a higher EV strategy (i.e. 3 betting a weak tight button in the SB) may not be the best strategy because the BB is loose and may call, foiling our plan.

I can't think of any cases where this would have a profound impact when you are last to act. like. in phat mack's example he cannot call UTG's open with impunity because someone may raise behind him, allowing UTG to reraise. if phat mack is closing the action this problem goes away, i.e. he gets his price to see the flop.

obviously these two cases don't encompass CE which is much more general, but all the cases thus far (even jerrod's) have involved poor relative position.

--turnipmonster