Collusive Entanglement

[tpj]

I was wondering, how much more important does position become in the case where you know your opponents are colluding (at different levels)?

tpj

[Sredni Vashtar]

Zeno wrote, "Poker is an ephemeral mosaic and so is thinking about it." Which is a good quote to begin this post [img]/images/graemlins/smile.gif[/img]


Some closing thoughts:


Thanks everybody for your civil contributions. This thread is an example of how you can have exchanges, disagreements, clarifications, and various Zep lines without name calling and sarcasm. (Though I called Ikke a scoundrel in PM) [img]/images/graemlins/wink.gif[/img]

I also apologize to not have followed up on this thread as much as I could have.

Sredni Vashtar posted, "Using simulations and thought experiments as well as empirical data, it has become quite clear to me that there are sometimes situation in shorthanded *limit* play where if certain combinations of patterns continue to play out, it is difficult if not impossible to beat over the long run. In spite of the fact the opponents seem to have flawed strategies."

Tommy Angelo responded,

"This is either way over my head, or wrong, or applies only online."

And it does seem wrong, somehow, don't it?

Through the wonderful medium of internet, I received an email from a sometimes poker confidant, telling me that those game theory guys have already proven this sort of thing in a toy game. So off Sredni went spending about 8 hours, which seem like 8 score, searching Jerrod Ankenman's posts on rec.gambling poker. Still reeling from homogenous (or some such thing) equations, I failed to find anything matching this, though i got a thorough dose of game theory which was good for me. Luckily, an email arrived from Jerrod himself with this link, not exactly a proof in itself, just a reference to a proof.

http://groups.google.ca/groups?hl=en...gambling.poker


Quoting from the above post:

"
Here's a game theory example that takes the form of your "simplified
betting and calling rules, etc," but clearly has analogies in the real
poker world (credit to Bill Chen):

The following game is played by three players, a rock, a hero, and a
maniac. They play the game three-handed; the rock sits to the hero's
left, and the maniac to the hero's right. They each ante one unit.
They are each dealt one card from a large deck that contains about 18%
aces and the rest deuces. After they receive their cards, there is a
round of betting, where any player may bet a fixed amount of 3 units,
and the other players may fold or call at their option. After the
round of betting, all hands that have not folded are shown. All aces
split the pot. If there are no aces, then all deuces split the pot. It
can be shown that if the maniac will always bet, and the rock will
only call with an ace, that the hero is -EV in this game, no matter
what strategy he chooses. This is a pretty important result, as we
have here an example of a completely "fair" game, where the hero knows
every parameter of the game and exactly what his opponents' strategies
are, but cannot win or even break-even, despite the fact that both his
opponents are making serious mistakes in the game.

Consider the implications that might transfer from this to your
favorite poker game.

Jerrod Ankenman"


Now, to be realistic and practical, it really doesn't matter all that much to poker players whether a situation is completely unbeatable or just barely beatable. Either situation is something you would normally would like to evade if possible.

The concept of collusive entanglement is closely related to something similar I call strategic entanglement (which is more akin to what Tommy refers to as "playing good"). We use the opponents tendencies, possible future actions, and everything else, to try to forge a strategy. It doesn't really matter for practical reasons where the line between collusive and strategic is, except for academic reasons. It's like chasing a feather in the wind.


Of the posters to respond, one was from "raisins". Pretty good 2nd post, says the ferret. I hope no one ever drags up my 2nd post. Hate to think how discombobulated that was.

raisins wrote, "I agree with Ikke that an exploitative strategy is vulnerable to the collection of strategies possessed by your opponents. The solution to this is as Tommy Angelo says, play good. If you have maniacs behind you in the no limit example then that exploitative strategy is closed off...(snip)..I'm curious if it is possible for collusive entanglement to work against you if you are not using an exploitative strategy in the hand."

Well, if you are not using an exploitive strategy, what are you using? Your play, if not optimal, is either exploitive or exploitable, isn't it? And if it's optimal, then by definition, you can't be beaten by collusive entanglement or any other fair strategy.


raisins also adds some other thoughts, some of which were addressed above, and some which I am getting to right now.

Another concise question, tommy writes (responding to the still hung over Ikke, "I agree with every phrase of your paragraph. Driven by greed and laziness, I'd like to fastforward to the business end of this topic."

Tommy is getting too old for foreplay. He wants immediate carnal entanglement.

Tommy must realize though, that the theoretical side of this is rather fundamental to understanding how to work into a day to day strategy. And many of the posters here are still having some issues.

Three other points:

A)Like any other general theory, the examples are going to be (or seem) to be debateable. So going into that will require whole new threads, which will be rather time consuming.

B)Most of the thought experiments (and finally real hands) revolve around examining how you would be colluded against, and in order to delve into CE, I would have to in effect give collusion strategy. This is an ethical problem.

C)I'm already bored with it [img]/images/graemlins/frown.gif[/img]


Again, thanks..I'll leave you with one of my favorite quotes, that, hmmm, actually does sorta apply here


:Anyone who is not shocked by quantum theory has not understood it."
Niels Bohr (1885 - 1962)


Sredni Vashtar....a fool in the rain.

[Sredni Vashtar]

PM,
I don't think you are more likely to be entangled in short than full poker, just that those situations will repeat themselves over and over. Taking a non CE example, imagine you don't play well out of the big blind. won't hurt you much full. Short, you are doomed.

SV.

[Sredni Vashtar]

[ QUOTE ]
I was wondering, how much more important does position become in the case where you know your opponents are colluding (at different levels)?

tpj

[/ QUOTE ]

Very, you should usually be at another table [img]/images/graemlins/smile.gif[/img].

To answer generally, you don't want to be in the blinds when their at their peak collusion positions (late position). But there really isn't a good answer, the reason I use the term "entanglement" is because it's entanglment. Andy will like that.

SV

[zac777]

This thread reminds me of another I saw recently that involved a concept called Parrondo's Paradox. Maybe someone more knowledgable of the subject than I can assess whether there's any relation:

In the paradox, two -EV games with a direct interaction, when played alternately, produce a rachet effect that results in a +EV game. Maybe this is a "reverse ratchet" in which each player represents a +EV game individually, but the players combine to produce a -EV game collectively?

I guess that's not an especially interesting observation in itself, since it doesn't shed much light on the details of the interaction, but I thought I'd throw it out there.

Quick PP explanation

Cheers,
Zac

[Ikke]

[ QUOTE ]
raisins wrote, "I agree with Ikke that an exploitative strategy is vulnerable to the collection of strategies possessed by your opponents. The solution to this is as Tommy Angelo says, play good. If you have maniacs behind you in the no limit example then that exploitative strategy is closed off...(snip)..I'm curious if it is possible for collusive entanglement to work against you if you are not using an exploitative strategy
in the hand."

Well, if you are not using an exploitive strategy, what are you using? Your play, if not optimal, is either exploitive or exploitable, isn't it? And if it's optimal, then by definition, you can't be beaten by collusive entanglement or any other fair strategy.


[/ 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.

A few questions, because I can't figure them out myself:

-What is your definition of "optimal strategy" in a n-player game with n>2?

-Can you prove, by that definition of optimal strategy, that there exists such a strategy in a n-player game?

I could be that these question are quite stupid, but every thought I have these last two days leads at some point to a contradiction. So everyone that can give some thoughts on these questions, please do so.

Regards

[Ikke]

[ QUOTE ]
Do you think this is an effective strategy to adopt in the situation you described?

[/ QUOTE ]

Yes. But your making assumptions about the BB postflop style. What if I alter it a bit and say he's very loose aggressive (but thinking) on the flop as well? Now your "delayed isolation" doesn't work that well anymore. There likely is a counterstrategy to the example I gave. But that's a different subject.

[ QUOTE ]
More generally, do you think collusive entanglemet can be overcome (or even itself exploited) by recognizing and accounting for the effect that it will have on your general default strategies in dealing with each of your opponents individually, and coming up with a new strategy that either minimizes the effect of the entanglement, or operates in such a way as to exploit the tendencies of both opponents, even if those tendencies tend to work together and hurt you in a more general sense?



[/ QUOTE ]

In a lot of situations recognizing how different strategies influence eachother is a large part of solving the problem. But I'm not sure if it always can be done. Quite frankly, I believe there are situations which you can't overcome. And I found Jerrod Ankermans post a hint in that direction.

[ QUOTE ]
Also, in response to your response:
**I think collusive entaglement can often be overcome in cash-game situations, but maybe not so much in tournament/satellite situations. Do you agree?**

[/ QUOTE ]

Not really. I think in both game forms entanglement can occur which hurts you. But I really wouldn't know if these situation arise more in tournaments or cash games.

Regards

[Ikke]

[ QUOTE ]
In what way would a deep and rich understanding of CE affect my actual betting decisions in shorthanded games to increase my profit? In other words, can there exist specific or general plays that I now make, that before CE would have been judged by an expert panel to be correct, that now, because of the existence of the understanding of CE, would be judged incorrect?


[/ QUOTE ]

Without the existence of the understanding of CE you're missing a parameter that could influence your betting decision. If a play is judged by "an expert panel" to be correct without the knowledge of CE, then it could be that this judgement was based on a misrepresentation of the actual situation.

So yes, I do think an understanding of CE might earn you some money. I don't know how big the impact of this understanding is however.

Regards

[turnipmonster]

[ QUOTE ]
Without the existence of the understanding of CE you're missing a parameter that could influence your betting decision.

[/ QUOTE ]

this struck me as funny, as CE itself is about missing a parameter that is crucial to your decision (i.e. the action of the player next to act).

are there cases of CE that don't depend on position? I can't think of any.

--turnipmonster

[Ikke]

I'm not sure if I understand what you're saying and what's funny, but the action of the player next to act isn't IMO a parameter of the understanding of CE. Whether entanglement occurs will ofcourse be dependent on the actions of the players, but that is kinda irrelevant to your initial decision making process.
What is relevant to your betting decision is how the strategies of players (whether they are yet to act or not) might entangle and the possibility of this happening.

Regards