General Discussion Poker Forums

Of course there exists a Nash equilibrium for 6max poker. That's exactly what Nash's result proved.

The collusion argument doesn't make sense

wouldn't you have to calculate it again with a whole new set of assumptions against colluders?

edit: actually i dont think that makes sense lol

Of course there exists a Nash equilibrium for 6max poker. That's exactly what Nash's result proved.

The collusion argument doesn't make sense

I re-read chapter 29 in MoP. You are correct that if we allow mixed strategies, then every n-player game in which every player can choose from finitely many strategies admits at least one Nash equilibrium. So 6max poker does have (at least) one equillibria.

However my main point (allthough incorectly formulated), that there's no way to play in a 6max game that guarantees that u won't lose, is also valid! Because there is something called soft collusion that complicates things in a multiplayer game (and make Nash equllibria a poor solution concept for multiplayer games). So a computer can't solve a multiplayer game in a natural way.

I could try to expain more, but I feel I can't do better than MoP (actually I most certainly will do worse), so I suggst u study ch 29 on ur own! There are also a couple of examples that will help u understand it!

We already did this 8 months ago... This thread just started up all over again...

http://www.deucescracked.com/forums/4-General-Discussion/23003-How-long-will-poker-last-

Chaz this is sooo fun, we nits don't care !

In poker the objective for every player is to win as much money as possible and collusion is illegal; if you change that you're just talking about a whole different (Bayesian) game -- but not poker.

In poker the objective for every player is to win as much money as possible and collusion is illegal; if you change that you're just talking about a whole different (Bayesian) game -- but not poker.

Yes and no. It is illegial obv, but that's not relvant for mathematics. It presents a huge problem for a solver. Since soft collusion (when no information is exchanged) is not "illegal" in a game theory sense. It's possible that our opponents play this way by accident. And then we have to lose. So we can't play a mixed strategy that guarantee that we won't lose. If we are unlucky our opponents plays in a way that makes it impossible for us to win and this is still a Nash equillibria!

But I def think u should read it in MoP!

I don't think that's a Krantz quote

Funny you should mention this as he also mentions you in the same article.
Its the atricle he wrote for January's Bluff mag.
Titled 'The Professional'

Yes and no. It is illegial obv, but that's not relvant for mathematics. It presents a huge problem for a solver. Since soft collusion (when no information is exchanged) is not "illegal" in a game theory sense. It's possible that our opponents play this way by accident. And then we have to lose. So we can't play a mixed strategy that guarantee that we won't lose. If we are unlucky our opponents plays in a way that makes it impossible for us to win and this is still a Nash equillibria!

Well that just doesn't matter at all

Well that just doesn't matter at all

U are making so short answers so I'm not sure what u are not getting, so it's difficult to help.

Check the exampls in MoP (tell me if u don't have it I can try write something for u). If u still don't get it I could try to explain more, but it's difficult in print on a foreign language. But MoP ch 29!

Well that just doesn't matter at all

what matters is what will happen when you sit down and play the game. in an unmediated environment people could collude all day long and you need a strategy that works. i don't think anyone has denied that you'd have to solve a game with totally different assumptions have they?

@sushiglutton:

I get what you're saying and I did all along but it's just a moot point. There is a Nash equilibrium. Yeah you can play optimal and lose, but so what?

If you are referring to something I said earlier in response to someone asking what 'solving' poker means, then you should know that I was talking about headsup poker (note how I said 'opponent' and not 'opponents'). If you aren't, I just have no idea why you are bringing up this point.

we're just having a conversation...hielko said he didn't think there was a GTO multiway strategy and sushi expanded.

i don't think anyone has denied that you'd have to solve a game with totally different assumptions have they?

Yes I have ! Let's say ur 2 opponents randomly choses strategies from all possible (mixed) strategies. Then there's a chance >0 that u won't be able to win no matter what u do! Even if they do NOT cheat by exchanging information their strategies may fit eachother in a way that makes it impossible for u to win.

And this is still a Nash equillibria! There's an exmple in MoP!

Yes I have ! Let's say ur 2 opponents randomly choses strategies from all possible (mixed) strategies. Then there's a chance >0 that u won't be able to win no matter what u do! Even if they do NOT cheat by exchanging information their strategies may fit eachother in a way that makes it impossible for u to win.

And this is still a Nash equillibria! There's an exmple in MoP!

yeah i just meant to maximize your expectation, not to nec. make money

I don't get ur angry tone .

@sushiglutton:

I get what you're saying and I did all along but it's just a moot point. There is a Nash equilibrium. Yeah you can play optimal and lose, but so what?

Well it means that we can't define what a solution really is and that's super important. There are several equillibria, but the players have different EV in the different ones. So which equillibria is the solution? This means we can't solve 6max poker. And that is pretty imortant point considering what OP was asking?

what matters is what will happen when you sit down and play the game. in an unmediated environment people could collude all day long and you need a strategy that works. i don't think anyone has denied that you'd have to solve a game with totally different assumptions have they?

It would be really complicated. You'd have to allow colluding (because a rule is irrelevant if people don't abide by it) and determine how exactly players can collude. In addition you'd have to sort of guess what their objectives are -- maximizing their own profit, maximizing the combined profit of themselves and their partner which they split afterwards, etc. It would be a whole nother kind of game.