What is "Nash equilibrium" as it relates to NLHE?

[_D&L_]

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In poker, my own calcs is that a nash eq. will beat virtually all of the opposing strategy space; your chance of playing by luck a non-nash strategy that breaks even is virtual zero.


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that last comment is especially stupid, most everyone out there is playing non nash poker trying to exploit the other players' weaknesses rather than trying to play unexploitably

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I typed a response...but i deleted it - no point. Think i'm gonna take another break from these forums. To many monkeys running around throwing feces. I'll try to discuss gametheory, bots, etc., somewhere where the dialog and intelligence is a bit more evolved.

[indianaV8]

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In poker, my own calcs is that a nash eq. will beat virtually all of the opposing strategy space; your chance of playing by luck a non-nash strategy that breaks even is virtual zero.


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that last comment is especially stupid, most everyone out there is playing non nash poker trying to exploit the other players' weaknesses rather than trying to play unexploitably

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I typed a response...but i deleted it - no point. Think i'm gonna take another break from these forums. To many monkeys running around throwing feces. I'll try to discuss gametheory, bots, etc., somewhere where the dialog and intelligence is a bit more evolved.

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1. Often people will disagree or offend you to extract more info. If you make a claim like the one above but say "i have the calcs but will not show them or make further proofs etc" people will at least try to provoke you on that.

2. Why would you join a thread like this (see OP)? To help people. And you response was quite helpful! But when you help people in such posts don't expect to reach the bottom of the rocket science. If you see a good spot for that - take it but don't complain.

3. Don't take a long break but drop for a day or so, skip some threads and join later on (that's what I do) and if I rejoin later usually the posters changed (so same old trolls are again good! ;-)

4. Look at my last response. Do you agree that playing exploitive (in poker not in roshambo) in some cases (in REALLITY) is actually better than playin NE, although NE could be good enough against most popular strategies?

[jstill]

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In poker, my own calcs is that a nash eq. will beat virtually all of the opposing strategy space; your chance of playing by luck a non-nash strategy that breaks even is virtual zero.


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that last comment is especially stupid, most everyone out there is playing non nash poker trying to exploit the other players' weaknesses rather than trying to play unexploitably

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I typed a response...but i deleted it - no point. Think i'm gonna take another break from these forums. To many monkeys running around throwing feces. I'll try to discuss gametheory, bots, etc., somewhere where the dialog and intelligence is a bit more evolved.

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dude whats ur problem? relax a bit dont attach personal sentiment to every post, if someone disagrees with something u said , dont get distraught its inevitable... in fact if noone counters any point u make on a strategy/theory forum thats when theres no point in posting there and exemplifies that there are no intelligent monkeys (even if throwing feces) worth corresponding with...

secondly there is a very good chance I am smarter than you by all quantitative measures IQ, SAT, GRE, AP exams ect and theres almost no chance even 1% of the pop understands stuff like game theory and statistics to the level I do since its my life in grad school (economics, econometrics ect)however that doesnt mean I know even close to everything about poker so Im always up for hearing diametrically opposed opinions

Thirdly back up that above statement: "In poker, my own calcs is that a nash eq. will beat virtually all of the opposing strategy space; your chance of playing by luck a non-nash strategy that breaks even is virtual zero."

unless I misinterpreted it, that above statement is not even close to true, every winner isnt playing nash poker (even right out of the gate with no info about a player) and saying u cant win without it is not even close to true and the fact is if u think u play nash eq poker all the time u probably dont really understand the concept...

and yes obvi i wont a rebuttle if im wrong id like to be corrected, this forum is for discussion (debate) dont be so sensitive we re all wrong and dont agree all the time its not a big deal

[_D&L_]

Your right - i did let it get to me too much.

But its tiring to be attacked as "especially stupid" for points that I never made. I admit you probably have a good share of intelligence, but for you its like testosterone. Your eager to make arguments where they don't exist.

So lets see, what's wrong with my comment that a poker Nash EQ beats virtually all opposing strategy space, as opposed to a Rock-Paper-Scissor Nash EQ which can't even earn a profit versus any other strategy? There's nothing wrong with that point. It goes to the question asked - what is a Nash EQ? Well some are weak, some are strong, and some are inbetween.

Yet, you go ad hominem and then start arguing that a Nash EQ is not an optimal strategy versus a flawed opponent who we have the know-how to exploit. I agree...if you know your opponent is going to play rock, play paper. If you know the magic buttons to press to make your opponent play what you want him to, more power to you. But that was never my point, and of course u know that.

Here's something we can disagree on though. I get the impression u don't think there's much value to knowing how to play a Nash EQ. All u and i can do is speculate as to its value since no one's solved it. I've only solved bits and pieces of it. But what I have solved for - the strategies for information masking, exploiting assymetric infomation, etc, allows for much more aggressive play while increasing EV.

Thats a tough strategy to beat, to force your opponent to play with more of his stack and with a losing strategy. Sure, if your opponent plays imperfectly - and you know what aspects of his game he's imperfect on - you can deviate from the Nash EQ for a greater profit. But usually you know at best only a few chinks in your opponents armor. E.g. weak on the flop, fails to defend big pots, etc.

The same algorithms used for a Nash EQ can be used to play an adjusted Nash (my madeup term) - that is one that deviates to try to take advantage of a known weakness (e.g. weak on the flop), then plays perfect thereafter (e.g. when your opponent calls on the flop).

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...I am smarter than you by all quantitative measures IQ, SAT, GRE, AP exams

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Is that so? I like the confidence, if you start doing serious work on this maybe we could work together as long as your ego doesn't object. j/k. P.s. The best you could have done is tie me on the math and analytical. And my background does, like u, include graduate economics (taken as an undergrad) - though i went into law.

----_Dirty & Litigious_----

[jogsxyz]

Pretty sure no one knows the Nash EQ for 10-hand hold'em.
Haven't even seen anyone publish the Nash EQ for a
one street 3-handed game.

[Hielko]

A Nash EQ doesn't exist for 3 handed games because of the possible implicit collusion.

Also, position does matter. The EV of the guy that opens is less then the EV of the player that has position. The only reason that the EV is equal or greater then 0 is the fact that the EV of the blinds is less then 0.

[curious123]

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A Nash EQ doesn't exist for 3 handed games because of the possible implicit collusion.

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Yeah, it's no surprise John missed this, as we know he was a complete wackjob.

[rufus]

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A Nash EQ doesn't exist for 3 handed games because of the possible implicit collusion.

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Nash equilibria exist for all finite games with finite players.
So, for 3 player hold-em there are strategies for each of the players so that no player can improve his or her expected return by unilaterally changing strategies. However, it's possible that two players who collude can as a team, have a better expectation than the sum of their individual expectations.

[Paxinor]

nash equilibria can be broken through implicit collusion meaning people colluding unintentionally that is true.

but it can only be broken to a certain extend (depends on the game) and it will only be broken if players are NOT trying to maximize their EV... meaning that if everybody plays optimal, there is a nash equilibrium and important: implicit collusion to an extend that the optimal strategy is -EV there has to be a lot of implicit collusion meaning players using very extreme and exploitable strategies...

i have no proof for that, but if you don't create extreme samples its almost not possible that the calculated nash equilibrium turns into negative EV because of implicit collusion...

so implicit collusion is really not a big deal... again no proof just experience...

[jogsxyz]

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A Nash EQ doesn't exist for 3 handed games because of the possible implicit collusion.

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Nash equilibria exist for all finite games with finite players.
So, for 3 player hold-em there are strategies for each of the players so that no player can improve his or her expected return by unilaterally changing strategies. However, it's possible that two players who collude can as a team, have a better expectation than the sum of their individual expectations.

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I'm not convinced this 1949 proof is valid for dynamic multi-street poker games. Every example shown is a one street static payoff game. In poker there is more than one street. Also the payoffs change with every street in an unpredictable manner.