Hello sir,


I 'm new in the nash equilibrium chart theory.......


SIt and go example
NL HU blinds $100/$200

SB: $2800
BB: $13000

SB: J5suited
BB: ?
I see for example J5suited is 14.7

So let's presume I have about $2800 chips
If i understood well I can push my J5suited in the SB and if the BB has K7suited he could call.
Am i right?
What i did do for this?
I went to the callers charts and found a calling range of 15.2 and saw K7suited?




Did i understand this right?
And if i'm wrong where did i go wrong?
Are the numbers in the chart of the caller in accordance with the pushersstack ?





thx sir/and ladys





Always believe in the beauty of your dreams

Yes it seems like you're right.

The calling range for the big blind with an effective stack of 14 big blinds is:

a-3o+,a2s+,k8o+,k-6s+,q-10o+,q-9s+,j10s,22+

Are you referring to the chart from the Mathematics of Poker?

Could someone copy this chart here, because it may be of great use in 7BB-15BB situations where SAGE doesn't say anything.

That seems a whole lot looser than sage, and I don't think calling 14bbs with k7 is optimal (not to mention shoving them with J5s).

i think thats the one ....from a certain brian A.


Im still ok with that but on the chart they say that is ok to push with A7suited with 20+

Now my question is .....?
Can be this really profitable?
Even with Aces by the way......
I can push more than 20 blinds with pocket ducks

really?

Sorry this can be al stupid questions?
but you can see i'm new.....




Always believe in the beauty of your dreams

I'm ok with sejje by the way that this can't be so profitable
It says that you can push more than 20 blinds with pocket 2???????

CAN THIS BE










tHX FOR the answers
You can see i don't understand




Always believe in the beauty of your dreams

It is game theory optimal if the small blind uses a raise or fold strategy otb. It is not maximally optimal against a player who is deviating from game theory strategy.

It is interesting to note that pocket 2's should be jamming even with a stack of 50 big blinds and that you should be willing to defend with an effective stack of 15.1 big blinds.

See this wonderful post.

http://forumserver.twoplustwo.com/sh...d.php?t=138668

A raise or fold, or a shove or fold?


Anyway, even if the guy is shoving or folding, I doubt it's optimal unless the opponent is shoving every profitable hand.

I'm never calling 15 (or even 4) bbs with J5.

I'm sure there's something I'm missing, and I'm sure it's one of those clever little games that has some optimum strategy that is almost useless and can only very loosely be correlated to real life. I think this should be mentioned to OP by someone who knows it to be the truth (I could say it but can't back it up with anything).

Here's what I can say: OP: calling 50bbs with 22 is very bad poker. Calling 15bbs with J5 is extremely bad poker--J5 is an underdog to a random hand, if I'm not mistaken.

Whatever Steve Nash is to basketball, the Nash Equilibrium theory is the opposite for real HU poker.

Hey sejje i do understand what Jay is meaning.
THis is optimum shoving and calling .
Now from there on .....if im not wrong

If Jay knows i can shove with J5suited he only has to look at the chart and can call me with slightly better hand.

Jay am i near the answer?


Sejje: It's shoving with pocket 2. Calling is not profitable!!


Always believe in the beauty of your dreams

The small blind is using a LOSING strategy if he adopts a shove or fold otb with a stack of 7 big blinds or more . It is only accurate when the effective stack after the blinds have been taken is 6 big blinds or less. Read the bottom of this post.

http://www.cardplayer.com/magazine/article/15250

If he's only shoving or folding otb, then you may use the recommendations given in the chart for a Nash optimal solution. If he's raising, limping or shoving, then it is no longer game theory optimal to be calling with pocket 2's with 15.1 big blinds. At this point, you may need to use your best judgment for what hands to call with as it is not clear how to proceed using game theory. If you're otb,then you do better by varying your game when your stack is not so shallow which may include mini-raising, limping, shoving, etc.

By the way, shoving with pocket 2's with 50 big blinds is right if there is a RESTRICTION to shove or fold otb. It is NOT recommended that you do this because you can do MUCH better than this by not restricting your choices to shoving and folding otb.

Wow even people who take the time to register and post on poker strategy boards think nash equilibrium is a theoretical thing not relating to real headsup poker? The games will never dry up .

there is no such thing as maximally optimal.

what you mean is there are more effective, exploitative strategies against most opponents bc they dont shove or call nearly as light.

all that the nash equilibrium strategy does is creates a range of hands to shove and call with at various blind levels where no deviation from exactly the strategy they suggest can unilaterally improve your EV against a person who knew exactly what you were doing.

as in, presuming your only choices were shove or fold, if you told someone that your shoving range was exactly what is prescribed by the nash-equlibrium for that stack size before each hand you had on the button, they could do no better than to use the nash-equilibrium calling range. and vice versa.

Please educate me, I'm only a graduate Mathematics and Economics student.

a short idea of how the nash-equilibrium would develop

say im playing an opponent in a husng w 15bb effective stacks where we can only shove or fold from the button and call or fold from the bb. say this opponent shoves the button with only aces and calls shoves in the bb with only aces. my strategy would obviously be to jam 100% of buttons and call out of the bb with only AA.

my opponent realizes he can unilaterally improve his strategy by starting to shove and call with 99, TT, JJ, QQ, AK and AQ. as a result, i realize i can now unilaterally improve by expanding my calling range and (although it might still be right to jam 100% of buttons, i dont feel like running the math) reducing my 100% button shoving range. this system of back and forth adjustments, strategies and counter strategies, eventually would result in both people employing the exact strategy suggested by the nash equilibrium, bc at that point, nothing either of them could do would unilaterally improve their EV.

so obviously if you're playing some idiot nit who only calls shoves with 5bb stacks with like A2+, K9+, 22+, you dont use the shoving range assigned by the nash equilibrium bc you can profitably shove more hands.

um. optimal and what i think you mean by maximally optimal are different things. but the term optimal already implies that it's "maximally" optimal. it's a weird sort of redundancy that ends up confusing the meaning of optimal

any time someone employs a non GTO strategy, the most profitable strategy is exploitative in some way. we're just disagreeing on terms.

maximally exploitative strategies are not "optimal" strategies in the rigorous meaning of the term we're using here.
edit: google "maximally optimal" and tell me how long it takes you before you find the two words directly next to each other. it took me under a page to find a link to something called "optimal player vs. maximal player."

Good, I'm glad you understand now.

jay shark,
i have little doubt you know a lot more math and econ than i do, but appealing to the fact that you're a grad student doesnt change the fact that what you said was confusing. especially since it seems like most of the people posting in this thread dont really understand what the nash equilibrium strategy is doing.

terms are very important when their contextual meaning is different from their use in casual conversation.

i could say something like "optimal strategy isnt optimal against this opponent" and im sure you know what i mean, but that might confuse people who dont understand the significant difference between the definition im using in the first optimal vs the definition in the second.

What JayShark said was not confusing at all. I think that you are confusing what Optimal means. Optimal means as close to break/even as possible, whether you are winning or losing. In GT, if one player is playing optimal (unexploitable), then he will be guaranteed a long-term result. Any less than that is not maximally optimal. In other words, he is moving his edge further away from break/even, whether that is more winning or more losing, that subject is moot.

You seem to be on the right thinking track. If you understand what optimal strategy is, then you know will have a greater understanding of how to exploit mistake. Now you are playing an exploitive strategy.

However, exploitive strategies are exploitable. But in GT land, that deviation from optimal (0 sum) is also exploitable.

To make the example clear:

Say you are facing a shove on the river with the following:

Hero hold AK

Board: KK789

Lets say you are getting 2-1 on your call.

Optimal calling would be that if you know your opponent is bluffing 66% of the time here, then you call. This is a neutral EV situation.

Exploitive is the following:

Your opponent is obviously a bluff monkey. You call because you figure he is bluffing enough that this call is +EV.

Your oppoent is a rock, who has never bet on the river. You fold because there is little chance that you will see a profit on the call.

Inversely, if you are a bad player, then you are either calling too much against the rock, or folding too much against the monkey. And on an on goes the logic loop.

Nash is unexploitable and only optimal vs. someone else playing an unexploitable strategy. ./thread

I wrote that in another post may be it helps...don't know...it's not very clear but I put it here anyways:

I think that it might be a common misunderstanding amongst some 2+2er.
As I understand it, the Nash Push fold tables have been designed to be un-exploitable meaning that villain can not improve his EV by playing differently from the optimal play but this does NOT mean that you will gain EV if he deviates from his un-exploitable play! If he deviates from the un-exploitable play you are probably costing yourself money by not also deviating, meaning that you could get a better EV gain by doing something else that sticking to the un-exploitable strategy.

Or that:
With an-exploitable play your opponent cannot improve his EV but that doesn't mean you can't improve yours

take it for FWIW

+1

For instance if your opponent only calls with AA and nothing else you would be really stupid to follow the unexploitable (nash) play. Even if it is unexploitable! You would cost yourself money...

That's not true. It's a zero sum game, thus if villain's ev is +2 (magic units for the sake of conversation), your ev is -2, and vica versa. If you play unexploitably, your ev will be at the least 0. However, if you keep playing unexploitable and he deviates from the optimal counterstrategy, by definition his EV will drop, hence yours will go up.

This is fairly obvious when you have the SB and act first since an unexploitable strategy is easy to compose. When he has the SB, it's trickier. I'm not entirely sure if playing the Nash on BB is in fact exploitable or not. Obviously mixing limps and minraises might confuse villain and create a greater edge in conditions where villain has incomplete knowledge of your actual strategy, but this is dependant on being able to create a superior exploitative strategy.

I think you have a good point and I must admit I was wondering about two facts:
1.there is only two players and
2.it's a zero sum game.

But then I have a problem explaining my exemple with the player calling with AA and only AA in the BB. Surely I would have a better EV shoving every hands than following the unexploitable strategy?? Can you help??

This is just not hard. Nash is the equilibrium.

If they call wider than nash you shove tighter than it. If they call tighter than nash you shove wider than it. If they shove wider than nash you call wider than it. If they shove tighter than nash you call tighter than it.

You still need to know nash, it's like learning to walk before you learn to run.

As Elmeri has pointed out it's a zero sum game therefore in a nash equilibrium if vilain deviates your EV increases because his diminishes. But if you start deviating too, your EV diminishes too and his increases. This is what I have a problem grasping in the case of my villain calling with AA only. If I understand Elmeri properly if villain calls only with AA His EV diminishes (because he deviates) and mine increases. But if I deviates and shove all hands my EV should decreased and his increase. I don't believe this is true but I believe Elmeri is right this is what confuses me.

And to answer OP, use the tables when you are down to 7-8 BB.