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HUSNG and Nash Equilibrium

What is Nash Equilibrium?

In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision. Likewise, a group of players is in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others. However, Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved; in many cases all the players might improve their payoffs if they could somehow agree on  strategies different from the Nash equilibrium (e.g., competing businesses forming a cartel in order to  increase their profits).

 

That's Fantastic, but how can it help my HUSNG game? 

Glad you asked. Basically it is a strategy that is used in a HUSNG game when the effective stacks are about 20bb or less. Forget the above crap and check out the following charts.

 

 

Pusher = you shove

Caller = you call after he shoves

 

Source of the above charts   | http://www.holdemresources.net/hr/sngs/hune.html |

 

Still Confused? Good, you should be.

When using the above charts some things to keep in mind are.

  • Nash is really going to be optimal vs a very good player who is also using Nash......supposedly
  • Probably should only be used around 10bb not 20bb.
  • Is player dependent. If you are up against someone who openshoves every hand or someone who only plays AA then the theory is out the window. These are obviously extreme cases but you get the idea.

Considering all of the above I think the best idea is to give a couple of examples.

Group 1 Examples

You are in the SB(in position). The blinds are 50/100 and the effective stacks are 800. (this means bb=8)

Note :All the following examples use the pusher chart.

(a) You are dealt

     

ACTION = Shove (as bb=8 and nash says push at 20+ bb)

(b) You are dealt

     

ACTION = Fold  (as bb=8 and nash says push at bb=3.7 or less)

(c) You are dealt

        

Marginal spot , Nash says you should shove if bb=7.9 but bb=8. Probably shove anyway depending on opponents tendencies.

 

Group 2 Example

You are in the BB(out of position). The blinds are 10/20 and the effective stacks are 500. (this means bb=25)

If bb=25 don't worry about Nash. You still need to play some real Poker.

 

Group3 Examples

You are in the BB(out of position). The blinds are 100/200 and the effective stacks are 1100. (this means bb=5.5)

Note : All the following examples use the caller chart.

(a) You are dealt 

              and the sb shoves!!!!

 

ACTION = Fold (as bb=5.5 and nash says call a shove at bb=3.7 or less.)

 

(b)  You are dealt

            and the sb shoves!!!!

ACTION = Call (as bb=5.5 and nash says call a shove at bb=8.4 or less.)

 

 

OK. I hope that helps but keep in mind that the above is only a guide but definitely a good guide for end-game HUSNG poker.

 

 

 


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