Nash Equilibrium charts

[plexiq]

SAGE is a simplification of the NE. It gives up some edge, but is much easier to memorize.

[ger664]

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ger : it's heads up. It has nothing to do with ICM.

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Yeah my bad not reading OP correctly.

[Fightins11]

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Important:
Only the *smaller* players stack is relevant.



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does this chart only apply when your opponent's stack is the smaller stack or does it always apply?

[plexiq]

It always applies. But you always look up the smaller stack in the chart, the bigger stack is irrelevant.

[jukofyork]

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@Yuk:
Didnt calculate the max. EV we give up when simply pushing these 3 suited cons. I'll try later and let you know. One thing i also want to check is how much edge the NE has against a player using the SAGE system.

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Could you modify your algorithm so as to make each player attempt to minimize the EV of the pusher? In other words: find the equilibrium pushing range vs dedicated spite callers?

Obviously for the HU situation then minimizing your opponent's EV will yield the same strategy as trying to maximize your own and when you are pushing into multiple players some very strange strategies might emerge, but it would be especially interesting for SB vs BB situations to see which pushes are "unspitable" (as opposed to "unexploitable").

Juk [img]/images/graemlins/smile.gif[/img]

[IFoldPktOnes]

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Could you modify your algorithm so as to make each player attempt to minimize the EV of the pusher? In other words: find the equilibrium pushing range vs dedicated spite callers?

Obviously for the HU situation then minimizing your opponent's EV will yield the same strategy as trying to maximize your own and when you are pushing into multiple players some very strange strategies might emerge, but it would be especially interesting for SB vs BB situations to see which pushes are "unspitable" (as opposed to "unexploitable").

Juk [img]/images/graemlins/smile.gif[/img]

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That sounds like a good idea. The ranges from early position probably wouldn't be much use but the late position ranges would be interesting. I like the term "unspitable" as well since using the word "unexploitable" for everything can get confusing.

[plexiq]

Interesting idea, and would not be much of a change to the implementation. I'll look into this once i have some extra spare time [img]/images/graemlins/smile.gif[/img]

[Tuvey]

Are the calling ranges for opponents who are using the shove ranges in the upper chart?
Can these same ranges can be used in bvb in mtt where icm is not a factor?

[plexiq]

Basically, the calling ranges can be used no matter what the pushing ranges are. The "chart-callers" EV will be minimized if the pusher is shoving w/ the upper chart. So, if the pusher deviates from the chart, your EV will increase. (And the other way around, the "chart-pushers" EV will be minimized if the caller calls w/ the lower chart.)

But keep in mind that exploiting weak opponents will have better EV than playing the NE.

The charts can be used in MTTs BvB situations if chipEV~$EV. (e.g. if the payout structure is very top heavy and/or you are still far from the money.)

[jukofyork]

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Interesting idea, and would not be much of a change to the implementation. I'll look into this once i have some extra spare time [img]/images/graemlins/smile.gif[/img]

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Cool! It'll be interesting too see what it comes up with.

Juk [img]/images/graemlins/smile.gif[/img]