pushing/equilibrium problem

[ahmngrn30]

I've played almost 10k sitgnos and am still having problems with this. Every time I plug a hand like this into sngpt or sngwiz I get frustrated and don't come away with any conclusion on what my range should be.

Example:

Blinds: 100/200

BB: 1780
SB (you): 1760
BUTTON: 1855
CO: 1945
CO+1: 1570
CO+2: 4590

It folds to you in the SB. The BB is a great player that you've played with a lot before. Say your typical shoving range is 70%. He knows this so he's calling with 29.9%, but I now know that he knows this. so now I'm shoving 51.1% but now he knows that I know that he knows so now he's calling with 21%, but now I know..... etc,etc for infinity.

It obviously gets insanely more complicated when it's not just two players but I'll just start with the previous example.

[Slim Pickens]

Welcome to Root-Finding 102: [censored] That Doesn't Converge Easily. Sometimes it helps to actually start plotting out the pushing ranges vs calling ranges. SNGWhiz does this, doesn't it?

[fluorescenthippo]

so are you wondering how to find the NE? its pretty easy. just stick to one side like the pushing range. (and...i just realized that you must have an edge on which is why this problem is impossible for you)

anyways if you push70% he should call 25.8%. if he calls 25.8% you should push less. so try 65% in sngpt, then he should call 24.3%. if he calls like that you should push more than 65%. so we need to try a number between 65 and 70. so i think you messed up by having an edge on. but i could be wrong since im drinking beers and watching the brewers game [img]/images/graemlins/smile.gif[/img]. im ienjoymoney btw, good to see you posting finally.

[jonkeponke]

wouldn't this require a mixed strategy Nash Equilibrium, or am i just imaganing that? as you both continuously adjust your ranges, it never converges at a pure Shoving/Calling %. you'd have to start pushing 100% of your hands 50% of the time and 30% 50% of the time (made up numbers).

is that completely off-base for this question? it makes sense in my head, but i'm not sure how applicable it would actually be here.

[microbet]

I don't have any of those programs anymore or I'd do the numbers, but drunkenhippo (edit: and, of course, slim) is right. If you think 70% is about right, look at his calling ranges when you push like 80%, 75%, 70%, 65%, 60% or something and then do check it from his point of view with his appropriate calling ranges. You'll see at some point they will be close to matching up and you try the in between numbers. At some point you'll get really close to your push range giving you a calling range for him, such that his calling range indicates the push range you started with.

phew.

It gets screwy when you should push 100% and won't necessarily converge at all.

Jonke,

Interesting thought. Is it possible to find a mixed strategy that defeats a non-mixed Nash Eq. strategy? Seems like no. Seems like when you are not pushing hands in the non-mixed Nash Eq. range you are -EV and when you push hands outside of that range you are also -EV.

[Jago]

But when the villain sees you pushing wider than the equilibrium, they will start calling wider hence making your non-mixed NE range more +EV.

[microbet]

[ QUOTE ]
When the villain sees you pushing wider than the equilibrium, they will start calling wider hence making your non-mixed NE range more +EV.

[/ QUOTE ]

FYP?

[dafrk3in]

[ QUOTE ]
But when the villain sees you pushing wider than the equilibrium, they will start calling wider hence making your non-mixed NE range more +EV.

[/ QUOTE ]

however, there is a lag, because this is a game of incomplete information (villian does not know that hero is adjusting in the short run)

also, this means that there may be value in pushing with something near the bottom of the range (39o) in order to signal that you are pushing with a much wider range (ie push top 70% + 39o)

thoughts?

[ahmngrn30]

[ QUOTE ]
so are you wondering how to find the NE? its pretty easy. just stick to one side like the pushing range. (and...i just realized that you must have an edge on which is why this problem is impossible for you)

anyways if you push70% he should call 25.8%. if he calls 25.8% you should push less. so try 65% in sngpt, then he should call 24.3%. if he calls like that you should push more than 65%. so we need to try a number between 65 and 70. so i think you messed up by having an edge on. but i could be wrong since im drinking beers and watching the brewers game [img]/images/graemlins/smile.gif[/img]. im ienjoymoney btw, good to see you posting finally.

[/ QUOTE ]

Hey, yea I actually knew that somehow.. I'm on here pretty much every day. just don't post a lot

[ahmngrn30]

[ QUOTE ]
If you think 70% is about right, look at his calling ranges when you push like 80%, 75%, 70%, 65%, 60% or something and then do check it from his point of view with his appropriate calling ranges. You'll see at some point they ill be close to matching up and you try the in between numbers. At some point you'll get really close to your push range giving you a calling range for him, such that his calling range indicates the push range you started with.



[/ QUOTE ]

Alright so if any one else does all this with the hand in the OP, I got about 80% push for the SB and 35% call for the BB (I didn't try the in between numbers so it's not exact). I'm not sure I did it right so any confirmation would be great.