'-EV' calls 10bb deep? theory question

Originally posted by wiarygodny
Originally i disagreed and tbh im still not convinced. i always thought that Nash already kinda accounts for us losing chips on average when in blinds

This isn't the reason XYZ has stated though.

When we know that our opponents are playing Nash equilibrium strategy, we should keep playing Nash ourselves.
The issue is that it is difficult to calculate Nash equilibrium and in many cases we simply aren't able to do it.
Most algorithms today use ICM (indipendent chip model) to calculate the approximate Nash equilibrium strategy but we know that ICM isn't perfect. The imperfections are strongest in situations where the stacks are very small compared to the blinds becuase ICM doesn't take into account who will be forced to pay blinds in the next couple of hands, it calculates your $equity only from the stack sizes and payout structure, which aren't the only factors in reality. (Note that this is only an example where the ICM is often very far from reality and that's why it is often cited - such as you should push wider than what ICM tells you if you are UTG and short stacked. In fact ICM always has these issues, only in many cases they are small enough that we can ignore them and the ICM ranges will be very close or identical to the real Nash equilibrium ranges.)

XYZ is now saying that this situation is another example where ICM fails to calculate your equity well enough because your possition on the table vs. the bigstack and his ability to push into you a lot in the next few orbits, which will lower your equity comperad to what ICM predicts.
Now I'm not playing 6max myself so I don't really know much the real Nash ranges would be wider compared to the ICM-calculated ranges if at all, but hopefully I made the idea a bit clearer.

Originally posted by Meiffert

Originally posted by wiarygodny
Originally i disagreed and tbh im still not convinced. i always thought that Nash already kinda accounts for us losing chips on average when in blinds

This isn't the reason XYZ has stated though.

You're right abt that. I guess i should have explained my doubts differently in the original post, especially that XYZ has pointed to me as well that the fact that Nash takes into consideration that blinds losing chips because of their position has nothing to do with why he wants to make a -EV call in this spot.

I'm also aware of the ICM imperfections, although tbh until now i always thought abt them only when shortstacked (or pushing for the chip lead). I guess a simplified approach of what youve said "In fact ICM always has these issues, only in many cases they are small enough that we can ignore them and the ICM ranges will be very close or identical to the real Nash equilibrium ranges."

so my question should be rather - do you deviate from Nash to such a great extent (-0.8% is a lot imo) when you're not in a "common -EV spot" (short and desperate), like here where we have 11bb? Cause im simply calling Nash and not even one hand outside of it and im more than happy abt it. Do you guys take one of those approaches or maybe go for one somewhere in the middle (for example you call wider than Nash, but not wider than -0.4% EQDiff)?

I don't usually call outside nash range if I know villain is shoving nash. However, I can think of a reason for calling outside nash. In sngs, if you keep playing against some regs, and you call outside nash, and they know it, then they will be forced to shove less against you because if you call wider, both of you will lose equity provided he shoves nash.

thanks for the input ligualong! So i undersstand you're not making such calls for the reasons mentioned in my posts (FGS/unfavorable stack setup).

im aware of spite calls although i dont make them myself. Im not really convinced that it will actually work against a good opponent since if i were him i would treat it as a misclick, tilt, maybe a bad day or simply not being aware of the correct calling ranges so unless i see it at least a few times im not gonna adjust my pushing range. So i believe that i would have to do it repeatedly and be almost sure that he notices. Not a very appealing plan for me. Its even less of an option against weak regs imo since its just gonna be a pure guessing game: do they notice? do they care? do they know how to adjust? do they actually adjust? etc.

Okay, there are 3 completely different issues mentioned in this post.

a) Whether Nash accounts for losing the blinds and forms your range accordingly.
Answer: Yes. But only in the current hand, imo it has nothing to do with why XYZ is calling outside of Nash.

b) What liguolong has brought up, about ICM being "imperfect" in small-stack scenarios. Well, it is related to "c", but this is still not the direct reason for which XYZ calls in a -EV way.

c) It's "simply" FGS, or Future Game Simulation. Essentially, the situation is the following: the bigstack wins a lot on the bubble, and the others loose a lot. XYZ says that he goes ahead of these losses, takes a -EV call here, and if he doubles up he is going to be the bigstack on the bubble, so he will be able to abuse everyone, so he will be able to get a lot of +EV spots, as opposed to the others.
I'm sceptical about this, since this isn't yet a bubble. I think there are better examples for such, let's just take out the CO for example.

Now I'm pretty sure that certain -EV calls can be correct because they will be compensated in future +EV spots. How -EV we can exactly go, I have never seen an algorythm calculate that. I don't think anyone knows it exactly, or if anyone does, he is hiding it well

lessthanthreee has made a video titled Future Game Simulation, check it out

p.s. saying that ICM is imperfect is simply incorrect. ICM is only a method of calculating how much our stack is worth, it doesn't even have anything to do with ranges
p.p.s. saying that Nash is imperfect, now that has something in it, but it essentially comes from the fact that it can't calculate with the future (eg lost fold equity, blinding out the next round, or having many abuse spots as a result of a certain decision). But Nash ranges have never promised to do that either, they just offer to calculate an equilibrium in a vacuum. And they do that well enough, even if the algorythms use approximations.

I'm not sure ICM Trainer works correctly in that respect :\ If anyone else could clarify that?

Originally posted by akrammon
a) Whether Nash accounts for losing the blinds and forms your range accordingly.

This question doesn't make sense at all.
In games we have something called strategies. These determine the way we play the game. For example in rock-paper-scissors our strategy can be always use rock or in poker our strategy can be to go all-in every hand.
Now it is easily seen that these two strategies are easily exploitable by observant opponents who will beat us by using paper and by calling an appropriate range which has good enough equity against our ATC range.

Now a pair of strategies for players A and B is called Nash equilibrium when they both maximally exploit each other and neither player can therefore improve his winnings by changing his strategy.

Nash equilibrium is simply a strategy with a certain property. When you use this strategy, you minimize your losses against perfectly adjusting opponents because they can never exploit you more than playing the Nash themselves.

Better question to ask is: When we use the indipendent chip model to calculate the aproximate Nash ranges, does the algorithm account for the blinds in the given hand? The answer is yes.

Now I think we should be careful about wording our thoughts correctly in a thread like this. Usually I ignore these mistakes when discussing something but in a theory thread it is important.

Originally posted by akrammon
p.s. saying that ICM is imperfect is simply incorrect. ICM is only a method of calculating how much our stack is worth, it doesn't even have anything to do with ranges
I can't see how you came to your conclusion.
ICM is method which assigns money value to chipstacks. You input the payout structure and the stacks and it tells you how much the stacks are worth.
For example the stacks are 5000, 3000, 2000 and 500 chips. Their value according to ICM in a 9 man SNG (with 50/30/20 prize distribution and total $100 prize money) are $36.94, $30.37, $ 25.22 and $7.46.
In reality though these values are a bit different, they depend on the blind level, on the relative possition of the players on the table, on who is going to be in the blinds the next hand and possibly other factors. ICM doesn't take any of these factors into account though, it only uses payout structure and stack sizes to calculate the money equity.
It is therefore safe to say that ICM is in fact imperfect because it doesn't calculate the money equities exactly.
Now when we use the ICM to calculate the dolar equities of our stack after a fold and after a shove and use these equities to calculate the approximate Nash ranges, these ranges can also be wrong.

Originally posted by akrammon
p.p.s. saying that Nash is imperfect, now that has something in it

Nash is a property of a strategy.
Your strategy can either be Nash equilibrium or not. It makes no sense to call it perfect/imperfect.
(As an example a car is either blue or it isn't. It makes no sense to say that blue is right or wrong. Blue in only a possible property of the car.)

One more thing I wanted to clear are these -EV plays. Obviously we never intentionally make a -EV play. That would clearly be stupid.
What this is about are spots where we have a +EV all-in in a situation where using the ICM we calculated that the all-in is -EV, but that calculation was simply wrong because ICM only gives you an approximation which isn't good enough in a given spot.

FGS is indeed a better way to calculate money equity than ICM. It is also way more complicated and therefore rarely used in practise.

So, in summary, ICM is not accurate after all. It assumes ppl go all in every hand and assumes only one person will win the all in. However, we often don't know which side is the error, but on bubble, it is believed big stack has more equity than ICM suggests.

About the equilibrium, the problem is Nash equilibrium may not be unique or may not exist at all in multiplayer games. In MTT, even when it is down to two men in pot, it can be a non-zero sum hand, which doesn't have unique equilibria either, see e.g. prisoner's dilema.

However, Nash theory in poker is modelled in such a way that each person makes the decision that maximizes his EV provided players behind him knows his strategy and make the play maximizes their EV in turn. But the equilibrium might again not be unique, because there might be spots where for BB, calling or folding CO's shove with A9s is 0-EV say, and if he calls with A9s, then CO shouldn't shove A5s otherwise he should and so on. Also about meta game, there might even exist spots where you should show your hand etc.. E.g. you shove 77, and you don't want to get called by A10-AK, because of ICM issues, then it might actually be +EV to show your hand to later player so that they won't call with those anymore.

Originally posted by liguolong
About the equilibrium, the problem is Nash equilibrium may not be unique or may not exist at all in multiplayer games. In MTT, even when it is down to two men in pot, it can be a non-zero sum hand, which doesn't have unique equilibria either, see e.g. prisoner's dilema.

Games with a certain property (poker is one of these games) always have at least 1 equilibrium strategy. (This was proved by Nash, that's why it's called after him.)
Prisoner's dilemma actually has unique equilibrium (both prisoners betray the other), but there are indeed other games where multiple equilibria are possible (stag rabbit hunt is a popular example).

Some of the issues you are talking about can be solved by using a mixed strategy, where you fold sometimes (say 30 %) and go all-in other times.
For example in rock-paper-scissors neither of the basic strategies (throwing rock, throwing paper or throwing scissors) is equilibrium and they can easily be exploited. The equilibrium is to use each of them with 33 % probability.

The point is the game may be non zero sum. Rock paper scissor is a zero sum game. Nash only said that equilibrium exists for zero sum game. Non zero sum game's equilibrium can be strange. For example, Player A and player B choose 1 or 2, if they choose different number, they get zero, player A gets 1 if they both choose 1, and 5 if they both choose 2, player B gets 100 if they both choose 1 and gets 1 if they both choose 2. Then both of them choose 1 for 100% and both of them chooses 2 for 100% are all equilibriums. Obviously if we are player A we prefer both of us choose 2 for 100%

In poker, this is solved by letting A play first and then B, so A chooses 2, B is forced to choose 2. But if B just insists and choose 1 always, and A knows that , he will be forced to choose 1.

Well I understand what you mean, but I don't see where you are going with it.
It's true that some situation being non zero sum means that your opponent can hurt your equity by spite calling you, but that doesn't mean that the equilibrium doesn't exist.
He would have to gain more by spite calling you which he doesn't. He loses himself as well.

Equilibrium exists, but might not be unique and the EV for the equilibrium might be different. This is the problem for game theory. It is possible you can force the better equilibria for yourself. It is possible that he calls and sacrifice some EV in this game, or a few games, but later on, to adjust, you have to shove less to give him better equity. This is probably unlikely to happen in online poker much. But I have experience in some sngs with my friends, and I try to do that and think it is useful.

The idea behind this is the difficulty in cooperative game. An example would be, we found 100 pound on street, if we can come with an agreement, we divide the 10 pound otherwise we have to hand it to the police. Then I can say:"I want 90 pound, and don't mind hand in the money to the police if I can't get 90." If I can convince you I am telling the truth, you should agree with taking 10 pound rather than disagree with my offer and get nothing. This is exactly what is happening in the game if we play many games against each other, I want to convince my friends that I am calling wide and I don't mind losing EV or I just don't know it is bad, then they will be forced to shove less against me.

Thanks guys for all your input, it certainly is an interesting discussion! The thing is that i believe we've kinda changed the subject It would be really great if more ppl want to join and give me their answer for the following question (from my 2nd post in the thread):

Originally posted by wiarygodny
so my question should be rather - do you deviate from Nash to such a great extent (-0.8% is a lot imo) when you're not in a "common -EV spot" (short and desperate), like here where we have 11bb? Cause im simply calling Nash and not even one hand outside of it and im more than happy abt it. Do you guys take one of those approaches or maybe go for one somewhere in the middle (for example you call wider than Nash, but not wider than -0.4% EQDiff)?

so far we've got:

Originally posted by liguolong
I don't usually call outside nash range if I know villain is shoving nash.

just to clarify - you mean in the given situation, right? i assume you are calling wider than Nash when you're the only desperate shorty.

Originally posted by akrammon
I'm sceptical about this, since this isn't yet a bubble. I think there are better examples for such, let's just take out the CO for example.

Now I'm pretty sure that certain -EV calls can be correct because they will be compensated in future +EV spots. How -EV we can exactly go, I have never seen an algorythm calculate that.

would you call any hands outside of Nash (4handed situation as described in the opening post)? I understand that you can't give any exact numbers when it comes to the value of -EVDiff % but maybe at least some estimations? e.g. "-1% seems reasonable" or "-0.5% seems like definitely too much, i wouldnt go wider than -0.1% probably, -0.2% tops"

if u don't mind me asking - do u personally call wider than Nash in the situation described by you (3handed - all the same minus the CO)? if you don't want to answer ill understand, just pretend you didn't see this question

I won't really call wider than nash even if I am desperate short. This is because in nash shortstack is supposed to call wide anyway, and I need to call with like atc to be wider than Nash, and I won't do that.

It makes no sense whatsoever to make -EV calls in this particular spot. I wouldn't say that pushing 40% from the BTN and 26% from the CO as a big stack is abusing the situation. Therefore all of the other players should get enough folds from him to get a chance to push first in.

It is more or less a tradeoff. If you call for example in a -0.5% Spot ICM wise and you have the chance to become the bigstack if you win the allin then 2 things will happen:

1. You will get more first in Spots because the other player cant abuse the bubble anymore

2. Every Hand where you come first in has a bigger Equity to shove then if you were a midstack.

For example: 6 max hyperturbo Blinds 50/100/10Ante at the Bubble

Chips:
Bu 1500
SB 600
BB 900

We are in the BB and the BU shoves. We have a Hand that is -0.5% EV icmwise against his shove.

1. Situation: We fold and Sb fold

Then in the next Hand the chipstacks are :

BU 540
SB 790
BB 1670

Now we look at how much we can shove from the SB:

it is: 43.3%, 22+ Ax+ K2s+ K7o+ Q5s+ Q9o+ J6s+ J9o+ T6s+ T9o 96s+ 98o 86s+ 75s+ 65s 54s nashwise

2. Situation: we call and become the bigstack:

Chipstacks:

BU 540
SB 1860
BB 600

Nashrange from SB: 100.0%, Any two

A Hand like 98o which has +0.02% Equity in the first Situation has now +1.6% Equity in the second Situation.

But of course there is also the Case were you lose the allin and bust out with the -0.5% Equity play.

But i dont know how you could solve this Situation mathematically.I think that your future +ev Situations must be far greater than +0.5% to make this -EV Call profitable overall.
You lose 0.5% equity in both Situations(call and win or call and lose) but in one situation you have no chance to get it back.

But on the other Hand ,if the theory is right, then you should also fold some slightly +ev Spots as the Bigstack especially if you become the midstack if you lose the allin. But to recognize all these things while mass multitabling could be hard.

edit: I used Holdemressources Calculator with 4 Hands Futuregamesimulation for the Situation above.

Here are the Results:

First standard ICM without Futuregame:

Then with Futuregame:

Both times i gave the Bigstack the same shoving Range. But as you can see for Example KTs is -0.93% without Future game and +0.42% with Future game. So probably you can solve the mathematical Problem just with this program.

Thanks a lot for your input! I really like the way youve used to finally add some numbers to the discussion (98o push in the next hand in case we win this one)!

thanks as well for the Holdemresources results. By the looks of it in this particular spot we can go as low as -1.17% (66) which is much more than i would ever imagine!!! It looks like i reaaly have to finally get this tool, it seems pretty amazing.

just one more question if u dont mind - do you make such calls in your games (even if only supporting them with your intuition, without knowing exactly how much of 'negative edge' you can/should take in a given spot)? if you don't want to answer dont worry, ill understand