Heads up Theory

[Jman28]

Hey guys. I don't know if this is something that has been talked about or not. I responded to a question/critique in this post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=3093132&page=0&view=c ollapsed&sb=5&o=&fpart=1) and discussed something that I think about while playing. I realized that I'd gotten it from nowhere and that I hadn't heard it talked about, so I wanted to hear some comments.

If it's a new idea, I'd like it to be talked about and named after me, so that I feel important. It's not worded that well so let me know if you need clarification.

Here is a copy of my response:


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***** Hand History for Game 2503905585 *****
500/1000 Tourney Texas Hold'em Game Table (NL) (Tournament 14678948) - Tue Aug 09
02:58:28 EDT 2005
Table Mini Step 5 1014193 (Real Money) -- Seat 8 is the button
Total number of players : 2
Seat 8: skinsftbl (6690)
Seat 10: aks47 (3310)
skinsftbl posts small blind (250)
aks47 posts big blind (500)
** Dealing down cards **
Dealt to skinsftbl [ 2c, 9c ]
skinsftbl raises (6440) to 6690
skinsftbl is all-In.
aks47 folds.
Creating Main Pot with $7190 with skinsftbl
** Summary **
Main Pot: 7190
skinsftbl balance 7190, bet 6690, collected 7190, net +500
aks47 balance 2810, lost 500 (folded)

[/ QUOTE ]

I don't think this one pencils out.

[/ QUOTE ]

I'm not exactly sure about his range here, and if the push is +EV, but this is an example of a play that I sometimes make with thinking that I haven't heard mentioned anywhere.

Heads-up, I often make very marginal pushes because they will lead to more +EV situations. Here's what I mean...

When you are the bigger stack, generally your pushing range gets wider as the smaller stack-blind ratio goes down. (until he almost is so small that he has to call with any two). This means that the smaller the short stack is, the more advantageous it is for the more aggressive player.

If I fold this hand, he has ~3500 chips next hand. If I push and he folds, he has ~ 2800. Now obviously it's always advantageous to pick up chips, BUT I believe there is an intrinsic advantage to DECREASING the size of the smaller stack.

Therefore, when faced with marginal heads up decisions, I err on the side that decreases the smaller stack. That means folding if I already am the smaller stack, and pushing if I'm the bigger stack.

I'd like to hear thoughts on this one.

[/ QUOTE ]

[Myst]

No $hit. The advantage to heads up play in a game where the stack/blind ratio is so small is making your opponent fold more hands then he is supposed to.

Thats why a pushing any two strategy while heads up isnt too far from optimal.

The secret to heads up poker. Voila!

[Jman28]

[ QUOTE ]
No $hit. The advantage to heads up play in a game where the stack/blind ratio is so small is making your opponent fold more hands then he is supposed to.

Thats why a pushing any two strategy while heads up isnt too far from optimal.

The secret to heads up poker. Voila!

[/ QUOTE ]

This response makes you think you didn't read my post.

That, or my post is worded even worse(ly?) than I thought.

[Myst]

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[ QUOTE ]
No $hit. The advantage to heads up play in a game where the stack/blind ratio is so small is making your opponent fold more hands then he is supposed to.

Thats why a pushing any two strategy while heads up isnt too far from optimal.

The secret to heads up poker. Voila!

[/ QUOTE ]

This response makes you think you didn't read my post.

That, or my post is worded even worse(ly?) than I thought.

[/ QUOTE ]

Its exactly what your post implies, except I would use my statement more as a fundamental theorem than yours.

And I disagree in NOT pushing as the small stack. Why? The same reason you start making desperation pushes at level 4/5.

Make your opponents fold is key to HU, and this applies whether you are a big stack or a small stack. And the way to apply maximum pressure for them to fold is to go all in.

[Jman28]

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No $hit. The advantage to heads up play in a game where the stack/blind ratio is so small is making your opponent fold more hands then he is supposed to.

Thats why a pushing any two strategy while heads up isnt too far from optimal.

The secret to heads up poker. Voila!

[/ QUOTE ]

This response makes you think you didn't read my post.

That, or my post is worded even worse(ly?) than I thought.

[/ QUOTE ]

Its exactly what your post implies, except I would use my statement more as a fundamental theorem than yours.

And I disagree in NOT pushing as the small stack. Why? The same reason you start making desperation pushes at level 4/5.

Make your opponents fold is key to HU, and this applies whether you are a big stack or a small stack. And the way to apply maximum pressure for them to fold is to go all in.

[/ QUOTE ]

Please reread my OP.

[SuitedSixes]

If your name is "Unexploitable Game Theory" I think you've got a very good chance of having this named after you.

[Jman28]

[ QUOTE ]
If your name is "Unexploitable Game Theory" I think you've got a very good chance of having this named after you.

[/ QUOTE ]

[censored], that's my brother's name. He always gets all the credit.

[Myst]

OMG, I just stated in more fundamental terms WHY you want to push PERIOD, whether you are a big stack or a small stack.

Uh, why is it an advantage for a big stack to take 700 chips from a small stack?

Answer: The small stack has less chips to double up with and is forced to push with a mediocre hand.

Uh, why does a small stack want to steal from a big stack?

Answer: To maintain folding equity and keep afloat in the SNG.

And how do both types of stack obtain these goals?

By going all in.

[Jman28]

When the EV difference between pushing and folding are minimal, and you are heads up, err on the side that will decrease the size of the smallest stack (increase stack disparity).

*assuming you are more aggressive than your opponent heads up.

[Jman28]

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OMG, I just stated in more fundamental terms WHY you want to push PERIOD, whether you are a big stack or a small stack.

[/ QUOTE ]

OMG OMG

[Myst]

[ QUOTE ]
When the EV difference between pushing and folding are minimal, and you are heads up, err on the side that will decrease the size of the smallest stack (increase stack disparity).

*assuming you are more aggressive than your opponent heads up.

[/ QUOTE ]

DUH. DUH. DUH. I was just explaining why you want to do that.

In fact, Ill put it more succinctly for you:

(PUSH ANY TWO)

[Jman28]

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When the EV difference between pushing and folding are minimal, and you are heads up, err on the side that will decrease the size of the smallest stack (increase stack disparity).

*assuming you are more aggressive than your opponent heads up.

[/ QUOTE ]

DUH. DUH. DUH. I was just explaining why you want to do that.

In fact, Ill put it more succinctly for you:

(PUSH ANY TWO)

[/ QUOTE ]

You were not explaining what I said at all.

I am saying that there is an intrinsic advantage in increasing stack difference (until the point before you have very little FE).

This means that when a decision to push or fold is EV nuetral, it is better to increase the stack size disparity (THAT MEANS FOLDING AS THE SMALL STACK).

You clearly don't understand this.

I really shouldn't be explaining this to you since you're being a huge floppy weiner, and I will not respond to you further in this thread if you don't say anything constructive.

[YourFoxyGrandma]

Let me make sure I understand...

The bigger the difference between 2 stacks heads up, the more +EV pushing any hand becomes for either the big or small stack. Therefore, as a small stack facing a marginal push/fold situation, it would be correct to fold, sacrificing chips, but increasing the gap between the 2 stacks providing the opportunity for more +EV pushes in later hands. As a big stack it would mean pushing these marginal situations.

Yes?

[Jman28]

[ QUOTE ]
Let me make sure I understand...

The bigger the difference between 2 stacks heads up, the more +EV pushing any hand becomes for either the big or small stack. Therefore, as a small stack facing a marginal push/fold situation, it would be correct to fold, sacrificing chips , but increasing the gap between the 2 stacks providing the opportunity for more +EV pushes in later hands. As a big stack it would mean pushing these marginal situations.

Yes?

[/ QUOTE ]

Yes, this is pretty much it. And better worded than my post, I might add.

I'm a little uncomfortable with the 'sacrificing chips' wording, because it may lead some people to think that I'm saying you are better of with 30% of the chips than with 31%. You are not.

I'm pretty confident that you understand this though.

[Matt R.]

Hi,
OMGOMGOMG. I understood your post on the first read-through. Not sure what the problem is.. lol.

Anyway, I couldn't think of a logical mathematical argument for why this should be true. I think that a given number of chips in a pot preflop should have the same value regardless of whether you're the big stack or the small stack (assuming exact opposite chip distributions in each case). But I think yourfoxygrandma gave me an idea for a non-mathematical argument.

If you are a better heads up player than your opponent (which often means more aggressive in these games), you should forego marginal pushes if getting called and losing will bust you. This is because you can find more +EV spots later as long as you're still in the game. However, if you're the chip leader, then you should take these small +chip EV pushes because even if you lose the hand you can still continue to play, and continue to exploit your +EV opportunities. Basically you're saying there's an intrinsic value for simply surviving if you're a better HU player than your opponent, whereas most models suggest (I think) that it's all about your chip stack. I like the idea, but I'd like a more rigorous proof to fully convince me that this is true, and the chips you're sacrificing by folding as the short stack really are less valuable in terms of $EV than if you're the big stack.

[Jman28]

[ QUOTE ]

If you are a better heads up player than your opponent (which often means more aggressive in these games), you should forego marginal pushes if getting called and losing will bust you. This is because you can find more +EV spots later as long as you're still in the game. However, if you're the chip leader, then you should take these small +chip EV pushes because even if you lose the hand you can still continue to play, and continue to exploit your +EV opportunities. Basically you're saying there's an intrinsic value for simply surviving if you're a better HU player than your opponent, whereas most models suggest (I think) that it's all about your chip stack. I like the idea, but I'd like a more rigorous proof to fully convince me that this is true, and the chips you're sacrificing by folding as the short stack really are less valuable in terms of $EV than if you're the big stack.

[/ QUOTE ]

Yeah. This is an interesting thought. Makes sense to me.

However, it isn't the same thing I said so you and Foxy can go get your own theory and name it after yourselves.

My idea is more about the value of chip disparity than the value of surviving. However, both theories would often yeild the same results.

Here's where they differ/don't differ:

Hero (3500)
Villain (6500)

Push and fold are EV nuetral.

Jman's Theory says: FOLD
Matt's Theory says: FOLD

Hero (6500)
Villain (3500)

Push and fold are EV nuetral.

Jman's Theory says: PUSH
Matt's Theory says: Doesn't matter

If you want one where we fully disagree:

Hero (6500)
Villain (3500)

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[Jman28]

I'm going to add two other theories and their veiws on these hands. Probably a combination of these thoughts should work together in close situations and you should weigh the consequsnces. I'll recap the main ideas here.


Matt's Theory: In EV Nuetral spots (or close to it) where hero may be eliminated, fold in order to take advantage or your skill edge.
Jman's Theory: In EV Nuetral spots (or close to it) do whatever increases stack disparity(to a point).
Theory ICM: Do whatever ICM says
Theory 2+2*: Adhere to ICM. When decisions are very close, fold in order to help your image.


*(as I understand it, what we usually recommend)

Here's where they differ/don't differ:

Hero (3500)
Villain (6500)

Push and fold are EV nuetral.

Jman's Theory says: FOLD
Matt's Theory says: FOLD
Theory ICM: Doesn't Matter
Theory 2+2: FOLD

Hero (6500)
Villain (3500)

Push and fold are EV nuetral.

Jman's Theory says: PUSH
Matt's Theory says: Doesn't matter
Theory ICM: Doesn't Matter
Theory 2+2: FOLD

If you want one where we fully disagree:

Hero (6500)
Villain (3500)

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD
Theory ICM: Doesn't Matter
Theory 2+2: FOLD

I use a lot of these guys ((())) (afraid to spell them wrong so I made a visual aid)

[flyingmoose]

It took me like fifty tries but I finally get it. And I like what you're saying. I hadn't thought of anything quite like that before. Probably not even intuitively.

I think your post would have gotten a lot more credit if you added about 40 pages of math that nobody bothered to read but assumed was well thought out.

[Jman28]

Please note that the actual consequences of these thoughts are pretty minimal.

Even if there is merit to my theory, ignoring it will not hurt your ROI much at all.

I just like to think things through sometimes.

[Jman28]

[ QUOTE ]
It took me like fifty tries but I finally get it. And I like what you're saying. I hadn't thought of anything quite like that before. Probably not even intuitively.

I think your post would have gotten a lot more credit if you added about 40 pages of math that nobody bothered to read but assumed was well thought out.

[/ QUOTE ]

Haha. Yeah, I should've done that. I prefer word problems myself though.

Anyways, glad you got it, and that you liked it.

[Dex]

[ QUOTE ]
DUH. DUH. DUH. I was just explaining why you want to do that.

In fact, Ill put it more succinctly for you:

(PUSH ANY TWO)

[/ QUOTE ]

At what ratio of blinds to small stack does pushing any two become correct, then?

[eastbay]

[ QUOTE ]

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[/ QUOTE ]

Here's a novel idea: test your theory.

I think you will find it is false.

If you can't test it on full scale poker (although I don't see why it's not possible), come up with a simplified model that retains the properties that you think are essential to making your theory correct.

eastbay

[microbet]

My boring theory is that the better player is able to more precisely put his opponent on a range and then do the math to calculate the best EV decision. Seems to me that every time you make a -EV decision you are losing chips and that doesn't seem good.

I think that 92 push cost you about 600 Sklansky chips.

[johnny005]

I understand what your saying here jman, I've been thinking along the same lines at times when heads....
At times I will be ahead say 6000-2000 with blinds of 150-300

I will push Every hand at this point. My reasoning being that I'f I can get him down to the point where he has to call he has to win like 3 hands in a row to get even again. If I lose now he thinks I'm pushing 9 2 all the time and will call me with any 2 when We are even and I have a2 or k3 or something like this... which again is +ev cause he will be callling with worse hands now..

Not sure if I made any sense or if this is the same thing your talking about Jman, But just some thoughts I had on the same situation.

[johnny005]

yes but Can It gain you more on later hands.. By loosing 600 sklansky chips can you gain say 1000 ?

[microbet]

I don't think so.

Say you are in this situation 1,000,000 times and on average you lose 600 chips. How are you going to turn that to your advantage?

A big percentage of the time, maybe 60%, you will just pick up the blinds. The fact that you won those chips is already accounted for in the average amount won/lost. You have pushed one more time (already pushed quite a bit recently) and have thus opened your opponents calling range even further. This means you will have fewer pushable hands. This isn't a huge factor, but I don't think it is positive.

A decent percentage of the time you will lose - about 25 - in those cases you will lose a bunch of chips (which are already accounted for) and you will show down 92, which will widen your opponents calling range and leave you the short stack and much more likely to be called.

The rest of the time you win. All good there.

[nykenny]

hi Jman,

what kind of blind sizes are you assuming here?

thanks,

- Kenny

[Jman28]

[ QUOTE ]
My boring theory is that the better player is able to more precisely put his opponent on a range and then do the math to calculate the best EV decision. Seems to me that every time you make a -EV decision you are losing chips and that doesn't seem good.

I think that 92 push cost you about 600 Sklansky chips.

[/ QUOTE ]

Slightly off topic, but what calling range do you put my opponent on in the specific hand we were discussing?

I'm giving him a range of 22+,A2+,K5+,Q8+,J9+,T9 and getting a +EV push, right? (This of course, before applying my theory)

Edit: I think his actual calling range is even less.

[Jman28]

[ QUOTE ]
[ QUOTE ]

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[/ QUOTE ]

Here's a novel idea: test your theory.

I think you will find it is false.

If you can't test it on full scale poker (although I don't see why it's not possible), come up with a simplified model that retains the properties that you think are essential to making your theory correct.

eastbay

[/ QUOTE ]

I would like to do this.

As for full scale poker, I think it would take many years to come up with a sample significant enough.

A full scale model, sounds good. Unfortunately I have no idea whatsoever how to do this. Wanna help?

[Jman28]

[ QUOTE ]

Say you are in this situation 1,000,000 times and on average you lose 600 chips. How are you going to turn that to your advantage?


[/ QUOTE ]

I wouldn't turn this to my advantage.

I'm talking about situations where I average losing, say, 20 chips.

[microbet]

You had just pushed a bunch. I think that calling range is fair. I might have used a bit broader range though.

I don't have any tools with me now - what's the result with that range?

BTW, what part of the world are you in? I'm in Southern California.

[Jman28]

[ QUOTE ]
You had just pushed a bunch. I think that calling range is fair. I might have used a bit broader range though.

I don't have any tools with me now - what's the result with that range?

BTW, what part of the world are you in? I'm in Southern California.

[/ QUOTE ]

That range made a push +.3%.

I'm in the midwest, so central time zone. Usually not awake at this hour (I like to wake up at 3:30 pm and go to bed at 4 am) but I got two phone calls while sleeping and couldn't go back to bed. I assume that's what this question was about. right?

[A_PLUS]

Well, I get it, so thats a start.

I agree when you have more chips. Basically, it takes a situation where against a perfect opponent it would be EV neutral and puts him ina spot to makea decision which can only increase your EV over time.

Pretty much standard aggressive poker theory.

Now onto the real 'theory'

From a game theory perspective, I can see where this comes from.

As the chip disparity grows, the leading player can afford to make riskier and riskier plays b/c losing a hand still leaves him with enough chips to win a reasonable amount of the time.

So, your premise is that when given a situation to which we are EV indifferent, we should choose the one which will make our opponent make riskier moves going forward. If I am wrong with my thoughts so far, skip the rest.

My problems:
-Your opponent gets off easy. He increases his equity without having to make a decision. When we put out opponent on a range and get an EV neutral spot, any hand he plays outside of that range is +EV. So you are putting a lot of faith in your reads and your opponent here.

-So for this to make any sense, we are assuming our opponents are playing near optimal poker. So his range will slide wider by a small amount given the new disparity in stack sizes. For us to take advantage of this. He needs to be dealt a hand in exactly that new portion of his range that was adde, coupled with us being dealt a hand that makes a call +EV.

-The problem with this is, his increased range is directly affected by the stack/blind ratio of both players. So, the higher the blinds the more likely we are to be able to take advantage of it. BUT, the higher the blinds the less equity we will have if we do win the favorable hand after folding the neutral hand.

**Basically, I think this strategy would work in a game where the cost associated with waiting (paying blinds) was lower, and/or the edge you expected to gain was larger.

[eastbay]

[ QUOTE ]
[ QUOTE ]
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Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[/ QUOTE ]

Here's a novel idea: test your theory.

I think you will find it is false.

If you can't test it on full scale poker (although I don't see why it's not possible), come up with a simplified model that retains the properties that you think are essential to making your theory correct.

eastbay

[/ QUOTE ]

I would like to do this.

As for full scale poker, I think it would take many years to come up with a sample significant enough.

A full scale model, sounds good. Unfortunately I have no idea whatsoever how to do this. Wanna help?

[/ QUOTE ]

Not really, no.

I will just say that I have done investigations along these lines before, however, both with simpler model games as well as full preflop push/fold NL Hold'Em and have consistently found that there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does. In fact, very strong strategies will collapse very quickly once you add -cEV moves to them.

eastbay

[Jman28]

[ QUOTE ]

So, your premise is that when given a situation to which we are EV indifferent, we should choose the one which will make our opponent make riskier moves going forward. If I am wrong with my thoughts so far, skip the rest.

[/ QUOTE ]

You are close, but this is a misunderstanding.

The reason we want to increase chips disparity is that it widens OUR pushing range, creating more +EV opportunities, whether we are the small stack or the big stack.

To reword, 'widening our own pushing range' is the same thing as 'finding ourselves in more +EV situations' since we should only widen our range if the extra hands in there are +EV.

[ QUOTE ]
So for this to make any sense, we are assuming our opponents are playing near optimal poker.

[/ QUOTE ]

I know you said to ignore the rest, but I think this is where your confusion might be though.

For my idea to work, we are assuming the opposite of this. We assume that WE play near optimally, and our opponent does not.

When chip disparity increases:

It becomes +EV to push more.
It becomes +EV to call more pushes.

These are both adjustments that we count on our opponent to NOT make.

For example:

Hero 4600
BB 5400

Blinds 300/600

Hero has 86s.
BB will call with 22+,A2+,KT+,QJ+
Push is +.9%

Now...take 1k and move it.

Hero 3600
BB 6400

Blinds 300/600

Hero has 86s.
BB will call with 22+,A2+,KT+,QJ+
Push is now +1.1%

This is the effect of our villain not adjusting his calling range. Pushes become better for us as the stack disparity increases.

I realize (now more than before) that the difference is minimal. I don't think this idea is a very big deal, as I said before, in that it will have much impact on your game. It will not.

[Jman28]

In addition to this last post, I want to add that if your opponent has different leaks (calls/pushes too frequently) you would want to employ a different strategy.

This time, leaning toward DECREASING chip disparity, since then he will often be making pushes and calls that are even more -EV.

The reason my basic idea is to increase the difference is because generally, our opponents leaks are not pushing/calling enough.

[microbet]

Ok, It looks like a marginal spot. Maybe a few hands could be added to the range, maybe not. Villian himself would be unlikeky to be able to answer the question.

As far as asking where you are, I was just wondering if you might be in SoCal (20 million people are).

I'm thinking about looking for a live tourney tonight. Anyone interested? Hopefully Yugo can come. He wouldn't have a date, would he?

[A_PLUS]

I think you are making the mistakes I mentioned, but I likely did a bad job explaining what I mean

I think you are confusing the EV difference (pushing vs folding) and overall equity. You mention how the same situation turns from +.9% to 1.1%. This is a direct result of the size of our stacks. We have less equity to begin with in the 2nd example, so increasing it by a larger % still makes us worse off.

We have 392$ in equity to start #1
We increase this by .9% with a push = $395.5

We have 372$ in equity to start #2
We increase this by 1.1% with a push = $376.1

So yeah, we have more higher % pushes in case #2, but I'd rather have an EV neutral push when I start with 392$ in equity than a 1% positive spot when I star t with 372$.

That is the basics as to why I think it is wrong. For this strategy to work, you would need the starting equity of #1 and #2 to be closer (392$ ~ 390), and/or the difference in EV % to be much higher.

[Jman28]

[ QUOTE ]
I think you are making the mistakes I mentioned, but I likely did a bad job explaining what I mean

I think you are confusing the EV difference (pushing vs folding) and overall equity. You mention how the same situation turns from +.9% to 1.1%. This is a direct result of the size of our stacks. We have less equity to begin with in the 2nd example, so increasing it by a larger % still makes us worse off.

We have 392$ in equity to start #1
We increase this by .9% with a push = $395.5

We have 372$ in equity to start #2
We increase this by 1.1% with a push = $376.1

So yeah, we have more higher % pushes in case #2, but I'd rather have an EV neutral push when I start with 392$ in equity than a 1% positive spot when I star t with 372$.



[/ QUOTE ]

I think you're still misunderstanding. I realized this would be a problem for some:

[ QUOTE ]

I'm a little uncomfortable with the 'sacrificing chips' wording, because it may lead some people to think that I'm saying you are better of with 30% of the chips than with 31%. You are not.

[/ QUOTE ]

I know that you are ALWAYS worse off with less chips. My point is, in a sense, that you aren't AS bad off as ICM leads you to believe. (because of the more +EV pushes you can make)

[ QUOTE ]
That is the basics as to why I think it is wrong. For this strategy to work, you would need the starting equity of #1 and #2 to be closer (392$ ~ 390), and/or the difference in EV % to be much higher.

[/ QUOTE ]

I'm quite sure that you will always be better off with more chips than with less, (all other factors the same) no matter how small the difference.

[Jman28]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[/ QUOTE ]

Here's a novel idea: test your theory.

I think you will find it is false.

If you can't test it on full scale poker (although I don't see why it's not possible), come up with a simplified model that retains the properties that you think are essential to making your theory correct.

eastbay

[/ QUOTE ]

I would like to do this.

As for full scale poker, I think it would take many years to come up with a sample significant enough.

A full scale model, sounds good. Unfortunately I have no idea whatsoever how to do this. Wanna help?

[/ QUOTE ]

Not really, no.

I will just say that I have done investigations along these lines before, however, both with simpler model games as well as full preflop push/fold NL Hold'Em and have consistently found that there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does. In fact, very strong strategies will collapse very quickly once you add -cEV moves to them.

eastbay

[/ QUOTE ]

Here's one for you.

You're playing against opponent X. You've been playing with him for 6 hands heads up.

Hero: 6000
X: 4000
Blinds 250/500

Opponent X is a tall slender man with a rugged handsome face. He has been folding every hand except for AA.

He's waiting for those aces baby! And he's gonna bust you so good when he gets em.

Now you are dealt 94s in the sb. He will only call with AA. However, this opponent X has decided that if you push 4 times in a row into him (you've already pushed 3) that he will adjust his range for the rest of the tournament to calling and even pushing himself with 22+, Ax, Kx, Qx.

Clearly, the optimal strategy is to fold this 94s, even though pushing the hand is +cEV. Then push the next three chances you get, then fold again.

Now, in real life, examples aren't this clear cut. They are more like the one's which I am trying to describe in this thread.

Would you mind opening your mind and thinking about them now that I have shown you how +cEV plays are not the optimal strategy 100% of the time? I would like to hear your thoughts on the idea based on it's own merit rather than based on the fact that you have tested different situations and come up with the conclusion that what was +cEV in those situations was always best.

I would be glad to help set up a simulation if anyone with the knowledge to do something like that would assist me.

[A_PLUS]

Ok, I did misunderstand what you were trying to say. I see now.

You can't use ICM $EV calcs to 'prove' that ICM is flawed for one.

The positive +EV spots that are created are just a result of the fact that you have taken away most of your down-side risk when making a risky bet.

You have 3600 chips, you have only lose 72$ in equity in the portion of the ICM where you get called and lose. So with the upside held constant, lowering your starting equity always makes a situation more +$EV than having more chips would.

So the increased $EV has nothing to do with the $ equity when a steal is successful.

It also has nothing to do with the $EV when you are called and win.

It only is effected by the times you get called and lose, b/c you dont have much to lose to begin with.

So these +EV situations are real, and from what I can see compltely accounted for by the ICM. But the only time you are going to feel benefit of this higher $EV is when you bust out "hey, I didnt have many chips anyway!"


I understand that you are saying "we are not as bad off as we think, b/c of these new higher $EV opps." and not "we are better off with less chips."

I think you are wrong here, but I may not be explaining my point well. My point is the the $EVs are just a construct of having little left to lose, not any higher upside. And since you cant rebuy constantly at a certain chip level, I think passing up EV neutral spots when SS is a big big mistake. (BTW, this is the basis of buying in short at a NL table. It works there b/c you can always rebuy. Basically limits your reverse implied odds)

[eastbay]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[/ QUOTE ]

Here's a novel idea: test your theory.

I think you will find it is false.

If you can't test it on full scale poker (although I don't see why it's not possible), come up with a simplified model that retains the properties that you think are essential to making your theory correct.

eastbay

[/ QUOTE ]

I would like to do this.

As for full scale poker, I think it would take many years to come up with a sample significant enough.

A full scale model, sounds good. Unfortunately I have no idea whatsoever how to do this. Wanna help?

[/ QUOTE ]

Not really, no.

I will just say that I have done investigations along these lines before, however, both with simpler model games as well as full preflop push/fold NL Hold'Em and have consistently found that there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does. In fact, very strong strategies will collapse very quickly once you add -cEV moves to them.

eastbay

[/ QUOTE ]

Here's one for you.

You're playing against opponent X. You've been playing with him for 6 hands heads up.

Hero: 6000
X: 4000
Blinds 250/500

Opponent X is a tall slender man with a rugged handsome face. He has been folding every hand except for AA.

He's waiting for those aces baby! And he's gonna bust you so good when he gets em.

Now you are dealt 94s in the sb. He will only call with AA. However, this opponent X has decided that if you push 4 times in a row into him (you've already pushed 3) that he will adjust his range for the rest of the tournament to calling and even pushing himself with 22+, Ax, Kx, Qx.

Clearly, the optimal strategy is to fold this 94s, even though pushing the hand is +cEV. Then push the next three chances you get, then fold again.

Now, in real life, examples aren't this clear cut. They are more like the one's which I am trying to describe in this thread.

Would you mind opening your mind and thinking about them now that I have shown you how +cEV plays are not the optimal strategy 100% of the time?

[/ QUOTE ]

Would you mind applying basic reading comprehension and reasoning skills to see what you're posting is a complete non-sequitur?

eastbay

[Jman28]

First let me say that I hope I don't come off as offended or overly-argumentative. I appreciate your contribution to this thread.

I think we are finally on the same page almost. I'm gonna respond to different parts of your post out of order.

[ QUOTE ]
The positive +EV spots that are created are just a result of the fact that you have taken away most of your down-side risk when making a risky bet.


[/ QUOTE ]
Right

[ QUOTE ]
You have 3600 chips, you have only lose 72$ in equity in the portion of the ICM where you get called and lose. So with the upside held constant, lowering your starting equity always makes a situation more +$EV than having more chips would.


[/ QUOTE ]
Right.
[ QUOTE ]
So the increased $EV has nothing to do with the $ equity when a steal is successful.

It also has nothing to do with the $EV when you are called and win.

It only is effected by the times you get called and lose, b/c you dont have much to lose to begin with.


[/ QUOTE ]

Right.

[ QUOTE ]

So these +EV situations are real, and from what I can see compltely accounted for by the ICM.

[/ QUOTE ]

I disagree. I'm having trouble explaining myself better than I already have. I'll keep trying.

I do not think that ICM accounts for the fact that aggressive opponents have more of an advantage when stack sizes are far apart.

Do you agree? If not which part do you disagree with?

That aggressive opponents have more of an advantage when chip stacks are far apart?

or

That ICM doesn't account for this?

I think after you answer that, I may be able to explain further.

also..
[ QUOTE ]

You can't use ICM $EV calcs to 'prove' that ICM is flawed for one.

[/ QUOTE ]

In a sense, you are right. I used ICM only as an example though to clarify my thoughts. I also am not looking to 'prove' ICM is flawed. Just that it isn't all-powerful, which I think you'll agree with (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=3186409&page=0&view=colla psed&sb=5&o=14&vc=1) .

Basically, my argument is:

Aggro players do better when there is a greater chip disparity.

ICM does not take that into consideration.

Therefore, if the conditions are right (you are more correctly aggresive than your opponent), you should lean toward decisions that increase chip disparity when ICM says it's very close.

[Jman28]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

Pushing has EV difference of -.000001% of prize pool (edited this for clarity)

Jman's Theory says: PUSH
Matt's Theory says: FOLD

Am I making sense?

[/ QUOTE ]

Here's a novel idea: test your theory.

I think you will find it is false.

If you can't test it on full scale poker (although I don't see why it's not possible), come up with a simplified model that retains the properties that you think are essential to making your theory correct.

eastbay

[/ QUOTE ]

I would like to do this.

As for full scale poker, I think it would take many years to come up with a sample significant enough.

A full scale model, sounds good. Unfortunately I have no idea whatsoever how to do this. Wanna help?

[/ QUOTE ]

Not really, no.

I will just say that I have done investigations along these lines before, however, both with simpler model games as well as full preflop push/fold NL Hold'Em and have consistently found that there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does. In fact, very strong strategies will collapse very quickly once you add -cEV moves to them.

eastbay

[/ QUOTE ]

Here's one for you.

You're playing against opponent X. You've been playing with him for 6 hands heads up.

Hero: 6000
X: 4000
Blinds 250/500

Opponent X is a tall slender man with a rugged handsome face. He has been folding every hand except for AA.

He's waiting for those aces baby! And he's gonna bust you so good when he gets em.

Now you are dealt 94s in the sb. He will only call with AA. However, this opponent X has decided that if you push 4 times in a row into him (you've already pushed 3) that he will adjust his range for the rest of the tournament to calling and even pushing himself with 22+, Ax, Kx, Qx.

Clearly, the optimal strategy is to fold this 94s, even though pushing the hand is +cEV. Then push the next three chances you get, then fold again.

Now, in real life, examples aren't this clear cut. They are more like the one's which I am trying to describe in this thread.

Would you mind opening your mind and thinking about them now that I have shown you how +cEV plays are not the optimal strategy 100% of the time?

[/ QUOTE ]

Would you mind applying basic reading comprehension and reasoning skills to see what you're posting is a complete non-sequitur?

eastbay

[/ QUOTE ]

Clearly I don't have these skills that you speak of.

The way I see it, I have continually countered everything you've said (with style).

If you could show me why what I said is stupid, I'd really appreciate it.

[Newt_Buggs]

quiz time: You have the option to play an average $55 PP SNG players heads up in a $50 freeze out as many times as you want at the blind level that you choose. If your only goal is to maximize the $ that you make, do you choose
A. 100 BB stacks
B. 10 BB stacks
C. 5 BB stacks

I think that one of the keys to Jmans post is realizing why C is the correct answer (at least I think its the correct answer, correct me if I'm wrong). There are two reasons for this:
1. Hourly rate
and more importantly
2. Average players suck at heads up, and even more so with big blinds because they will often make mathematically incorrect folds. When the OP states that pushing in his example will lead to a situation (shorter stacks) that favors the aggressive player, it doesn't so much imply that the good player is going to exploit the bad player by pushing but that the bad player is going to defeat himself by folding mathematically correct pushes. When your opponents lack a fundamental understanding of simple HU math you can best exploit this ignorance with shorter stacks.

[eastbay]

[ QUOTE ]

If you could show me why what I said is stupid, I'd really appreciate it.

[/ QUOTE ]

Come on, Jman.

I said that taking -cEV pushes appears to be always wrong.

You then "countered" (with style, no less) that passing on +cEV pushes can be right.

Don't you see that a strategy can pass on +cEV pushes and yet take no -cEV pushes? That these are two completely different things?

Your "counter" is a non-sequitur. I didn't say passing on +cEV pushes was always wrong (and in fact, I've even quantified this effect in some detail in the past). I said taking -cEV pushes is.

eastbay

[Jman28]

[ QUOTE ]
[ QUOTE ]

If you could show me why what I said is stupid, I'd really appreciate it.

[/ QUOTE ]

Come on, Jman.

I said that taking -cEV pushes appears to be always wrong.

You then "countered" (with style, no less) that passing on +cEV pushes can be right.

Don't you see that a strategy can pass on +cEV pushes and yet take no -cEV pushes? That these are two completely different things?


Your "counter" is a non-sequitur. I didn't say passing on +cEV pushes was always wrong. I said taking -cEV pushes is.

eastbay

[/ QUOTE ]

Thank you. I guess I misread this:


[ QUOTE ]
there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does.

[/ QUOTE ]

to mean that no situation where making a play that is -cEV is best, whether that be pushing or folding.

By 'situation' I assumed you meant 'situation' and not 'push'

If I understand you now, you are saying that making -cEV pushes always appear to be wrong. Okay.

You opponent is now Lawanda. She is a friendly woman, though pretty new to poker.

Chip Stacks
Hero: 6400
Lawanda: 3600

Blinds, 300/600.

Hero has 32o.

Lawanda is calling pushes right now with 22+,A2+,K2+,Q6o+,Q2s+,J9o+,J7s+,T8s+, (45% of hands), and pushing 22+,A2+,K2+,Q2+,J2+,T3o+,T2s+,95o+,93s+,86o+,84s+, 76o,75s+,65s (75% of hands).

ICM says a push here would be -EV (only -.125%)

However, Lawanda gets very scared when she gets below 3400 chips. When she has less than 3400 chips, she folds every hand except for QQ+ in the SB, and doesn't call a push without AA.

So, pushing, while slightly -EV according to ICM, would be best since you would immediately get Lawanda to under 3400 chips and then run over her from there.

Please now type some short angry comment, then allow me to ask you to expand on it, and then tell me why this example doesn't satisfy your requirements.

[Jman28]

[ QUOTE ]
quiz time: You have the option to play an average $55 PP SNG players heads up in a $50 freeze out as many times as you want at the blind level that you choose. If your only goal is to maximize the $ that you make, do you choose
A. 100 BB stacks
B. 10 BB stacks
C. 5 BB stacks

I think that one of the keys to Jmans post is realizing why C is the correct answer (at least I think its the correct answer, correct me if I'm wrong). There are two reasons for this:
1. Hourly rate
and more importantly
2. Average players suck at heads up, and even more so with big blinds because they will often make mathematically incorrect folds. When the OP states that pushing in his example will lead to a situation (shorter stacks) that favors the aggressive player, it doesn't so much imply that the good player is going to exploit the bad player by pushing but that the bad player is going to defeat himself by folding mathematically correct pushes. When your opponents lack a fundamental understanding of simple HU math you can best exploit this ignorance with shorter stacks.

[/ QUOTE ]

This is a pretty good representation of a key to my post.

To be a little bit more similar, and a bit more controversial, we might say:

'quiz time: You have the option to play an average $55 PP SNG players heads up in a $50 freeze out as many times as you want at 300/600 Blinds. If your only goal is to maximize the $ that you make, do you choose'

A. You each have 5k chips
B. You alternate games, each time someone starting with 7.5k and the other with 2.5k.

[A_PLUS]

Dude, you owe me like an hour of my life back. why you introduced the ICM $EV calcs into this I will never know. Is what you are saying that typically, opponents make more mistakes with high blinds and widely varied stacks? So when given a choice that is EV neutral pick the situation they are more likely to make mistakes in?

If so, gotcha. Dont know if I agree, but I see your point.

Now that $EV stuff was just a bad example. You see why that was complete BS right?

[dfan]

The theory is slowly becoming better defined as this debate goes on. It now seems to me to be:

Jman's specific hypothesis:

Since most tournament opponents stray farther from optimal play strategy as the difference in stack sizes increases, in neutral or very slightly -cEV situations, you should push if you are the large stack and fold if the small stack since each of these actions is more likely to increase the disparity in stack sizes.

Large form emerging from Jman/Eastbay discussion:

A betting decison that is neutral or even slightly -cEV can be +$EV IF the more usual outcome of the decision is to create a subsequent game situation that your opponent sucks even more at.

[eastbay]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

If you could show me why what I said is stupid, I'd really appreciate it.

[/ QUOTE ]

Come on, Jman.

I said that taking -cEV pushes appears to be always wrong.

You then "countered" (with style, no less) that passing on +cEV pushes can be right.

Don't you see that a strategy can pass on +cEV pushes and yet take no -cEV pushes? That these are two completely different things?


Your "counter" is a non-sequitur. I didn't say passing on +cEV pushes was always wrong. I said taking -cEV pushes is.

eastbay

[/ QUOTE ]

Thank you. I guess I misread this:


[ QUOTE ]
there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does.

[/ QUOTE ]

to mean that no situation where making a play that is -cEV is best, whether that be pushing or folding.

By 'situation' I assumed you meant 'situation' and not 'push'


[/ QUOTE ]

No, that just happened to be the context you had brought up to attempt to display something (which didn't make sense and still doesn't). The principle is the same for calling, for example.

[ QUOTE ]

ICM says a push here would be -EV (only -.125%)


[/ QUOTE ]

Why are you invoking ICM? ICM is irrelevant HU.

I suspect at this point there is some confusion over the use of EV of a play vs. differences in EV by comparing different plays. It seems you are using "EV" to actually mean "the difference in EV between two different moves."

This could cause you to confuse things like what I was calling "passing on +cEV" and "taking -cEV." This helps explain your non-sequitur.

The reason you can't discuss EV in terms of differences like this in general is that there's often more than two options (and really there are always a very large number). Now you can't talk about the "EV of the play" in the sense you're using because it isn't clear what you're comparing it to.

So let's get on the same page. When I say EV I am talking about the cEV of the play, not the cEV _difference_ between two different plays. Clear?

[ QUOTE ]

However, Lawanda gets very scared when she gets below 3400 chips. When she has less than 3400 chips, she folds every hand except for QQ+ in the SB, and doesn't call a push without AA.

So, pushing, while slightly -EV according to ICM, would be best since you would immediately get Lawanda to under 3400 chips and then run over her from there.

Please now type some short angry comment, then allow me to ask you to expand on it, and then tell me why this example doesn't satisfy your requirements.

[/ QUOTE ]

My requirements for what?

You might want to look at some of my old posts refuting Sklansky's assertion (he calls it a "proof", even) that HU equity must be linear. I think you're getting at what I've said many times in those posts.

I think it is clear that when you add absolute stack dependence to a strategy, linear equity HU is wrong. You can make it a step function in the extreme case.

So I guess I'm agreeing with you that for strategies that exhibit absolute stack dependence, you can generate this kind of pathology.

However, I think what you are saying is that this effect also exists in non-pathological strategies (to be a little more precise 'something that might earn me money to know about'). So I'm back to my original challenge: try to find a reasonable example. I've looked, and never been able to find one. What I found is that strategies blew up when they started choosing -cEV plays. Of course, I didn't use a pathological counter-strategy of folding everything below 5000 chips and pushing everything above. I used counter-strategies based on stack/blind ratios and ranges that approximated both "correct" and "guesses at typical" play.

If you're just saying that you can construct these pathological examples, then there's no disagreement. Try searching for "step function HU" or something to see where I've often said the equivalent in the past.

eastbay

[dfan]

Didn't see your post A_Plus before I wrote essentially the same thing. I did add the general form though, which to me seems like it would be true. Not as sure about the specific blind size hypothesis, but can't see any holes in it either.

[gumpzilla]

[ QUOTE ]

Thank you. I guess I misread this:


[ QUOTE ]
there are no circumstances HU where taking -cEV situations is superior to some other strategy which never does.

[/ QUOTE ]

to mean that no situation where making a play that is -cEV is best, whether that be pushing or folding.

[/ QUOTE ]

I agree that eastbay's statement was unclear at best, since "situations" are going to include more things than pushing. I also think that the old specter of the double usage of EV - to describe the results of a particular move or a particular situation - is showing up here. One could certainly consider a move -EV in a relative sense - even if it is +EV in an absolute sense in that you expect to gain chips by making the move - if you are passing on better absolute +EV plays to make this one. I don't think this is what eastbay means, but this interpretation would make sense, too - strategies that routinely pick less than optimal moves at each point are going to be inferior to those that always pick optimal moves. This seems kind of tautological, but I guess it depends on how you define optimal.

I've seen people mention both cEV and ICM $EV in this conversation. People do realize that heads up these return exactly the same results, right?

EDIT: I see while I was writing this eastbay wrote and covered pretty much all of the things I just mentioned and then some.

[Jman28]

Thank you for finally contributing positively to this thread.

The reason I used ICM is that your 'Power Tools' is the easiest method I have for quickly calculating the EV of plays. I understand that ICM is unnecesary in heads up calculations, but it doesn't hurt them, so I used what was easiest.

I appreciate you changing your tone, and I will do the same.

I'll search for the thread you are talking about and get back to you on these ideas later tonight (maybe much later) because I'm at 8 tables right now.

[Jman28]

[ QUOTE ]

Dude, you owe me like an hour of my life back. why you introduced the ICM $EV calcs into this I will never know. Is what you are saying that typically, opponents make more mistakes with high blinds and widely varied stacks? So when given a choice that is EV neutral pick the situation they are more likely to make mistakes in?

[/ QUOTE ]

I think this is pretty much it, yes. It seems that it can be put into many different forms.

[ QUOTE ]

If so, gotcha. Dont know if I agree, but I see your point.


[/ QUOTE ]

Good enough for me.

[ QUOTE ]

Now that $EV stuff was just a bad example. You see why that was complete BS right?

[/ QUOTE ]

Other than the fact that ICM is of no more value than cEV, which I just addressed in my last response to Eastbay, no, I don't see why.

It was another way to explain myself since I wasn't coming across as clearly as I wanted to. Why is it a bad example?

[microbet]

Ok, I didn't notice, but this was my Carpal Tunnel post. I was hoping it was the one in the Science, Math, Philosophy room that David Sklansky called a stupid comment.

Carpal Tunnel in under a year; that's a lot of goofing off.

[Jman28]

Hey... I'm having trouble finding your (eastbay's) posts that you (eastbay) mentioned.

If anyone could point me in their general direction, I'd appreciate it. Thanks.

Are they in the archives?

[gumpzilla]

I think your best plan is to look through the shadow's favorite threads post. I'm pretty sure some of the stuff is linked in there. There's also this (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=singletable&Number=2345875 &Forum=,,f22,,&Words=&Searchpage=2&Limit=25&Main=2 345875&Search=true&where=bodysub&Name=30065&datera nge=1&newerval=&newertype=w&olderval=2&oldertype=m &bodyprev=#Post2345875) lengthy thread from May that is very ICM focused that I think will lead you one way or another to where you want to go.

[Jman28]

[ QUOTE ]

I suspect at this point there is some confusion over the use of EV of a play vs. differences in EV by comparing different plays. It seems you are using "EV" to actually mean "the difference in EV between two different moves."


[/ QUOTE ]

You are right. This is how I was using it.
[ QUOTE ]

This could cause you to confuse things like what I was calling "passing on +cEV" and "taking -cEV." This helps explain your non-sequitur.

The reason you can't discuss EV in terms of differences like this in general is that there's often more than two options (and really there are always a very large number). Now you can't talk about the "EV of the play" in the sense you're using because it isn't clear what you're comparing it to.


[/ QUOTE ]

I'll take your word that I'm using the vocabulary incorrectly because you know more about this than me. However, is it a big deal? at all? I'm honestly asking.

It's clear that we are either pushing or folding in all of the situations I described (I think) so they are the only two options we might compare. Anyways, I don't wanna get hung up on this technicality.

[ QUOTE ]
So let's get on the same page. When I say EV I am talking about the cEV of the play, not the cEV _difference_ between two different plays. Clear?


[/ QUOTE ]

Cool. I'll do my best to use it the same. No promises though.



[ QUOTE ]

You might want to look at some of my old posts refuting Sklansky's assertion (he calls it a "proof", even) that HU equity must be linear. I think you're getting at what I've said many times in those posts.


[/ QUOTE ]

I'm still searching for these posts, but I'm thinking I may not be arguing the same thing that you were.

If David specified that the two players are of equal skill (with no weird-ass absolute stack dependent strategies like I made up), I think he is correct that heads up equity is a linear function. (This is just what I believe intuitively, and from what I've read in his books. I've done nowhere near the research you have into it)

[ QUOTE ]
However, I think what you are saying is that this effect also exists in non-pathological strategies (to be a little more precise 'something that might earn me money to know about').

[/ QUOTE ]

Yes. This is what I'm saying, however with the disclaimer that the difference it makes is probably very minimal.

[ QUOTE ]
So I'm back to my original challenge: try to find a reasonable example.

[/ QUOTE ]

I think I've already explained what you are looking for. Let me know if I misunderstood:

When HU, with chip stacks both around 5k, correct strategy suggests pushing less and calling less than if the stacks were, say 3k and 7k. Since our average opponent doesn't push and call pushes much, he doesn't play THAT far from optimally

When the stacks are far apart (up to a point), say 2500 and 7500, our average opponent is making more mistakes than he does.

This is somewhat similar to the example of the beautiful Lawanda, although much less obvious. Her leak was that when below 3400 chips, she didn't push or call enough. Our average opponents leak is that they never push or call enough heads up. However, that leak is more pronounced when one of the stacks is below 3k chips. (more pronounced at 4k /6k than at 5k/5k, most pronounced probably around 2k/8k)

Therefore, just like we brought out Lawanda's leak by getting her below 3400 chips, we can bring out (or really just magnify) the leaks of our average opponent by getting them into situations where the chip stacks are nearest to (complete estimate) 2k/8k.

Just it was in our best interest to sometimes make a -cEV play (am I still saying this wrong?) against Lawanda in order to take advantage of her leak, it is in our advantage to make similar plays (although they have to be very close, I assume) against our average opponents because of their leaks.

[ QUOTE ]
I used counter-strategies based on stack/blind ratios and ranges that approximated both "correct" and "guesses at typical" play.

[/ QUOTE ]

My assumptions are that players don't adjust properly to stack/blind ratios, and that the smaller the stack/blind ratio gets, the further away our average opponent gets from optimal strategy.

I believe that I can define the parameters for a simulation of this for you, but I have no idea how to do it on my own. Nor do I have any idea how hard it is. If it's a huge deal, obviously, don't worry about it.

I think we are on the same page now. I hope.

[Jman28]

[ QUOTE ]
I think your best plan is to look through the shadow's favorite threads post. I'm pretty sure some of the stuff is linked in there. There's also this (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=singletable&Number=2345875 &Forum=,,f22,,&Words=&Searchpage=2&Limit=25&Main=2 345875&Search=true&where=bodysub&Name=30065&datera nge=1&newerval=&newertype=w&olderval=2&oldertype=m &bodyprev=#Post2345875) lengthy thread from May that is very ICM focused that I think will lead you one way or another to where you want to go.

[/ QUOTE ]

Thanks. I skimmed this thread and a few of the ones it links to. Still haven't found Sklansky v Easbay debate. Anyone who can find it = my hero.

I looked at JNash's S-Curve Hypothesis (http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&Number=1009515&page=&view=&s b=5&o=&vc=1) and though I've only been thinking about it for the past 5 minutes, I think there MAY be some merit in it. However, it doesn't or shouldn't apply to heads up poker, so I'm not gonna worry about it for now.

I'm confused as to why it was brought up so often in the post you linked me to.

My current stance:

I agree with Sklansky that two evenly matched players' equity is linear when heads up.

I believe that since our average opponent is not evenly matched with us, there are some exceptions to the linearity based on the way our opponents play at different stack sizes.

[eastbay]

[ QUOTE ]

Thanks. I skimmed this thread and a few of the ones it links to. Still haven't found Sklansky v Easbay debate. Anyone who can find it = my hero.


[/ QUOTE ]

There was never any "debate." I made the refutation and it's clearly true. I'm not the only one to have pointed this out, I don't think.

[ QUOTE ]

I agree with Sklansky that two evenly matched players' equity is linear when heads up.


[/ QUOTE ]

Huh? You already demonstrated a counter-example earlier.

Two players play the following strategy:

Push if they have more than half the chips. Fold if they have less than half. Flip a coin if they have exactly half as to what to do.

Both players are playing identical strategies and therefore must be "evenly matched". Equity is a step function, not linear.

The family of curves between the linear and step function extremes is the S-curve family that's been much discussed.

eastbay

[eastbay]

[ QUOTE ]

I'll take your word that I'm using the vocabulary incorrectly because you know more about this than me. However, is it a big deal? at all? I'm honestly asking.


[/ QUOTE ]

Yes it is. It leads to confusion like there was earlier about equating "passing up +cEV" with "taking -cEV." They're not the same, but they will get confused if you use EV the way you were using it.

[ QUOTE ]

If David specified that the two players are of equal skill (with no weird-ass absolute stack dependent strategies like I made up), I think he is correct that heads up equity is a linear function. (This is just what I believe intuitively, and from what I've read in his books. I've done nowhere near the research you have into it)


[/ QUOTE ]

I think stack dependence is a requirement for deviations from linearity, or at least it is a sufficient condition to generate it. But what's not clear is how "weird ass" it has to be before the deviations from nonlinearity make any practical difference.

[ QUOTE ]

I think I've already explained what you are looking for. Let me know if I misunderstood:

When HU, with chip stacks both around 5k, correct strategy suggests pushing less and calling less than if the stacks were, say 3k and 7k. Since our average opponent doesn't push and call pushes much, he doesn't play THAT far from optimally

When the stacks are far apart (up to a point), say 2500 and 7500, our average opponent is making more mistakes than he does.


Just it was in our best interest to sometimes make a -cEV play (am I still saying this wrong?) against Lawanda in order to take advantage of her leak, it is in our advantage to make similar plays (although they have to be very close, I assume) against our average opponents because of their leaks.

[ QUOTE ]
I used counter-strategies based on stack/blind ratios and ranges that approximated both "correct" and "guesses at typical" play.

[/ QUOTE ]

My assumptions are that players don't adjust properly to stack/blind ratios, and that the smaller the stack/blind ratio gets, the further away our average opponent gets from optimal strategy.

I believe that I can define the parameters for a simulation of this for you, but I have no idea how to do it on my own. Nor do I have any idea how hard it is. If it's a huge deal, obviously, don't worry about it.

I think we are on the same page now. I hope.

[/ QUOTE ]

I'm not going to pursue it now, sorry, I have too many other projects going.

What I'm saying here is that these effects of people actually using stack-dependent strategies (these additional mistakes you postulate for short-stacked high blind situations) probably aren't nearly big enough for anyone to actually make a -cEV play to try to exploit them. Narrowing the margin a little for passing on +cEV, sure. Just not taking -cEV. I think it would take something really extreme to get there that just doesn't exist in the wild.

eastbay

[Jman28]

[ QUOTE ]

[ QUOTE ]

I agree with Sklansky that two evenly matched players' equity is linear when heads up.


[/ QUOTE ]

Huh? You already demonstrated a counter-example earlier.

Two players play the following strategy:

Push if they have more than half the chips. Fold if they have less than half. Flip a coin if they have exactly half as to what to do.

Both players are playing identical strategies and therefore must be "evenly matched". Equity is a step function, not linear.
eastbay

[/ QUOTE ]

I wasn't careful this time to make the exception I made in the post prior to this one:

[ QUOTE ]

If David specified that the two players are of equal skill (with no weird-ass absolute stack dependent strategies like I made up), I think he is correct that heads up equity is a linear function. (This is just what I believe intuitively, and from what I've read in his books. I've done nowhere near the research you have into it)

[/ QUOTE ]

Of course, as we both agree, HU, anytime players will react differently based on their stack size (meaning they would play a hand differently with 70% of the chips than they would with 30% of the chips) the equity is not linear (or at least doesn't have to be).

I am saying, that assuming that players play the same, in that they make the same plays based on blind size and effective stack size, the relationship must be linear. I believe that playing both players playing optimally (pushing and calling the equilibrium ranges you discuss in your 'Mind The Gap' tutorial) will result in a linear model.

What about my other post? Any thoughts? Edit: you already got to it.

[Jman28]

[ QUOTE ]

What I'm saying here is that these effects of people actually using stack-dependent strategies (these additional mistakes you postulate for short-stacked high blind situations) probably aren't nearly big enough for anyone to actually make a -cEV play to try to exploit them. Narrowing the margin a little for passing on +cEV, sure. Just not taking -cEV. I think it would take something really extreme to get there that just doesn't exist in the wild.

[/ QUOTE ]

I think we basically are agreeing. You are granting that it makes sense that the ICM (cEV since we're heads up) doesn't take into account our opponents stack dependent errors, and in fact, you've argued for something similar in the past.

I guess I'm thinking that it is big enough of a difference to worry about. I do have no way to prove that to you or to myself, however.

Could you explain something for me?..

[ QUOTE ]
probably aren't nearly big enough for anyone to actually make a -cEV play to try to exploit them. Narrowing the margin a little for passing on +cEV, sure. Just not taking -cEV.

[/ QUOTE ]

I clearly still don't fully understand the correct usage of cEV. (and excuse my misuse of the terms again)

Why would it be better to pass on a +cEV play than to make a -cEV play.

To me, these seem identically wrong. I'm not arguing, I'm trying to understand.


I also did notice while browsing old equity posts that you often have an angry tone. I was under the impression that you had a personal vendetta against me. Now I see that I'm not special. What's that about?

[microbet]

Eastbay, seen below, is foriegn to some of our customs.

http://www.zenbutoh.com/charactergallery/images/Conehead.jpg

Alternate joke: Ya just don't get the big brain thing do ya?

[Jman28]

[ QUOTE ]
Eastbay, seen below, is foriegn to some of our customs.

http://www.zenbutoh.com/charactergallery/images/Conehead.jpg

Alternate joke: Ya just don't get the big brain thing do ya?


[/ QUOTE ]

Thank you. I understand now. Sorry I jumped to conclusions eastbay.

[Jman28]

I titled this results because that's what we do sometimes in HH threads, right? haha.

Anyways, there is nothing I can do to prove my hypothesis here. I would like to try, if only to see how much this edge really is that we can gain by altering our strategy to the guidelines I've worded so badly at least 7 times.

I am quite confident that I am right. So, what I will do is continue to apply this strategy to my game, although now more conciously, and respond to tons of HH posts with controversial play suggestions citing 'Jman's Squiggly Line Theory' (which I have just decided to name it), as my justification.

Please note that Jman's Squiggly Line Theory covers situations in heads up play and all other parts of the game. Here is an example of it in action on the bubble (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=3191783&Main=3186409#Post 3191783). This entire thread, all the heads up talk, has been about a very specific instance of Jman's Squiggly Line Theory. It is much more powerful than just that.

Goodnight.

[eastbay]

[ QUOTE ]
You are granting that it makes sense that the ICM (cEV since we're heads up) doesn't take into account our opponents stack dependent errors


[/ QUOTE ]

ICM is just stack ratios.

[ QUOTE ]

I clearly still don't fully understand the correct usage of cEV. (and excuse my misuse of the terms again)

Why would it be better to pass on a +cEV play than to make a -cEV play.

To me, these seem identically wrong. I'm not arguing, I'm trying to understand.


[/ QUOTE ]

Say I have two +cEV options, one bigger than the other. In your terminology, taking the smaller +cEV play is "making a -cEV play", which doesn't make any sense - you expect to gain chips, not lose them. It's not -cEV. It's +cEV.

So when discussing strategies that have various options, there's a difference between the set of strategies that pass on +cEV options in the usual sense and in your sense.

That's why it's important, and makes a big difference to keep this from getting mixed up.

[ QUOTE ]

I also did notice while browsing old equity posts that you often have an angry tone. I was under the impression that you had a personal vendetta against me.
Now I see that I'm not special. What's that about?

[/ QUOTE ]

A "vendetta" against you because I got annoyed when you said something silly? Please.

I think you are simply misreading me. I sometimes get annoyed when people waste my time, but don't read too much into it. I'm never "angry." Never.

I didn't get annoyed with you until you asked "would I mind opening my mind" (in what seemed to me to be an indignant tone that I dare disagree with you) and then shoveled a bunch of crap in there.

eastbay

[eastbay]

Haha. I got a spock post the other day on another forum. I guess I should study up on the natives or something.

eastbay

[microbet]

Glad you weren't pissed.

You don't really seem THAT nerdy to me. If you were over the top nerdy I wouldn't joke about it.

[PrayingMantis]

After reading most of this thread, I think you are saying this (very simply put):

"It's good to make a mistake, if it causes your opponent to make a mistake."

However, nowhere in this thread you have shown that our opponent's mistake is indeed bigger than our own mistake (yes, it might be bigger, but might be smaller, who knows), and therefore, nobody can really know if using this general advice is good or bad.

Of course I understand all you have said about avarage players who tend to make more mistakes when the gap between stacks is bigger, but obviously you still _want_ the small stack to get bigger if it's your own stack, and big stack to get smaller if it's your opponent's stack, because, well, no need to explain why. And it doesn't seem very clear why an approach that actually contradicts this in a deep sense, could be better, except in some very bizarre and rare cases.

[PrayingMantis]

OK I have been thinking about your ideas Jman a few more minutes and I think they are complete nonsense, no offence.

Here's why:

When you make a -CEV push as the big stack against your opponent HU, you are actually GIVING him chips, by definition. You can't do that and claim that you are decreasing the size of the smaller stack. That's absurd.


(Edit: you might claim that making a -CEV push at a certain spot as the big stack is actually better in terms of $EV than folding, due to chip-distribution considerations, but that's a completely different story)

[Jman28]

[ QUOTE ]

OK I have been thinking about your ideas Jman a few more minutes and I think they are complete nonsense, no offence.

[/ QUOTE ]

None taken. I disagree with you however.

[ QUOTE ]
Here's why:

When you make a -CEV push as the big stack against your opponent HU, you are actually GIVING him chips, by definition. You can't do that and claim that you are decreasing the size of the smaller stack. That's absurd.


[/ QUOTE ]

You are, in a sense, giving him chips, but it isn't that simple.

If we are in a situation with 300/600 blinds, and our push is going to be called 30% of the time, and the push is stil -cEV (compared to folding), we aren't simply giving him chips.

70% of the time, we are taking 900 chips. This puts us in the situation we are looking to get in (where they make more mistakes).

30% of the time, you are in a -ev gamble for a bunch of chips. This accounts for the -cEV of the play.

Giving them 'Sklansky chips' is not the same as giving them real chips.

I think this difference is most pronounced in the Lawanda example earlier in this thread:

[ QUOTE ]
You opponent is now Lawanda. She is a friendly woman, though pretty new to poker.

Chip Stacks
Hero: 6400
Lawanda: 3600

Blinds, 300/600.

Hero has 32o.

Lawanda is calling pushes right now with 22+,A2+,K2+,Q6o+,Q2s+,J9o+,J7s+,T8s+, (45% of hands), and pushing 22+,A2+,K2+,Q2+,J2+,T3o+,T2s+,95o+,93s+,86o+,84s+, 76o,75s+,65s (75% of hands).

ICM says a push here would be -EV (only -.125%)

However, Lawanda gets very scared when she gets below 3400 chips. When she has less than 3400 chips, she folds every hand except for QQ+ in the SB, and doesn't call a push without AA.

So, pushing, while slightly -EV according to ICM, would be best since you would immediately get Lawanda to under 3400 chips and then run over her from there.

[/ QUOTE ]

You must agree that while our push is -cEV compared to folding, we are not 'giving Lawanda chips' in the sense that you make it seem. We are, most of the time, taking a few chips.

[Jman28]

[ QUOTE ]


A "vendetta" against you because I got annoyed when you said something silly? Please.

I think you are simply misreading me. I sometimes get annoyed when people waste my time, but don't read too much into it. I'm never "angry." Never.

I didn't get annoyed with you until you asked "would I mind opening my mind" (in what seemed to me to be an indignant tone that I dare disagree with you) and then shoveled a bunch of crap in there.


[/ QUOTE ]

Oh, I totally understand getting annoyed at that. But, you had a tone from your first post in this and my other thread.

Whatever, I'm over it. No worries.

[Jman28]

After doing some thinking, I realize that the value of this heads up adjustment I'm suggesting is MUCH more pronounced when you are the big stack then when you are the small stack.

Since folding as the small stack does lead to greater chip disparity, which leads to more +EV opportunities for you, it still has some value. However, since these +EV opportunities will be pushing more, you will often quickly make the stacks more even, diminishing the advantage of the stack disparity.

When you are the big stack, and you push to increase stack disparity, you are making a play that will lead to more pushes, further increasing stack disparity, and further increasing your edge. This is why this play is much more valuable.

I believe that folding as the small stack, in situations where the cEV of the two plays are close, will have such a small effect that you can probably ignore it completely.

However, I still stand behind the idea that making pushes as the big stack which are even slightly -cEV, against average opponents, will be beneficial.

[eastbay]

[ QUOTE ]

However, I still stand behind the idea that making pushes as the big stack which are even slightly -cEV, against average opponents, will be beneficial.

[/ QUOTE ]

And I stand by my call of "bullshit" until you can demonstrate it with something more than hand waving.

eastbay

[Jman28]

[ QUOTE ]

After reading most of this thread, I think you are saying this (very simply put):

"It's good to make a mistake, if it causes your opponent to make a mistake."

However, nowhere in this thread you have shown that our opponent's mistake is indeed bigger than our own mistake (yes, it might be bigger, but might be smaller, who knows), and therefore, nobody can really know if using this general advice is good or bad.

[/ QUOTE ]

I have not shown how large our opponents mistake is because at this time, I have no way to measure it.

I have been careful to suggest that this play only be made when it is a very small 'mistake' from cEV standpoint. So, the 'mistakes' I am suggesting making our very small ones. I clearly was sensitive to the fact that your 'mistake' must be smaller than the mistakes it will lead to by your opponent.

Again, I don't know how large our 'mistakes' can be, since I haven't quantified the value our opponents future mistakes.

Does it makes sense at least, to lean toward the play which increases your opponents future errors if the two plays are nuetral in cEV? That was the main idea I started with.

[Jman28]

[ QUOTE ]
[ QUOTE ]

However, I still stand behind the idea that making pushes as the big stack which are even slightly -cEV, against average opponents, will be beneficial.

[/ QUOTE ]

And I stand by my call of "bullshit" until you can demonstrate it with something more than hand waving.

eastbay

[/ QUOTE ]

What do you want me to do eastbay? What do you want me to do?

[Jman28]

Did you disagree with this?...

[ QUOTE ]


I am saying, that assuming that players play the same, in that they make the same plays based on blind size and effective stack size, the relationship must be linear. I believe that playing both players playing optimally (pushing and calling the equilibrium ranges you discuss in your 'Mind The Gap' tutorial) will result in a linear model.


[/ QUOTE ]

[eastbay]

[ QUOTE ]
Did you disagree with this?...

[ QUOTE ]


I am saying, that assuming that players play the same, in that they make the same plays based on blind size and effective stack size, the relationship must be linear. I believe that playing both players playing optimally (pushing and calling the equilibrium ranges you discuss in your 'Mind The Gap' tutorial) will result in a linear model.


[/ QUOTE ]

[/ QUOTE ]

I think it is probably true that optimal play HU gives a linear equity, yes (or very nearly so).

Someone even made a very mathematical post that claimed they had proved it. I never pursued trying to verify it, because it used some terminology that I was unfamiliar with.

eastbay

[eastbay]

One way to settle the issue definitively is to define two strategies fully (there might be some bickering over how to define these mistakes you're assuming that people make short-stacked) and do monte carlo simulation.

It's probably -$EV for you to go to the trouble, though.

eastbay

[Jman28]

[ QUOTE ]
One way to settle the issue definitively is to define two strategies fully (there might be some bickering over how to define these mistakes you're assuming that people make short-stacked) and do monte carlo simulation.

It's probably -$EV for you to go to the trouble, though.

eastbay

[/ QUOTE ]

Well, I have issues about proving myself right. How long exactly would this take me? Would I even be able to do it or would I need to first study simulations for 2 years?

[eastbay]

[ QUOTE ]
[ QUOTE ]
One way to settle the issue definitively is to define two strategies fully (there might be some bickering over how to define these mistakes you're assuming that people make short-stacked) and do monte carlo simulation.

It's probably -$EV for you to go to the trouble, though.

eastbay

[/ QUOTE ]

Well, I have issues about proving myself right. How long exactly would this take me? Would I even be able to do it or would I need to first study simulations for 2 years?

[/ QUOTE ]

Can you program in a compiled language like C or C++? It's really not that hard, it just takes a little time.

eastbay

[Jman28]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
One way to settle the issue definitively is to define two strategies fully (there might be some bickering over how to define these mistakes you're assuming that people make short-stacked) and do monte carlo simulation.

It's probably -$EV for you to go to the trouble, though.

eastbay

[/ QUOTE ]

Well, I have issues about proving myself right. How long exactly would this take me? Would I even be able to do it or would I need to first study simulations for 2 years?

[/ QUOTE ]

Can you program in a compiled language like C or C++?

eastbay

[/ QUOTE ]

Nope. I'd like to learn anyway, but that would take a while.

If I have a friend who can, how long of a project are we talking here?

[microbet]

I don't see why the language has to be compiled. I think particularly for this project the path with the shortest development time should be taken and I don't think that would be C or C++.

[eastbay]

[ QUOTE ]

Nope. I'd like to learn anyway, but that would take a while.

If I have a friend who can, how long of a project are we talking here?

[/ QUOTE ]

It really depends a hell of a lot on your friend's skill. One programmer can take 20x as long as another on the same task.

eastbay

[eastbay]

[ QUOTE ]
I don't see why the language has to be compiled. I think particularly for this project the path with the shortest development time should be taken and I don't think that would be C or C++.

[/ QUOTE ]

We're talking about tiny differences here. The sample sizes (tournaments, which would be many hands each) required would be enourmous to get statistically reliable results. Then there'd be parameter spaces to be explored for each one of those results. Execution time would dominate development time. I've played with this stuff quite a bit.

eastbay

[Jman28]

[ QUOTE ]
[ QUOTE ]

Nope. I'd like to learn anyway, but that would take a while.

If I have a friend who can, how long of a project are we talking here?

[/ QUOTE ]

It really depends a hell of a lot on your friend's skill. One programmer can take 20x as long as another on the same task.

eastbay

[/ QUOTE ]

Cool. I'll look into it a little. Thanks.

I'm gone for the night, so no more responses today. Everyone please feel free to keep arguing with me while I'm gone. I'll get to it.

[microbet]

[ QUOTE ]
It really depends a hell of a lot on your friend's skill. One programmer can take 20x as long as another on the same task.

[/ QUOTE ]

I had a job as a web programmer and there was this guy who had me pretty much do all his programming. This wasn't that big a deal though because he would have me 'help' him with a line or two of code and then a week or so later he would have me 'help' him with the very next line or two.

No one besides me in that part of the company had a clue and he was widely regarded as a very smart guy and good programmer.

[microbet]

I don't know about his friend, but if he has to do it, he has to learn the language and development time will be huge. Also, development time is human time, which in some rare cases is more valuable than computer time. Plus, it's almost certainly a one-off thing with no practical purpose or deadline. Also, if you do have a purpose to reuse it a lot it isn't too hard to rewrite and/or a lot of easier to learn and develop languages can handle extensions in C for the crunching (I know this program is mostly crunching).

Ok, Ok, I'm just a PHP/Perl hack, I admit it.

[eastbay]

[ QUOTE ]
I don't know about his friend, but if he has to do it, he has to learn the language and development time will be huge. Also, development time is human time, which in some rare cases is more valuable than computer time. Plus, it's almost certainly a one-off thing with no practical purpose or deadline. Also, if you do have a purpose to reuse it a lot it isn't too hard to rewrite and/or a lot of easier to learn and develop languages can handle extensions in C for the crunching (I know this program is mostly crunching).

Ok, Ok, I'm just a PHP/Perl hack, I admit it.

[/ QUOTE ]

All valid points.

On the other hand...

I know a little bit about doing simulation work. If a code can turn around a result in an hour vs overnight, the difference in utility is vast. When it takes a day to turn around a result, it's too easy to forget exactly what your last run was supposed to show, and just give up. It's a human factors thing. Nobody has the patience to get good results out of a slow code.

So there's a strong nonlinear utility to fast execution times for these kinds of sim tools.

eastbay

[microbet]

Well, I'm working on a project where I may be learning this lesson the hard way. That'll be ok though, lessons learned the hard way are well learned. At any rate I actually think my development time will be shorter writing it in PHP first and then translating to C, than writing in C in the first place.

[PrayingMantis]

[ QUOTE ]
[ QUOTE ]
When you make a -CEV push as the big stack against your opponent HU, you are actually GIVING him chips, by definition. You can't do that and claim that you are decreasing the size of the smaller stack. That's absurd.

[/ QUOTE ]You are, in a sense, giving him chips, but it isn't that simple.

If we are in a situation with 300/600 blinds, and our push is going to be called 30% of the time, and the push is stil -cEV (compared to folding), we aren't simply giving him chips.

70% of the time, we are taking 900 chips. This puts us in the situation we are looking to get in (where they make more mistakes).

30% of the time, you are in a -ev gamble for a bunch of chips. This accounts for the -cEV of the play. You're account for what happens 70% of the time as opposed to what happens 30% of the time still adds up to simply giving your opponent chips _on avarage_.

It's not some imaginary "sklansky chips".

Giving them 'Sklansky chips' is not the same as giving them real chips.

[/ QUOTE ]

Jman, I think you're stepping deep into a logical and mathematical limbo here. In other words: you are making less and less sense. I think you have to address these theoretical points way before you are getting into any simulation thing.

Look, the way you are describing what happens 70% of the time as opposed to what happens 30% is meaningless, since you are still giving him chips _on avarage_.

These are not imaginary "sklansky chips", that are different from "real chips". This is absolutely ridiculous thinking. You are going against the fundamental idea of EV here (I'm not sure if you fully understand that that's what you're actually doing). You don't need sklansky and his "imaginary chips" to see this.

The fact that there might be strange cases, that you enjoy inventing, that for them making -EV moves might be right because it will DEFINITELY cause your opponent to make bigger -EV moves down the road, has very little to do with all this. That's very simple to understand, no need to invent a "theorem" or something for this. But these are your invented cases, which are fun, yet are very far from any poker reality.

And now for another new point that you make later on:

[ QUOTE ]
After doing some thinking, I realize that the value of this heads up adjustment I'm suggesting is MUCH more pronounced when you are the big stack then when you are the small stack.

[/ QUOTE ]

That's very funny, because now all you're actually saying, is nothing more than this: "It might be correct to make -CEV moves that increase your stack's size". well, Doh? If they increase your stack's size they are +CEV by definition.

[Jman28]

[ QUOTE ]
Jman, I think you're stepping deep into a logical and mathematical limbo here. In other words: you are making less and less sense. I think you have to address these theoretical points way before you are getting into any simulation thing.


[/ QUOTE ]

I think I've been explaining myself fairly well, but I must not be. You must not understand what I am thinking because my logic is entirely sound. I am sure of that.

[ QUOTE ]

Look, the way you are describing what happens 70% of the time as opposed to what happens 30% is meaningless, since you are still giving him chips _on avarage_.



These are not imaginary "sklansky chips", that are different from "real chips". This is absolutely ridiculous thinking.

[/ QUOTE ]

It is entirely not meaningless. The advantages I'm talking about have to do with chip stack disparities. If I have 6k chips vs. 4k chips, what matters is how many chips I have after this play is made. What does not matter is the fact that say, I lose 15 chips on average. What matters is that 70% of the time I gain X chips, 10% of the time I gain Y chips, and 20% of the time I lose Z chips.

What matters is the chip stack situation after the play, which will actually NEVER be 5985 vs. 4015. Therefore, the average chip equity is not the whole story, and what actually happens is not meaningless.

My thinking is not at all ridiculous, and I'm suprised that you don't see this.

[ QUOTE ]

The fact that there might be strange cases, that you enjoy inventing, that for them making -EV moves might be right because it will DEFINITELY cause your opponent to make bigger -EV moves down the road, has very little to do with all this. That's very simple to understand, no need to invent a "theorem" or something for this. But these are your invented cases, which are fun, yet are very far from any poker reality.

[/ QUOTE ]

These cases, while entirely unrealistic, are not as irrelevant as you seem to think. These fictional characters make mistakes based on stack size, which our real life opponents do too. Our opponents just aren't as exact, farfetched, and predictable about theirs.


[ QUOTE ]
And now for another new point that you make later on:

[ QUOTE ]
After doing some thinking, I realize that the value of this heads up adjustment I'm suggesting is MUCH more pronounced when you are the big stack then when you are the small stack.

[/ QUOTE ]

That's very funny, because now all you're actually saying, is nothing more than this: "It might be correct to make -CEV moves that increase your stack's size". well, Doh? If they increase your stack's size they are +CEV by definition.


[/ QUOTE ]

No, that is not what I'm saying at all. I am not talking about +cEV moves. I am talking about moves that are -cEV. Remember from above that cEV is an average and is not the entire story.

I am talking about moves that on average lose chips, but the majority of the time gain a small amount of chips. Therefore, the majority of the time, they lead to the advantages I'm talking about.

I can't see how you don't understand this. Clearly you must agree that in the 'strange' Lawanda case, it is correct to make a -cEV push. What?!? How? A -cEV move that is good for you? This is the same exact concept that you apparently can't grasp.

As strange as the case is, it explains how it is possible to make a push that is -cEV but still correct, and NOT +cEV.


I think that my posts have a tone of 'hey, check this idea out. What do you think?' while some posters have more of a tone of 'This is fact.' or 'Haha. You're obviously wrong.'

I think this leads to some of my points being taken too lightly, and me sounding unsure of myself.

I've been thinking about this a lot lately. I am sure that my logic is sound. I am sure that I am correct and that these advantages that I am talking about exist.

I will continue, as I said in a previous post, to employ these strategies in my game. I should not care that not everyone agrees with me, but I honestly do for some reason. If I can think of a way to explain it so that you will understand it, I'll post it.

[PrayingMantis]

Jman, I'm sorry, but I understand everything you're saying with 100% certainty, and I repeat that your logic is very very confused. It's not that you're advocating some advanced concpet, you are simply confusing some contradicting ideas and somehow arrive at the conclusion you want to arrive at.

You sound like a clever guy, so it's not about disrespecting your intelligence or anything, but I suspect you don't fully comprehend the meaning of the term "EV", and that's part of the reason you're using it in some very illogical manners (there are other reasons).

I'll try to address your last points, but in my exprience in such discussions (as I did had a few.....), I have a feeling you won't be convinced, which is fine, but it is still NOT a matter of opinion, or of misunderstanding you.




[ QUOTE ]
It is entirely not meaningless. The advantages I'm talking about have to do with chip stack disparities. If I have 6k chips vs. 4k chips, what matters is how many chips I have after this play is made. What does not matter is the fact that say, I lose 15 chips on average. What matters is that 70% of the time I gain X chips, 10% of the time I gain Y chips, and 20% of the time I lose Z chips.

What matters is the chip stack situation after the play, which will actually NEVER be 5985 vs. 4015. Therefore, the average chip equity is not the whole story, and what actually happens is not meaningless.

[/ QUOTE ]

You have a very confused idea of EV, that's all I can actually say. If you really think that there's a differece between what you'll have in "reality", and what you'll have on "avarage" according to some simple EV calcultion, you don't understand the concept of EV. It is difficult to discuss your "ideas" when the way you are talking about EV is so confused (BTW, you are making some similar fundamental mistakes in other posts on this thread, not only as a reply to my posts).

I'll move to the second part of your post, in which you deal with your last point (after I wrote: all you're actually saying, is nothing more than this: "It might be correct to make -CEV moves that increase your stack's size". well, Doh? If they increase your stack's size they are +CEV by definition.)

In reply you say:

[ QUOTE ]
No, that is not what I'm saying at all. I am not talking about +cEV moves. I am talking about moves that are -cEV. Remember from above that cEV is an average and is not the entire story.

[/ QUOTE ]

Again, you don't seem to understand what EV means. If you make a -CEV move, the result is BY DEFINTION a decrease in your stack size (this is when we are talking about specific EV for a move WITHOUT comparing it to other moves. A move can be -EV but still +EV in comparison to another one. Note that this is NOT what we're talking about).

Therefore, what you are saying is essentially nonsense.

[ QUOTE ]
I am talking about moves that on average lose chips, but the majority of the time gain a small amount of chips. Therefore, the majority of the time, they lead to the advantages I'm talking about.


[/ QUOTE ]

I'm sorry, I really hate to repeat it, but you don't understand the meaning of EV.

[ QUOTE ]
I can't see how you don't understand this. Clearly you must agree that in the 'strange' Lawanda case, it is correct to make a -cEV push. What?!? How? A -cEV move that is good for you? This is the same exact concept that you apparently can't grasp.

[/ QUOTE ]

Lawanda's example, as presented, is confused, for the reasons already mentioned. And still, it's very far from being a good example for what you're trying to say, because in that case, you might make a -EV move that will cause your opponent to make some clear and bigger -EV mistakes down the road the big majority of the time. So what you're actually doing is RISKING giving her chips (i.e, sacrificing chips), for this purpose. Saying that you are decreasing her stack is confused thinking.

[ QUOTE ]
As strange as the case is, it explains how it is possible to make a push that is -cEV but still correct, and NOT +cEV.


[/ QUOTE ]

I'm not arguing with the idea that a -CEV push might be correct in some very specific circumstances, HOWEVER, claiming that you are actually WIDENING the gap between the stacks by doing so (as the big stack), is completely absurd.

[Jman28]

[ QUOTE ]
If you really think that there's a differece between what you'll have in <font color="green"> "reality"</font>, and what you you'll have on <font color="blue">"avarage"</font> according to some simple EV calcultion, you don't understand the concept of EV.

[/ QUOTE ]

Okay, I have 1000 chips.

I make a push that 80% of the time gains 100 chips, and 20% of the time loses 405 chips.

On <font color="blue">average</font>, I lose 1 chip.

However, I never actually lose 1 chip. I never have 999 chips the next hand. Ever. Do you disagree?

I will often have 1100 chips and sometimes have 595 chips. These are the outcomes in '<font color="green"> reality</font>'

I really think that is a difference. Really.

[ QUOTE ]
If you make a -CEV move, the result is BY DEFINTION a decrease in your stack size

[/ QUOTE ]

On average.

In the above example, 80% of the time I increase my stack slightly, and 20% of the time I decrease it greatly.

I usually increase my stack. Do you disagree?

[Jman28]

[ QUOTE ]

Lawanda's example... It's very far from being a good example for what you're trying to say, because in that case, you might make a -EV that will cause your opponent to make some clear and bigger -EV mistakes down the road the big majority of the time.

[/ QUOTE ]

What? This is exactly the same as what I'm trying to say except that it is much more clear cut. That is the point of examples like these. They illustrate a concept at work in a much more obvious setting.

In fact, I can express my exact idea using your own words to describe the Lawanda example.

"you might make a -EV [play] that will cause your opponent to make some ... -EV mistakes down the road"

How is it not a good example? It leads you right to the point I'm trying to make, and shows that point at work in an obvious way.

[PrayingMantis]

[ QUOTE ]
I usually increase my stack. Do you disagree?

[/ QUOTE ]

Of course not (that is, I'm not disagreeing). Note also that this is a good reason to make -EV moves in a lot of situations in poker, because there are often cases in which "you are usually increasing your stack". The sad fact is that you are losing money by doing them, i.e, you are DECREASING your stack.

I don't have an intention to keep this discussion going. As I said, you have a very confused idea of EV (the way you are thinking about "in reality" as opposed to "in avarage", etc), and I don't think this is getting anywhere. I think that I've made my points quite clear, and there's not much to add here as far as I'm concerned.

[Jman28]

[ QUOTE ]
I don't have an intention to keep this discussion going. As I said, you have a very confused idea of EV (the way you are thinking about "in reality" as opposed to "in avarage", etc), and I don't think this is getting anywhere. I think that I've made my points quite clear, and there's not much to add here as far as I'm concerned.

[/ QUOTE ]

That's fine, but could you please explain to me before you leave how the 'average' and 'reality' are not different here?...

[ QUOTE ]
[ QUOTE ]
If you really think that there's a differece between what you'll have in <font color="green"> "reality"</font>, and what you you'll have on <font color="blue">"avarage"</font> according to some simple EV calcultion, you don't understand the concept of EV.

[/ QUOTE ]

Okay, I have 1000 chips.

I make a push that 80% of the time gains 100 chips, and 20% of the time loses 405 chips.

On <font color="blue">average</font>, I lose 1 chip.

However, I never actually lose 1 chip. I never have 999 chips the next hand. Ever. Do you disagree?

I will often have 1100 chips and sometimes have 595 chips. These are the outcomes in '<font color="green"> reality</font>'

[/ QUOTE ]

[PrayingMantis]

[ QUOTE ]
That's fine, but could you please explain to me before you leave how the 'average' and 'reality' are not different here?...


[/ QUOTE ]

That's really beyond my powers here and now. It's too fundamental.

I'll say just one more thing, that has something to do with it.

[ QUOTE ]
I make a push that 80% of the time gains 100 chips, and 20% of the time loses 405 chips.

[/ QUOTE ]

It is really still very very unclear (despite your argument that villain makes somewhat bigger mistakes when his stack is shorter) why the (fewer) times in which you actually lose much more chips than you gain when you gain, are not in fact working against you when you use this "tactic", because clearly you are letting villain get much deeper into a territory in which he'll be making less mistakes.

And now I leave.

[Jman28]

A consequence of my idea, which I just realized, is that when heads up, with an average Party SNG opponent, the value of chips is not constant.

When you are short stacked, the chips you lose are more valuable than the chips you gain.

When you are ahead, the chips you gain are more valuable than the chips you lose.

Therefore you will want to gamble more as a big stack, and less as a short stack, which is consistent with what I've been advocating thus far.

[Jman28]

[ QUOTE ]

It is really still very very unclear (despite your argument that villain makes somewhat bigger mistakes when his stack is shorter) why the (fewer) times in which you actually lose much more chips than you gain when you gain, are not in fact working against you when you use this "tactic", because clearly you are letting villain get much deeper into a territory in which he'll be making less mistakes.


[/ QUOTE ]

A good point that I have realized recently. What I decided is that your opponents mistakes become greater much faster (accelerate if you will) as you get toward the largest stack disparities. Therefore, it is more valuable to take them from 3k chips to 2k chips than it is harmful for them to go from 3k chips to 4k chips.

[parappa]

[ QUOTE ]
On <font color="blue">average</font>, I lose 1 chip.

However, I never actually lose 1 chip. I never have 999 chips the next hand. Ever. Do you disagree?

I will often have 1100 chips and sometimes have 595 chips. These are the outcomes in '<font color="green"> reality</font>'

I really think that there is a difference. Really.


[/ QUOTE ]

This is an illusion. No one will be able to argue you out of it. It is absolutely fundamental and there are premises, rather than arguments, supporting this claim. You are going to have a very difficult time doing anything other than hand-waving to support this. But if you are right and can prove it, the accepted thinking on these matters will have to change. However, based on all work to date, this idea is wrong.

I'd suggest that instead of coming up with anecdotes to illustrate your points, that you come up with a clearly defined, logical hypothesis that can fit into a couple of sentences and is testable.

I'd also suggest looking into the enormous work that's been done on modifying EV through betting sequences in casino games. The proponents of such ideas (which are incorrect, but, I think that the ideas themselves extremely seductive and well worth study) make claims that are extremely similar to the one above.

[PrayingMantis]

Just a last come-back to this thread.

After some hint I got from another poster, I have just understood now why you have colored the word "average" in blue. Originally I thought you were trying to emphasize your point, but obviously, it was some unique way to point out my spelling mistakes...

Well, I'm sorry about mispelling this word, but English isn't my first language, I basically only read and write in it (very few opportunities to actually talk, more opportunities to listen), and these forums are almost the only place where I use my English these days. I write here in English without checking my spelling, because it will take too much time.

So I apologize for writing "avarage" instead of "average" multiple times on this thread. /images/graemlins/grin.gif

(Edit: and for any other mistake)

BTW, Jman, next time you can simply tell me that I'm not spelling some word right. I think it's a much better way.

[microbet]

Jman, is there any connection to block theory?

PrayingMantis, your english is great. It has never occurred to me that it wasn't your first language.

[YourFoxyGrandma]

Yeah, your English is incredible, probably a bit better than mine and I was born here. Also, I don't think Jman was correcting your spelling mistakes. He colored average in blue and reality in green in quoting your post and in his post, I think just for clarification purposes.

As far as the actual discussion, I haven't been qualified to comment for a long time, so I'll butt out.

[Jman28]

[ QUOTE ]
Just a last come-back to this thread.

After some hint I got from another poster, I have just understood now why you have colored the word "average" in blue. Originally I thought you were trying to emphasize your point, but obviously, it was some unique way to point out my spelling mistakes...

Well, I'm sorry about mispelling this word, but English isn't my first language, I basically only read and write in it (very few opportunities to actually talk, more opportunities to listen), and these forums are almost the only place where I use my English these days. I write here in English without checking my spelling, because it will take too much time.

So I apologize for writing "avarage" instead of "average" multiple times on this thread. /images/graemlins/grin.gif

(Edit: and for any other mistake)

BTW, Jman, next time you can simply tell me that I'm not spelling some word right. I think it's a much better way.

[/ QUOTE ]

PM, your first impression was correct. I did not intend to point out your spelling mistake, but to highlight the two terms.

I think that pointing out spelling mistakes in an argument is stupid, and I'm sorry that it came across that way.

I make spelling mistakes all the time.

[Jman28]

[ QUOTE ]

Jman, is there any connection to block theory?


[/ QUOTE ]

I wish I could tell you. Probably there is, but I still don't fully understand the block theory myself, other than the point that sometimes the chips you lose are less valuable than the chips you stand to gain. In that respect, I suppose, it is similar.

At this point I've almost confused myself with what I'm saying as I have just been attempting to respond to arguments rather than think about the theory itself. Gimme a little time to regather my thoughts.

[MegaBet]

I've really been slumping in heads up for the past few days. I just can't seem to win! It seems like I'll either get caught on a steal and lose, the guy will call with a very mediocre hand which is slightly better than mine and I lose, or I'll try flop play and the guy will hit his card or get a runner runner and I lose, or I push with AK, QQ etc and I lose.

This culminated in me being 0-10 in heads up matches today and something like 5-28 in the last 3 days. I really want to find out if this is a leak or just plain old variance. To be honest, I am surprised I broke even over this run.

Anyway, the point of this post is to say thanks to Jman28 and all the others who have contributed here. I'm actually gonna read all these replies and hopefully get my back on target /images/graemlins/grin.gif

[scalafab]

You guys are going on in theorys about ev(+-) in a heads up situation without considering many details.
Consider this
Uncle Conrad with call you with any two cards.Knowing that you will push with any two it comes down to who's going to get the better pocket cards.You can play Black jack and the results in the headsup will be similar.
The other side it's that if I know you push every two I will call you with any middle strength hands and I will fold garbage.Than if you 94s will win against my A6 its not ev but its luck.

[PrayingMantis]

[ QUOTE ]
PM, your first impression was correct. I did not intend to point out your spelling mistake, but to highlight the two terms.

I think that pointing out spelling mistakes in an argument is stupid, and I'm sorry that it came across that way.

I make spelling mistakes all the time.

[/ QUOTE ]

Well then, I guess I made a wrong read there... /images/graemlins/frown.gif /images/graemlins/grin.gif

I apologize for accusing you, Jman (I hope accusing is the right word.)

[dfan]

Jman, you are correct that the fundamental reality is that for a particular action you will win X chips x% of the time, and lose Y chips y% of the time.

In most poker situations we can predict the long term outcome of the random process with the summary statistics like average win/loss or EV.

That is because in most poker situations the outcome of interest (total money or chips won) is a linear metric. If you win 20 bucks you are twice as well off than if you won 10 bucks.

But when the outcome of a process is NOT linear, then EV is like averaging dollars and pesos without converting the currencies first.

You are arguing that the outcome of interest (probability of winning tournament) is not a linear function of your stack size in a HU match. If you are correct then you are also correct in your argument that cEV is not an accurate metric to evaluate the long term outcome of this random process.

Posters who are patronizing you by saying you "clearly don't understand EV" seem to themselves not understand this limitation of EV. It is annoying to me when they do that, so I'm just posting this to let you know that this professor of statistics says you are correct and they are wrong.

[PrayingMantis]

[ QUOTE ]
Jman, you are correct that the fundamental reality is that for a particular action you will win X chips x% of the time, and lose Y chips y% of the time.

In most poker situations we can predict the long term outcome of the random process with the summary statistics like average win/loss or EV.

That is because in most poker situations the outcome of interest (total money or chips won) is a linear metric. If you win 20 bucks you are twice as well off than if you won 10 bucks.

But when the outcome of a process is NOT linear, then EV is like averaging dollars and pesos without converting the currencies first.

You are arguing that the outcome of interest (probability of winning tournament) is not a linear function of your stack size in a HU match. If you are correct then you are also correct in your argument that cEV is not an accurate metric to evaluate the long term outcome of this random process.

Posters who are patronizing you by saying you "clearly don't understand EV" seem to themselves not understand this limitation of EV. It is annoying to me when they do that, so I'm just posting this to let you know that this professor of statistics says you are correct and they are wrong.

[/ QUOTE ]

Ok, although I said I'm leaving, I'm back to this thread, because obviously this post was directed mostly to me (outside of Jman), and so it deserves a reply.

First I'm not a professor of statistics, very far from it.

Now to your points:

I understand what you are saying, but with all due respect it isn't relevant to the points Jman was making. Jman's points were wrong from a clear logical perspective. He was basically saying that by making a move that is -CEV (in his own words) you are increasing your stack size. Later on he agreed that you are increasing it only some percentage of the time, but now the whole "tactic" got into a mess, because clearly the rest of the time you are giving chips to your opponent and (even according to Jman's ideas) you are helping him quite a lot.

I fully understand that there could be models for which "the outcome of interest (probability of winning tournament) is not a linear function of your stack size in a HU match". These ideas were discussed on this forum and elsewhere several times. But again, that wasn't the issue of this discussion at all. Jman was (like most of us here) basing his idea on the simple model in which CEV=$EV for HU (and as an evidence, he even used the ICM [he didn't need to, of course] to illustrate his points), and thus he wasn't at all arguing with it but only making different claims with regard to CEV alone (without any relation to the outcome of the interest), IN this model.

I'm sorry if I sounded patronizing, and I am certainly aware of limitations of EV in many cases. However, I still stand behind the points I've made on this thread.

[LearnedfromTV]

[ QUOTE ]



Now to your points:

I understand what you are saying, but with all due respect it isn't relevant to the points Jman was making. Jman's points were wrong from a clear logical perspective. He was basically saying that by making a move that is -CEV (in his own words) you are increasing your stack size. Later on he agreed that you are increasing it only some percentage of the time, but now the whole "tactic" got into a mess, because clearly the rest of the time you are giving chips to your opponent and (even according to Jman's ideas) you are helping him quite a lot.

I fully understand that there could be models for which "the outcome of interest (probability of winning tournament) is not a linear function of your stack size in a HU match". These ideas were discussed on this forum and elsewhere several times. But again, that wasn't the issue of this discussion at all. Jman was (like most of us here) basing his idea on the simple model in which CEV=$EV for HU (and as an evidence, he even used the ICM [he didn't need to, of course] to illustrate his points), and thus he wasn't at all arguing with it but only making different claims with regard to CEV alone (without any relation to the outcome of the interest), IN this model.

I'm sorry if I sounded patronizing, and I am certainly aware of limitations of EV in many cases. However, I still stand behind the points I've made on this thread.

[/ QUOTE ]

J-Man is arguing that the value of having 1100 chips 80% of the time and 595 chips 20% of the time is greater than the value of having 1000 chips 100% of the time. (In reality, by choosing not to push you are folding and leaving yourself with less than 1000 chips but this is accounted for in the EV calculation so we can use the simple example).

So 1100 80% + 595 20% &gt; 1000 100%. Clearly this only works if chip equity and $ equity aren't linear. It seems J-Man is assuming they are by invoking a linear model in his argument. I think this contradiction is resolved as follows:

The reason the 1100/595 80/20 option is better, according to J-Man, is that the 80% of the time you get to 1100, your opponent modifes his hand range calling requirements such that we can push more hands profitably.

I think what most people who are disagreeing are saying is that the standard push/fold model already takes into account changes in the opponents calling range via adjustments in our pushing range. In other words, so long as we properly adjust our pushing requirements when the opponent adjusts his calling requirements, there is no such thing as an opponent making a "bigger" mistake at a given stack size... on every hand we can make an optimal play given his calling requirements so there is no way that having 1100 chips can be more than 1.1 times as valuable as having 1000 chips.

However, I think J-Man is trying to argue that if you are really close to the threshold for pushing any 2 *and* really close to a threshold where your opponent significantly changes his calling requirements and starts folding more, then there can be a nonlinear jump in chip value.

In other words, lets say the blinds and chip stacks are such that you should push any hand but 32 according to the standard model.. You have 32. If your opponent folds, not only do you move into push any two territory, but now he is much more likely to fold than he would have been had you folded and waited until the next hand. In that case the 80% chance of going to 1100 overrides the 20% of falling to 595.

Edited to add: The reason the "push any two" threshold is important is that this is the only point at which you can't fully compensate for an opponent tightening his calling standards by widening your push range. You can't push more than any two, although I'm sure a few here would like to try.

I have no idea if he is right, just my feeble attempt to parse the debate.

[PrayingMantis]

[ QUOTE ]
[ QUOTE ]
Now to your points:

I understand what you are saying, but with all due respect it isn't relevant to the points Jman was making. Jman's points were wrong from a clear logical perspective. He was basically saying that by making a move that is -CEV (in his own words) you are increasing your stack size. Later on he agreed that you are increasing it only some percentage of the time, but now the whole "tactic" got into a mess, because clearly the rest of the time you are giving chips to your opponent and (even according to Jman's ideas) you are helping him quite a lot.

I fully understand that there could be models for which "the outcome of interest (probability of winning tournament) is not a linear function of your stack size in a HU match". These ideas were discussed on this forum and elsewhere several times. But again, that wasn't the issue of this discussion at all. Jman was (like most of us here) basing his idea on the simple model in which CEV=$EV for HU (and as an evidence, he even used the ICM [he didn't need to, of course] to illustrate his points), and thus he wasn't at all arguing with it but only making different claims with regard to CEV alone (without any relation to the outcome of the interest), IN this model.

I'm sorry if I sounded patronizing, and I am certainly aware of limitations of EV in many cases. However, I still stand behind the points I've made on this thread.

[/ QUOTE ] J-Man is arguing that the value of having 1100 chips 80% of the time and 595 chips 20% of the time is greater than the value of having 1000 chips 100% of the time. (In reality, by choosing not to push you are folding and leaving yourself with less than 1000 chips but this is accounted for in the EV calculation so we can use the simple example).

So 1100 80% + 595 20% &gt; 1000 100%. Clearly this only works if chip equity and $ equity aren't linear. It seems J-Man is assuming they are by invoking a linear model in his argument. I think this contradiction is resolved as follows:

The reason the 1100/595 80/20 option is better, according to J-Man, is that the 80% of the time you get to 1100, your opponent modifes his hand range calling requirements such that we can push more hands profitably.

I think what most people who are disagreeing are saying is that the standard push/fold model already takes into account changes in the opponents calling range via adjustments in our pushing range. In other words, so long as we properly adjust our pushing requirements when the opponent adjusts his calling requirements, there is no such thing as an opponent making a "bigger" mistake at a given stack size... on every hand we can make an optimal play given his calling requirements so there is no way that having 1100 chips can be more than 1.1 times as valuable as having 1000 chips.

However, I think J-Man is trying to argue that if you are really close to the threshold for pushing any 2 *and* really close to a threshold where your opponent significantly changes his calling requirements and starts folding more, then there can be a nonlinear jump in chip value.

In other words, lets say the blinds and chip stacks are such that you should push any hand but 32 according to the standard model.. You have 32. If your opponent folds, not only do you move into push any two territory, but now he is much more likely to fold than he would have been had you folded and waited until the next hand. In that case the 80% chance of going to 1100 overrides the 20% of falling to 595.

Edited to add: The reason the "push any two" threshold is important is that this is the only point at which you can't fully compensate for an opponent tightening his calling standards by widening your push range. You can't push more than any two, although I'm sure a few here would like to try.

I have no idea if he is right, just my feeble attempt to parse the debate

[/ QUOTE ]

That's a nice interpretaion, although still very very obscure (BTW, in a sense it is not very different from some of Gigabet's ideas, that were presented here in the past).

However, there's one simple problem: that's NOT what Jman was claiming on this thread (except for maybe in one of his very last posts).

This is the idea that was repeated again and again, from the beginning of this discussion: (I quote from an earlier post by Jman, titled "CONCLUSION OF MY THEORY IN PLAIN ENGLISH" (the capitals by Jman)):

[ QUOTE ]
When the EV difference between pushing and folding are minimal, and you are heads up, err on the side that will decrease the size of the smallest stack (increase stack disparity).

[/ QUOTE ]

That is ALL. That is the theory, and as presented in this thread again and again IT DOESN'T MAKE SENSE, period. It is pure and absolute nonsense.

Of course you can "modify" it and word it differently (As Jman started doing as a reply to one of my last posts) and then come up with an explanation for why in fact you gain more the times you win chips than the times you lose, or why in fact it's only relevant when you are big stack or whatever, etc etc etc etc, but this calls for a whole new discussion (in the spirit of Giga's posts, maybe), in which you will discover that you need a completely new model for the EV of HU play, a thing that is way beyond what was suggested on this thread.

[curtains]

How come this thread never stops? Poker is not this complicated.

[PrayingMantis]

Listen to curtains. /images/graemlins/laugh.gif

[LearnedfromTV]

[ QUOTE ]

That's a nice interpretaion, although still very very obscure (BTW, in a sense it is not very different from some of Gigabet's ideas, that were presented here in the past).

However, there's one simple problem: that's NOT what Jman was claiming on this thread (except for maybe in one of his very last posts).

This is the idea that was repeated again and again, from the beginning of this discussion: (I quote from an earlier post by Jman, titled "CONCLUSION OF MY THEORY IN PLAIN ENGLISH" (the capitals by Jman)):

[ QUOTE ]
When the EV difference between pushing and folding are minimal, and you are heads up, err on the side that will decrease the size of the smallest stack (increase stack disparity).

[/ QUOTE ]

That is ALL. That is the theory, and as presented in this thread again and again IT DOESN'T MAKE SENSE, period. It is pure and absolute nonsense.

Of course you can "modify" it and word it differently (As Jman started doing as a reply to one of my last posts) and then come up with an explanation for why in fact you gain more the times you win chips than the times you lose, or why in fact it's only relevant when you are big stack or whatever, etc etc etc etc, but this calls for a whole new discussion (in the spirit of Giga's posts, maybe), in which you will discover that you need a completely new model for the EV of HU play, a thing that is way beyond what was suggested on this thread.

[/ QUOTE ]

I suppose I should just let the thread die but I find theoretical crap like this interesting and liked thinking through the arguments people were making. Anyway, I agree that through most of the thread J-Man is saying something stronger than my interpretation, basically that it is a good idea to try to manipulate your opponent's future calling range by making a -EV push even when outside the extreme push any 2 threshold. I think he's wrong to think that this is the case because an optimal strategy will exist each of the new possible stack scenarios. As explained in my last postin the 23 example, I think you can make an exception in the case where you are nearing the push any two threshold. So, I think he might be on to something, albeit something that is more theoretical than practical, if he restricts himself to the case I talked about.

Also, although I do see the superficial similarities to the Gigabet blocks theory, I am pretty sure what Gigabet was saying wouldn't apply in a heads up setting. My understanding was that the advantages of gaining a block come via the dynamics of multihanded play. In other words, being chip leader with roughly 4:2:2:2:1:1:1 ratios is more valuable the a linear model would indicate partly because of the way the other stacks interact with each other and with the big stack. Not applicable to headsup play, which is why I think any J-Man theory has to be extremely restricted. (There may be an analogy to the three-body gravity problem in physics here, or it may be too late for me to be trying to think.)

Regardless, an interesting thread. Hope I contributed something.