Heads up Theory

[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... [img]/images/graemlins/frown.gif[/img] [img]/images/graemlins/grin.gif[/img]

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% > 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% > 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. [img]/images/graemlins/laugh.gif[/img]

[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.