Heads up Theory

[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]

[ QUOTE ]
[ 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)

[/ 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.