Theory: Gigabet's "bands" and "The Finch Formula" Grand Unification

[kamrann]

Okay, obviously the disagreement here is a very fundamental one. Do chips have a constant value in a winner take all MTT? For instance Atticus, regarding your comment about your method trying to deal with cases of more than two players, you were missing curtains' point. What occurs in an individual hand is irrelevant. ICM is a static model, if after tripling up your model says a player does not have exactly 3x greater $EV than he did prior to the hand, then it doesn't fit with the constant chip value idea. And if so, then no matter how you refine it, it's never going to be a model that curtains, mantis, etc will accept as valid, since it's effectively based on what to them is a false assumption.
I'm not sure where I stand on this, though to be honest I can't think of an intuitive reason why stack value would follow some form of S-curve. Or are you intending to try to fit it to just a section of the logistic curve?

On a separate note, I have a question for curtains. Are you then of the opinion that we already have a satisfactory model for MTTs in ICM, but that it simply isn't all that useful because of the extra effort involved in using it with so many players, and the vastly larger number of possible scenarios?

[schwza]

i haven't read the thread, so forgive me if i'm repeating. are you talking about a winner take all (WTA) tourney or a regular MTT where the hero personally only cares about winning? in a WTA, the current cannon is that you have a (your chips) / (total chips) chance to win. i.e., your win % is purely linear in you chip stack. (i think that this doesn't actually work out perfectly because being all-in gives a player a slight advantage in that they can't be moved off of the eventual winner).

in a regular MTT, i'll believe that your expected cash moves up something like logarithmically with increases in stack, but in a WTA i think they move up roughly linearly. in a MTT where hero only cares about first, i'd expect your chance of winning moves faster than linearly because hero can exploit others' desire to increase their place (i.e., hero will sacrifice cash to increase first place %).

[AtticusFinch]

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You take a set of phenomena, and try to come up with a formula that provides a good approximation.

[/ QUOTE ] What you are missing is your set of phenomena. What is your phenomena (data), other than your "intuitive understanding" of how things ought to work?

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Working on that. I have to gather a bunch of tourney records to run some tests on. At the present, anecdotal evidence and math from analogous situations are all I have available to me.

I'll say it again. It's a THEORY. I want to go through a couple more refinements before I invest the time to write code to test it.

I'm well acquainted with the scientific method. You start off with a hypothesis, and then go about proving it, either mathematically or by gathering data. The thing is, I still haven't fully formulated the hypothesis yet. I don't ask anyone to agree with me. Rather the opposite, actually. But simply tossing out flames for my lack of proof is putting the cart before the horse, and of no use to anyone.

So, please, constructive comments only henceforth. If you simply think I'm full of [censored], then move on to another thread.

[AtticusFinch]

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I'm not sure where I stand on this, though to be honest I can't think of an intuitive reason why stack value would follow some form of S-curve. Or are you intending to try to fit it to just a section of the logistic curve?


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My theory is that it does follow an S-curve, because I believe the value of your stack is related not only to its size, but the rate at which you can continue to grow it, which reduces as your stack gets large relative to the field.

I contend that each chip you add DOES add value, but chips you can invest in a hand are of greater value than those you cannot, assuming you are a winning player.

The trouble with linear models is that they start with the false assumption that everyone is equally skilled. My main goal in this effort is to find a formula that models the things that ICM are missing:

1) Blind size
2) Field size
3) Relative skill
4) Forward-looking equity

I believe the logistic curve provides a way to model all of these things in an efficient and intuitive manner. For example, have another look at the page and consider the growth-rate parameter. I propose setting this to a value proportional to your relative skill level in the field. The result would (hopefully) predict how fast you can continue to grow your stack. And that must say something about your chances of winning the tournament.

My plan is to work with the parameters until I get a curve shaped like I believe the true shape should be. Then I will test it against tourney data I collect.

By the way, I don't intend to focus on the winner-take-all scenario forever. That was just a starting point.

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On a separate note, I have a question for curtains. Are you then of the opinion that we already have a satisfactory model for MTTs in ICM, but that it simply isn't all that useful because of the extra effort involved in using it with so many players, and the vastly larger number of possible scenarios?

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I'd love to hear the answer to this in light of ICM's deficiencies that I list above.

[AtticusFinch]

Great comments. Thanks. Here are my thoughts in response:

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i haven't read the thread, so forgive me if i'm repeating. are you talking about a winner take all (WTA) tourney or a regular MTT where the hero personally only cares about winning? in a WTA, the current cannon is that you have a (your chips) / (total chips) chance to win. i.e., your win % is purely linear in you chip stack. (i think that this doesn't actually work out perfectly because being all-in gives a player a slight advantage in that they can't be moved off of the eventual winner).


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I suspect that this may be true if everyone in the field is equally skilled. Of course, they aren't. Sklansky and others have often said that it can be correct to pass on small edges if you are one of the best players in the tournament. I'm looking for a way to quantify this. My first formula doesn't provide it, of course, but it was just a first cut. I've made some progress toward this end since then. Check out my first "to the naysayers" post for details.

In the hands of a skilled player, my theory is that a stack's value follows an s-curve even in a winner-take-all tournament, because the larger the stack is relative to the field, the more hindered a skilled player is in his ability to grow it, simply because no one can cover him.

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in a regular MTT, i'll believe that your expected cash moves up something like logarithmically with increases in stack


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This would depend on the payout structure, of course.

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in a MTT where hero only cares about first, i'd expect your chance of winning moves faster than linearly because hero can exploit others' desire to increase their place (i.e., hero will sacrifice cash to increase first place %).

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Interesting point. I think that notion is something that could be factored into a skill-level parameter, but I'll have to think about it.

[kamrann]

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My theory is that it does follow an S-curve, because I believe the value of your stack is related not only to its size, but the rate at which you can continue to grow it, which reduces as your stack gets large relative to the field.

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Interesting idea. Certainly sounds plausible, question really is I guess whether it's a significant factor in reality.

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On a separate note, I have a question for curtains. Are you then of the opinion that we already have a satisfactory model for MTTs in ICM, but that it simply isn't all that useful because of the extra effort involved in using it with so many players, and the vastly larger number of possible scenarios?

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I'd love to hear the answer to this in light of ICM's deficiencies that I list above.

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Yes, but 3 of the 4 problems you list are also problems for STTs as well as MTTs. We all know that ICM isn't perfect. I was really wondering whether people thought that there were specific reasons why ICM is better for STTs than for MTTs.

As far as hoping to factor all these things into your formula, as well as payouts, all I can say is that, as I'm sure you realise, thats going to be seriously difficult! I hope you are successful to some extent anyway.

[jcm4ccc]

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You take a set of phenomena, and try to come up with a formula that provides a good approximation.

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I'm well acquainted with the scientific method. You start off with a hypothesis, and then go about proving it, either mathematically or by gathering data.

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I wonder if you see the contradictions in your two statements. In statement #1, you are starting with the phenomena (data). In statement #2, you are starting with the hypothesis.

My problem is that you created an incredibly complex formula with absolutely no data, anecdotal or otherwise. (if you do have some data from actual tournaments, tell us what it is so we can plug it into Excel and see for ourselves. Or anecdotally, can you tell us about a tournament where you increased your chances by a little less than 2X when you doubled up early)?

Science starts with observations, not formulas. Actual, tangible observations. By starting with a formula and then looking at data, you are putting the cart way before the horse.

Here's an example of the problem. Let's call your formula "Finch's formula." Here are 3 variations on your formula:

[Finch's formula] * 1.001
[Finch's formula] + 1.00056
[Finch's formula] / 0.995

Which one describes the data better? Answer: who knows? There is no data to describe.

Start with collecting some data--you should be able to enter that data in Excel, and make a graph which suggests the type of relationship you are looking for. Then you would be well on your way to developing a formula that's based on more than intuitive feeling.

Now you can argue that there is no data to support the ICM model, and I think you might be right. But ICM is based on a theory, and it has a certain internal logic. Your formula is not based on theory (other than a general theory that could apply to an infinite number of formulas), and it's not based on facts.

[curtains]

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On a separate note, I have a question for curtains. Are you then of the opinion that we already have a satisfactory model for MTTs in ICM, but that it simply isn't all that useful because of the extra effort involved in using it with so many players, and the vastly larger number of possible scenarios?

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There is no model for MTT's that's very useful, no. At least I've never used such a model, I basically play for +Chip EV for the most part, with some exceptions of course. I think that due to the top heavy prize funds of MTTs, they are easier to play instinctively as opposed to sit and gos, where it's often correct to make clearly -CEV plays.

[PrayingMantis]

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In the hands of a skilled player, my theory is that a stack's value follows an s-curve even in a winner-take-all tournament, because the larger the stack is relative to the field, the more hindered a skilled player is in his ability to grow it, simply because no one can cover him.

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Atticus, this assumption (or theory) doesn't make sense at all, unless you assume people way too frequently play to survive in a winner-take-all, which they clearly do not, or at least not more than they "play to survive" in a ring game. I don't know how you come up with these assumptions. There are more very problematic assumptions that you make in your recent posts, but I won't adress them, since obviously you don't seem to welcome criticism.

To Kamrann:

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I was really wondering whether people thought that there were specific reasons why ICM is better for STTs than for MTTs.

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The answer is basically 2-fold and is very simple: First, ICM is not "better" for STTs than it is for MTTs. The only thing is that when you play a MTT you are usually playing very far from the money most of the time, while in a SNG you start the game with a 30% chance to money (it is comparable maybe to a MTT where 70% of the field is already gone). This is a huge difference, and it will mean that for most of normal situations in a MTT, ICM will have very little relevancy, and CEV will be very close to $EV for all normal considerations.

Another important difference is the distribution of the prize money IN the money, which calls again for a very much winner-take-all approach (since the prizes are usually very top heavy), that also makes CEV relatively close to $EV unless in specific situations, that might happen during final table and ICM is certainly very helpful there (as in deal making too).

[AtticusFinch]

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Atticus, this assumption (or theory) doesn't make sense at all, unless you assume people way too frequently play to survive in a winner-take-all, which they clearly do not, or at least not more than they "play to survive" in a ring game. I don't know how you come up with these assumptions.


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They're not assumptions, they're theories. Big difference.

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There are more very problematic assumptions that you make in your recent posts, but I won't adress them, since obviously you don't seem to welcome criticism.


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Once again, they are theories, not assumptions. I have stated multiple times that they require testing. At the present I only suspect them to be true. Testing may well prove me wrong.

I welcome constructive criticism. Your comments qualify, for the most part. I don't, however, welcome flames which add nothing to the discussion.

The trouble with most of the criticism I've received in this thread is that it's not useful at this point, because it mischaracterizes what I am saying. I have an idea. A theory. Instead of telling me all the reasons why my "methods" are wrong, when I haven't even begun to employ any methods other than brainstorming, simply is not useful.

Instead, tell my why my idea is wrong. That would be very helpful.