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

[dfan]

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Forgive me if this is a dumb question, my math is rusty, but if S = Q then surely you are taking the log of zero, which is undefined? It seems you are missing a closing bracket in the formula though, so maybe this is leading to my confusion.

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Interesting idea Finch.

However I'm still stuck on the same question as kamrann. I tried to plug the formula into Excel, but I get an error due to ln(0) being undefined whenever S=Q. What am I missing here?

Also, if you could use brackets and braces as well a parentheses it would make the formula easier to read. Also please do an example with every number plugged in - this would make the formula crystal clear.

[AtticusFinch]

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Forgive me if this is a dumb question, my math is rusty, but if S = Q then surely you are taking the log of zero, which is undefined? It seems you are missing a closing bracket in the formula though, so maybe this is leading to my confusion.

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Interesting idea Finch.

However I'm still stuck on the same question as kamrann. I tried to plug the formula into Excel, but I get an error due to ln(0) being undefined whenever S=Q. What am I missing here?

Also, if you could use brackets and braces as well a parentheses it would make the formula easier to read. Also please do an example with every number plugged in - this would make the formula crystal clear.

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You're right. Looks like there is a discontinuity right at the center of the logit. I'll fix it and post a new version.

[HighestCard]

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I really don't understand? Doubling up oin the first hand in a 100 person tournament should increase your chances of winning by 100%, and thus make them 2%.


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Not quite. Your stack is not exactly 2Q, as Q has increased by the elimination of one player. The new Q is T/(N-1) where T is the total chips in play, and N is the starting number of players. Your stack after doubling is 2T/N, which is slightly smaller than 2Q after the elimination.
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This will however not increase your EV by 100%, assuming the tournament isn't winner take all.


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As I've said repeatedly, I'm not calculating EV. Just estimating odds of winning.

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I have a monkey wrench to throw into the formula.

What if your in the middle of the tournament. Everybody has the same stack size, but the blinds are large enough where if you push from a position not in the blinds AND your called by another player not in the blinds AND the blinds fold, by doubling up you have greater than 2Q because of the 1.5 bb's extra you have picked up.

Correct me if I am wrong but you might need to add a term to somehow account for the blinds relative to the average stack size.

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I really don't understand? Doubling up oin the first hand in a 100 person tournament should increase your chances of winning by 100%, and thus make them 2%.


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Not quite. Your stack is not exactly 2Q, as Q has increased by the elimination of one player. The new Q is T/(N-1) where T is the total chips in play, and N is the starting number of players. Your stack after doubling is 2T/N, which is slightly smaller than 2Q after the elimination.
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This will however not increase your EV by 100%, assuming the tournament isn't winner take all.


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As I've said repeatedly, I'm not calculating EV. Just estimating odds of winning.

[/ QUOTE ]

I have a monkey wrench to throw into the formula.

What if your in the middle of the tournament. Everybody has the same stack size, but the blinds are large enough where if you push from a position not in the blinds AND your called by another player not in the blinds AND the blinds fold, by doubling up you have greater than 2Q because of the 1.5 bb's extra you have picked up.

Correct me if I am wrong but you might need to add a term to somehow account for the blinds relative to the average stack size.

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Then the coefficient before Q is different. You rarely actually double up in a tourny; it's just nice to look at what the formula says if you do.

[EverettKings]

Atticus,

Run the ICM on a winnner take all structure. You'll see that chip EV = money EV the whole way. The ONLY reason chips ever have decreasing cash value is that you CANNOT win the whole prize pool in a normal tournament.

In fact, this exponential model is really only relevant for a non winner take all structure, for that reason.


It's a nice idea but I think this equation needs extreme remodeling before it can be applicable.

Everett

[AtticusFinch]

My present goal is not to convince anyone that I am correct (yet), so this thread has gone off in a direction other than the one I was hoping for.

This is just a first cut at a theory. I'm at the whiteboard stage, not the whitepaper stage. So I haven't been as thorough in my proof and explanation as I would for a formula in which I had some degree of confidence, and on which I had done some testing. Comments about my lack of rigor are not very helpful to me right now. They're sort of like criticising a diagram of a tank because the piece of paper can't fire ordnance. [img]/images/graemlins/wink.gif[/img]

If you simply fundamentally disagree with my non-linearity premise, that's cool. Come back at a later date when I've made some refinements and tested my model on some data, and we can talk then.

At the present, I have more need for people who understand and agree with my intuitive notion, and who can give me ideas about how to refine my model. THEN I can come up with more rigorious arguments in favor of it.

In the meantime, I'll give you a hint at the direction I'm heading in. I found a curve used in biostatistics which is shaped much like my initial idea. It is used to measure rates of population growth. Its premises are as follows:

* the rate of reproduction is proportional to the existing population, all else being equal
* the rate of reproduction is proportional to the amount of available resources, all else being equal. Thus the second term models the competition for available resources, which tends to limit the population growth.

If you think about it, these parameters are analogous to your stack in a tourney. Call your stack your "population." The amount of money you can add to your stack at any one time (i.e. population growth) is proportional to its current size, but limited by the total number of chips in play, and the sizes of your opponents' stacks.

Here's a page discussing the logistic curve, with its origins and applications:
http://en.wikipedia.org/wiki/Logistic_curve

Its shape is very similar to that of my original model, but allows for easier parameterization and normalization. Furthermore, and most intertestingly, it allows for easy addition of a parameter for your relative level of skill. Simply adjust your expected growth rate based on how good you think you are.

I'm still working on how to apply it properly, but I think it has significant potential.

[jcm4ccc]

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At the present, I have more need for people who understand and agree with my intuitive notion, and who can give me ideas about how to refine my model. THEN I can come up with more rigorious arguments in favor of it.

[/ QUOTE ] That's how science was done in the Soviet Union before the fall of communism.

You have no theory, you have no facts, you just have this complicated formula that seems to fit your notions of how things should be.

Your lack of understanding of the scientific method is an embarrassment.

[justT]

Sorry if I came off as a naysayer, trying to disprove something is my way of seeing if it has value or not, often comes off as naysaying. I've been thinking about some things that are related to your quest and wanted to toss a few things at you.

Tournament structure and what it means wrt optimal play: General consensus is almost straight out of HOH2, use M, Q doesn't tell you very much. The problem I have with that is M is reactive to the structure (i.e. when you get to this zone, you should do xyz), not proactive to the structure. Try playing a rebuy tourney like a freeze-out, don't rebuy, don't add-on. You very quickly get to the point where your M is okay, but your Q is killing you.

A while back I plotted the chip count for about 10 tourney's where the player went deep in the tourney, most were first place finishes. A couple of the tourney were mine, I was rather dismayed when I compared mine to those of better players. Mine were ugly, my chip count showed a lot of large gains and losses (lots of big hands), theirs tended to be more constant accumulation, picking up a lot of small pots here and there. The other thing I noticed, was that they very rarely "flat lined", very rarely did their accumulation stopped for a period longer than 20-30 hands.

Blinds definitely definitely add an exponential nature to the need for chip accumulation. I plotted the data from Burningyen's structure thread on a log chart, and all of them were straight lines (within reason). When you get around to calculating $EV, payout structure will probably also prove to be exponential in nature.

Anyhow, best of luck in your quest, I'm interested in seeing where you take it. Let me know if I can help.

[AtticusFinch]

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You have no theory, you have no facts, you just have this complicated formula that seems to fit your notions of how things should be.

Your lack of understanding of the scientific method is an embarrassment.

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It's called statistical modelling. You take a set of phenomena, and try to come up with a formula that provides a good approximation. Your lack of understanding of statistics is embarassing. So is your lack of manners.

[jcm4ccc]

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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?