Variance is Fractal

[TomCowley]

Let's see.. a few definitions for fractal:

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A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole. Fractals are generally self-similar and independent of scale.

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A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.

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A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry.

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Ok, so you are talking about a concept as though it's a geometric shape. Marijooana is good, mmmm-kay?

Let's list common properties of fractals:

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A fractal often has the following features:

It has a fine structure at arbitrarily small scales.

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Fail, poker actions are discrete.

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It is too irregular to be easily described in traditional Euclidean geometric language.

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Fail, even if I give you the benefit of the doubt translating to a graph, since sample variance is hardly irregular.

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It is self-similar (at least approximately or stochastically).

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Fail, sample variance curves aren't self-similar.

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It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

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Fail, obviously.

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It has a simple and recursive definition.

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Fail, obviously.

So I ask again, what the hell are you talking about when you say variance is fractal?

[_D&L_]

Variance is a meaningless term in poker. We talk about variance, but we are all talking about the variances of different things.

Some of us are talking about the variance of luck with the cards - which is actually very low. Some of us are talking about the variance of opponents.

For instance, pretend there is a player who does fairly poorly against 90% of players, but his strategy tends to get huge payoffs against a certain type of player. He will show high "variance." His luck (with the cards) isn't having any variance, what were measuring here is his luck finding suitable opponents.

Add to the fact that opponents adapt to your style over long periods, you have to ask what your trying to measure? Luck, opponents, adaptation of opponents...etc.

Keep in mind that variance is also function of our individual strategies. I can be a very consistent loser if I wanted to be; I am a very consistent winner also when I want to be; but when I try to push my edge...that's often when I experience my so called variance.

I can measure all these things. But when we talk about variance, meaningfully, we need a more precise definition of what we are trying to measure that varies....

P.s. lets stop using hyperbolic words like fractals...and other gibberish... Speak to be understood.

----_Dirty&Litgious_----

[MasterLJ]

A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

[Gonso]

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A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

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Classic imo

[MasterLJ]

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A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

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Classic imo

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Wrong thread =(.

So much for my first post here.

[onesandzeros]

By claiming variance to not be fractal you are saying the game is purely linear, and non-chaotic? This is obv incorrect.

Chart your poker stats for a few hundred sessions and tell me how fractals appear in charts of something that isn't chaotic and non linear?

[TomCowley]

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By claiming variance to not be fractal you are saying the game is purely linear, and non-chaotic?

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This is obv incorrect.

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Man, you did my work for me.

[rufus]

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Let's see.. a few definitions for fractal:
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A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales.

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The OP is, most likely, a loon, but noise (like variance or brownian motion) is self-similar. If you scale up the number of hands you consider at a time, you end up with a different (but similiar) variance.

[TomCowley]

A straight line meets more of the fractal criteria than a variance (deviation from sklanskybux) vs. #hands plot. Weak statistical self-similarity (expected value of point n+x is always the value of point n, for all x.. which is also true for a horizontal line) isn't particularly interesting. If you have a more interesting metric for variance vs. hands that's scale-invariant (and doesn't explicitly use scale in its calculation), I'd be curious.

A 1-d plot of possible deviations from sklanskybux (if the point has been traveresed, it exists), which is just a 1-d random walk, is self-similar because it's just the discrete analogue of a straight line (which is completely uninteresting).

Brownian motion is more interesting because it's 3D, and a random walk in 3D does NOT almost surely cover all points (a 1-D random walk, which variance is, does), so the points covered make a nicely irregular fractal shape.

[eMbAh]

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A small, albet important, reason that higher pp yield more money is because there are less hands that can flop a higher set.

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Classic imo

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Wrong thread =(.

So much for my first post here.

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ban