Central limit theorem

[VLSroulette]

In probability theory, the central limit theorem (CLT) states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed (Rice 1995). The central limit theorem also requires the random variables to be identically distributed, unless certain conditions are met. Since real-world quantities are often the balanced sum of many unobserved random events, this theorem provides a partial explanation for the prevalence of the normal probability distribution. The CLT also justifies the approximation of large-sample statistics to the normal distribution in controlled experiments.

In more general probability theory, a central limit theorem is any of a set of weak-convergence theories. They all express the fact that a sum of many independent random variables will tend to be distributed according to one of a small set of "attractor" (I.e. stable) distributions. For other generalizations for finite variance which do not require identical distribution, see Lindeberg's condition, Lyapunov's condition, Gnedenko and Kolmogorov states.

Full text here:

nolinks://en.wikipedia.org/wiki/Central_limit_theorem



I put this in here because it seems the central limit theorem is one of the reasons casinos provide roulette in the first place.

They are confident of this theorem and they expect it to hold true, the true winners are circumventing this theorem.

Heck, ANY long-term winning on a negative expectation game sure is quite a feat.

Feel free to debate on this topic.

Victor

[GARNabby]

I guess that article is about how well mathematics models nature?  Interesting to note how the "martingales" fit in... as the sciences actually become the nature modeled, meeting at consciousness or sentience, itself.

Perhaps if and when that sort of "theater of the mind" is finally unearthed, and fully(?) explained, also its parts will be defeated?  Eg, by some new ability to completely manipulate even probability (distributions).

Who knows? But ultimately, i doubt this is how to beat the casino-games.  That would be like "taking a sledge-hammer to a peanut"... have to be easier ways.

[GARNabby]

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