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The Problem
 

There is sound intuitive reason to expect linear estimators to work ill for individual strategy decisions: often only one unseen card is needed to resolve the situation, and very rarely are many (the most profitable strategy variation in single deck play, insurance, is completely linear in this sense). But when it comes to estimating the basic strategist's overall expectation, before the hand has been dealt, the fact that at least four cards (whose order is vital) will have to be used calls into questions the accuracy of this method.

An important and overlooked statistical fact is that the correlation coefficient betien the least square estimates and the actual expectations being estimated is equal to the quotient of the standard deviation of these estimates and the standard deviation of the distribution of the actual expectations themselves. This leads us to the conclusion that actual expectations will have a greater dispersion than their surrogate best estimators. This is so because the correlation coefficient will be less than one for all but the N-1 card subsets of an N card deck. in particular, this underestimation of dispersion (using least squares estimates) will be most severe for the smaller subsets, in which linearity is likely to be poorest. Hence i want to learn more about how the number of unplayed cards is related to this correlation coefficient.

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Lie Down With Dogs, Wake Up With Fleas
 
If you find out a site does this, do your best to ignore both them and their advertisers. Loose ethics in one area carry over to another. They may sell your name or private information, they may run worthless articles (one of the tricks designed to keep authors from finding out about stolen work is altering articles by rewriting a few lines or deleting titles and/or paragraphs; this practice sometimes ruins the article's point).

Their advertisers may or may not know what the rogue site is doing, but if you inform the advertiser the site's actions have cost the advertiser your business, the site will soon hear from someone with more clout than you or me.
Finally, I can't speak for the other writers, but anytime someone finds someone stealing some of my work, I offer the finder free lessons-or at least free answered questions-as a "thank you."
 
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