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.
|Lie Down With
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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."