# Chapter 20 STATS.docx

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31 Mar 2012
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Chapter 20
The House Edge: Expected Values
Expected Values
The expected value of a random phenomenon that has numerical outcomes is found by
multiplying each outcome by its probability and then adding all the products
Expected value = a1p1 + a2p2+ …+akpk
An expected value is an average of the possible outcomes, but it is not an ordinary average in
which all outcomes get the same weight
The idea of expected value as an average applies to random outcomes other than games of chance
It is used to describe the uncertain return from buying stocks or building a new factory
The Law of Large numbers
According to the law of large numbers, if a random phenomenon with numerical outcomes is
repeated many times independently, the mean of the actually observed outcomes approaches the
expected value
In many independent repetitions, the proportion of each possible outcome will be close to its
probability, and the average outcome obtained will be closed to the expected value (express the
long-run regularity of chance events)
How large is a large number\/
The law of large numbers says that the actual average outcome of many trials gets closer to the
expected value as more trials are made
Variability of the random outcomes how many trails are needed to guarantee an average
outcome close to the expected value
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