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## Main Question or Discussion Point

In the book "The mathematic of Gambling", the author considers a fair coin with 50% getting head and 50% for tail. The expectation of such coin, of course, will be zero. Here is what I read from the text, it reads

Consider the fair game example mentioned earlier in the chapter (fair coin). In a series of any length, we have an expection of 0. In any such series it is possible to be ahead or behind. Your total profit or loss can be shown to have an average deviation from expectation of about [tex]\sqrt{N}[/tex].

Firstly, what is average deviation from expectation? How to get [tex]\sqrt{N}[/tex]? I am thinking the bionomial distribution with standard deviation [tex]\sqrt{N p (1-p)}[/tex] with p =0.5, it is about [tex]\sqrt{N}/2[/tex], is that what the author call average of deviation from expectation?

Consider the fair game example mentioned earlier in the chapter (fair coin). In a series of any length, we have an expection of 0. In any such series it is possible to be ahead or behind. Your total profit or loss can be shown to have an average deviation from expectation of about [tex]\sqrt{N}[/tex].

Firstly, what is average deviation from expectation? How to get [tex]\sqrt{N}[/tex]? I am thinking the bionomial distribution with standard deviation [tex]\sqrt{N p (1-p)}[/tex] with p =0.5, it is about [tex]\sqrt{N}/2[/tex], is that what the author call average of deviation from expectation?