[CrayZee]

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obviously a careful explanation of the strong law of large numbers is a bit difficult to give to a layperson, but there's really no getting around it, because it is really what mathematicians mean by 'the long run'.

for example if i flip a coin a million times (a random walk on Z of 10^6 steps), my expected distance from the origin is about 2/pi*1000 ~ 600, even though my expected position is zero (equal heads and equal tails). mathematically, the law of large numbers says that the we get about half heads and half tails + a term that goes to infinity slower than n^(0.5+e) for ANY e>0 (this is related to the central limit theorem). this can still be a long ways from zero if n is large though.

qualitatively the important thing is that the mass of the distribution is clustered around {half tails, half heads} - this is the weak law of large numbers.

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I guess my thing is that people just have a hard time wrapping their heads around the whole infinity thing. I also prefer the integration of a more cognitive bias perspective/explanation.

Not that I have anything against the law of large numbers type of explanation. But, I mean, imagine if The Theory of Poker resembled The Theory of Gambling and Statistical Logic, all 8 copies would have sold as it's way too advanced for the average gambler. Sklansky's book is hard enough as it is.

I have a hard time seeing the OP's friend understanding such advanced concepts. I'd refer the student to the strong and weak laws of large numbers as an exercise. [img]/images/graemlins/smile.gif[/img]