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#11
11-19-2007, 10:47 PM
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Re: Standard Deviation Question
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] http://www.stat.wvu.edu/SRS/Modules/...malapprox.html Don't think the binomial converges to the normal. The normal is just a good approximation of the binomial. [/ QUOTE ] eh, doesn't everything converge to the normal? [/ QUOTE ] No. [/ QUOTE ] okay, what doesn't? [/ QUOTE ] Anything with non-finite variance, like for example poker and the majority of things that you encounter in your daily life. IMO, anyone who talks about normal distributions or the Central Limit THeorem on a poker website should be banned. A much shorter list are the things that do converge to the normal. 
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#12
11-19-2007, 10:57 PM
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Re: Standard Deviation Question
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Anything with non-finite variance [/ QUOTE ] What do you mean by this? flipping a coin, winning/losing a dollar per flip, forever has non-finite variance, no? or do you mean non-finite variance per event or whatever? how does poker not have finite variance per hand if this is what you mean?
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#14
11-20-2007, 01:50 AM
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Re: Standard Deviation Question
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Coin flipping has finite variance. Poker's variance has infinite possibilities. [/ QUOTE ] I'm still not getting this coin flipping has infinite possibilities too. The variance I believe is roughly proportional to the square root of the number of flips, hence it tends to infinity if the number of flips tends to infinity
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#15
11-20-2007, 02:04 AM
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Re: Standard Deviation Question
poker = continuous
coin flipping = discrete
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#17
11-20-2007, 02:58 AM
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Re: Standard Deviation Question
Poker results should follow normal distribution (a normal distribution is continuous). Coin flipping results follow a binomial distribution (a binomial distribution is discrete).
A distribution is continuous if there are an infinite number of possible outcomes over a finite region. It might make more sense if you think about radios. The FM radio in your car is discrete (you can only tune it to certain frequencies on the interval (88.1, 107.9). The crappy alarm clock radio you had as a kid, that was a pain in the ass to tune was continuous. You could tune it to any frequency you wanted on the interval (88.1, 107.9), even frequencies like 99.7966445. The point is discrete distibutions always stay discrete. After a while they look a lot like continuous ones and can be approximated very well by them, but they're still not continuous.
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#18
11-20-2007, 08:50 AM
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Re: Standard Deviation Question
oh right, I thought it was something more profound. What if I change my question to:
"eh, doesn't everything converge to the normal or binomial?" also, is Troll_Inc making any sense when he says: [ QUOTE ] Anything with non-finite variance, like for example poker and the majority of things that you encounter in your daily life. IMO, anyone who talks about normal distributions or the Central Limit THeorem on a poker website should be banned. A much shorter list are the things that do converge to the normal. [/ QUOTE ]
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#20
11-20-2007, 12:07 PM
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Re: Standard Deviation Question
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Coin flipping has finite variance. Poker's variance has infinite possibilities. [/ QUOTE ] Having infinite possibilities doesn't imply infinite variance. And the distribution of the outcome of a single hand in NLH has finite variance unless you assume two players have infinite bankrolls. Thus the outcome of n hands will converge to a normal distribution with large n. But this convergence is very much slower than most people suspect it to be. I.e. BB/100 is by no means normal, BB/1000 isn't, BB/1m probably comes close.
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Linear Mode
