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#1
October 26th, 2011, 08:35 AM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 3,201
standard deviation

say:
we have two games
one game has SD = X and is played f% of the time
the other game has SD = Y and is played z% of the time

mathematically what is the proper way to calculate the 'combined' standard deviation?
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mr fr0g MMOA honorary predator
STRENGTH - HONOR - HEART
that's my take on it your mileage may vary.
for senior citizen fuzzy count click link:
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#2
October 26th, 2011, 09:44 AM
 Canceler Executive Member Join Date: Apr 2005 Location: Minnesota Posts: 1,112

I would start with this thread, which seems like it was active only a couple months ago, but is actually two years old, WTF?
#3
October 26th, 2011, 09:57 AM
 iCountNTrack Senior Member Join Date: Oct 2008 Posts: 346

Quote:
 Originally Posted by sagefr0g say: we have two games one game has SD = X and is played f% of the time the other game has SD = Y and is played z% of the time mathematically what is the proper way to calculate the 'combined' standard deviation?
Assuming f and z are fractions rather than percents for simplicity.

Variance=(f*X^2+z*Y^2)

Sandard_Deviation=SquareRoot(Variance)
#4
October 26th, 2011, 10:03 AM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 3,201
lol, so a rehash

Quote:
 Originally Posted by Canceler I would start with this thread, which seems like it was active only a couple months ago, but is actually two years old, WTF?
lol, thanks as always, Canceler
but yeah, two years old, good reason i guess for not being able to remember how to do it, but hazily suspecting it had something to do with taking a square root before adding.... edit: (geesh, yeah two years, took that much time to realize how much i care about standard deviation)
some stuff you can just add, like i think EV is additive, other stuff, like standard deviation, errhh a bit trickier, lol

so this looks key here to me:
Quote:
 Yes. First of all, there's a question of how you're calculating SD to begin with. If you're playing on a computer which is tracking your results by hand, that's probably okay. SD(total) = sqrt(SD(1)^2 + SD(2)^2 + SD(3)^2). But more often, SD is calculated from session wins, which means you calculate SD(total) = sqrt((ActualWin(1)-ExpectedWin(1))^2 + (ActualWin(2)-ExpectedWin(2))^2 + ... (ActualWin(n)-ExpectedWin(n))^2).
__________________
________________________________________

best regards,
mr fr0g MMOA honorary predator
STRENGTH - HONOR - HEART
that's my take on it your mileage may vary.
for senior citizen fuzzy count click link:
http://www.youtube.com/watch?v=DrTiP4ZIUfI
#5
October 26th, 2011, 12:05 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 3,201

Quote:
 Originally Posted by iCountNTrack Assuming f and z are fractions rather than percents for simplicity. Variance=(f*X^2+z*Y^2) Sandard_Deviation=SquareRoot(Variance)
ok, thank you ICNT.
so digressing a bit......
say you have in the case of blackjack
SD = Z for a hand of blackjack
so to get the standard deviation for N hands would it be:
Z*SQRT(N) ?
__________________
________________________________________

best regards,
mr fr0g MMOA honorary predator
STRENGTH - HONOR - HEART
that's my take on it your mileage may vary.
for senior citizen fuzzy count click link:
http://www.youtube.com/watch?v=DrTiP4ZIUfI
#6
October 26th, 2011, 01:11 PM
 iCountNTrack Senior Member Join Date: Oct 2008 Posts: 346

Quote:
 Originally Posted by sagefr0g ok, thank you ICNT. so digressing a bit...... say you have in the case of blackjack SD = Z for a hand of blackjack so to get the standard deviation for N hands would it be: Z*SQRT(N) ?
yep that is why accumulated expectations overcome accumulated standard deviations as the number of hands increases, because the former (expectation) is proportional to the number of hands, while SD is proportional to the square root of the number of hands
#7
October 26th, 2011, 01:45 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 3,201

Quote:
 Originally Posted by iCountNTrack yep that is why accumulated expectations overcome accumulated standard deviations as the number of hands increases, because the former (expectation) is proportional to the number of hands, while SD is proportional to the square root of the number of hands
heh, heh, funny you should mention that, cause that's what i just noticed fooling around in excel with this stuff. kewl!
__________________
________________________________________

best regards,
mr fr0g MMOA honorary predator
STRENGTH - HONOR - HEART
that's my take on it your mileage may vary.
for senior citizen fuzzy count click link:
http://www.youtube.com/watch?v=DrTiP4ZIUfI
#8
October 31st, 2011, 12:53 PM
 blackjack avenger Executive Member Join Date: Feb 2007 Posts: 1,435
fixed is fixed

Those formulas are for fixed bets right? If you resize bets on wins and losses the long run is longer.
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