Search BlackjackInfo

 Blackjack and Card Counting Forums - BlackjackInfo.com standard deviation
 User Name Remember Me? Password
 FAQ Members List Social Groups Search Today's Posts Mark Forums Read

 Thread Tools Display Modes
#1
October 26th, 2011, 10:35 AM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 5,141
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?
#2
October 26th, 2011, 11:44 AM
 Canceler Executive Member Join Date: Apr 2005 Location: Minnesota Posts: 1,625

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, 11:57 AM
 iCountNTrack ChemMeister Join Date: Oct 2008 Posts: 780

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, 12:03 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 5,141
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).

Last edited by sagefr0g; October 26th, 2011 at 01:15 PM.
#5
October 26th, 2011, 02:05 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 5,141

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) ?
#6
October 26th, 2011, 03:11 PM
 iCountNTrack ChemMeister Join Date: Oct 2008 Posts: 780

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, 03:45 PM
 sagefr0g Executive Member Join Date: Apr 2006 Posts: 5,141

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!
#8
October 31st, 2011, 02:53 PM
 blackjack avenger Executive Member Join Date: Feb 2007 Posts: 2,267
fixed is fixed

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

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Welcome to the BlackjackInfo Forums     Site Announcements Blackjack Forums     Blackjack - General     Blackjack - Voodoo Betting Strategies     Blackjack - Card Counting     Blackjack - Advanced Strategies     Blackjack - Variations     Blackjack - Theory and Math     Blackjack - Online Casinos     Blackjack - Stories Land Based Casinos     Las Vegas     Nevada - Outside Vegas     Eastern US     Southern US     Midwest US     Western US     Canada     Australia     Europe     Asia, Africa & Far East     Caribbean & Latin America Online Casinos     Reputable Casinos     Problem Casinos     Latest Promotions Miscellaneous     Other Games     Gambling Law     Blackjack in the Media     Site Discussion     News     Sports Betting     Investing and Financial     Anything Else

All times are GMT -6. The time now is 01:59 AM.

 Contact Us - BlackjackInfo.com - Archive - Top

Forum Software vBulletin®
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
Copyright 2005-2011 Bayview Strategies LLC