SD and variance clarification

#1
I watched the videos by Symeon Dukach and got a little confused. He did a quick explanation about EV and Deviation but it is not 100% clear to me.

He explains that on an average bet of $100 with a 1% edge you can expect to win 1,000,000 on the same amount of hands. So basically you put in a hundred million and you can expect to get back 1 million. However, because of standard deviation, you will almost never get exactly what you expect. So he says on 1 million hands you have a standard deviation of $115,000 (square root of a million x115). Now is that the standard deviation or the variance? He calls it the SD.

Now I found out that SD is the square of the variance. So a variance of 100 means 1 stand deviation of 10. If that is true, a SD of 115,000 would have a variance of 13 billion, and doesn't seem to work. It would seem to me that 115,000 is the variance and the SD is $339. Do I understand this correctly or am I way off?

Now if 115,000 is the variance, does that mean that if we have an expected value of 1 million we will most likely make in the 1,115,000 - 885000, but that 66% of the time we will be + or - 339 from our expected value, and if we are 2 Standard Deviations off, 33% of the time we will see a divergence of $678?

thanks in advance!!!
 

Nynefingers

Well-Known Member
#2
silky28 said:
He explains that on an average bet of $100 with a 1% edge you can expect to win 1,000,000 on the same amount of hands. So basically you put in a hundred million and you can expect to get back 1 million. However, because of standard deviation, you will almost never get exactly what you expect. So he says on 1 million hands you have a standard deviation of $115,000 (square root of a million x115). Now is that the standard deviation or the variance? He calls it the SD.
This is the standard deviation.

Now I found out that SD is the square of the variance. So a variance of 100 means 1 stand deviation of 10. If that is true, a SD of 115,000 would have a variance of 13 billion...
Your math is correct, but you've got the terminology backwards. SD is the square root of variance, and variance is the square of SD.

Now if 115,000 is the variance, does that mean that if we have an expected value of 1 million we will most likely make in the 1,115,000 - 885000, but that 66% of the time we will be + or - 339 from our expected value, and if we are 2 Standard Deviations off, 33% of the time we will see a divergence of $678?

thanks in advance!!!
The SD is 115,000, so with an EV of 1,000,000, you will be within the range 885,000-1,115,000 roughly 68% of the time (EV +/- 1*SD). You will be within 2 standard deviations (230,000) of your EV roughly 95.5% of the time, so 2.3% of the time you will be below 770,000, and 2.3% of the time you will be above 1,230,000. You can use this site to calculate the percentage probability of being above or below different results.
 
#3
I think I am confused as to why variance is so high. If variance is SDxSD then it's 13.2 billion. How can the variance be so big? At this point does variance even concern us or should we pay attention only to SD as it's more relevant?

I understand variance as the maximum deviation from a median or expected outcome. Is SD then the proportional application of variance based on likelihood?
 

Canceler

Well-Known Member
#4
Nynefingers said:
The SD is 115,000, so with an EV of 1,000,000, you will be within the range 885,000-1,115,000 roughly 68% of the time (EV +/- 1*SD). You will be within 2 standard deviations (230,000) of your EV roughly 95.5% of the time, so 2.3% of the time you will be below 770,000, and 2.3% of the time you will be above 1,230,000.
I understand this part perfectly, and I’m eagerly awaiting a reply to silky28’s second post.

What does the ungodly huge number that is variance represent? Does it have any direct use? Or is it just a number that is arrived at on the way to calculating standard deviation, and is not really useful by itself?
 

Nynefingers

Well-Known Member
#5
I'm the wrong guy to ask about the significance of the variance itself, but the SD is the number you need for calculating the probability of any particular results after a given amount of play.
 

Sonny

Well-Known Member
#6
silky28 said:
If variance is SDxSD then it's 13.2 billion.
Correct. In this case the variance per hand is about 1.33 so the variance of 100M rounds at $100 per round will be about 13.3B.

silky28 said:
How can the variance be so big?
That ain't so big. For every $1 you bet, you expect to have a $1.15 swing most of the time. That's pretty close to an even money game. It could creep up to $2-$3.50, but that's nothing to worry about. Look at the variance of some other casino games and you will see much higher numbers. Blackjack is pretty tame in terms of variance.

silky28 said:
At this point does variance even concern us or should we pay attention only to SD as it's more relevant?
Variance is just a number. You calculate it but you can't really do much with it. You can't apply it directly to your situation. That's what SD is for. You can apply SD directly to your bet size, use it to calculate your range of results for a given number of hands, find the probability of being ahead after a given time, your risk of ruin, and some other cool stuff. You calculate variance but you have to convert it to SD in order to use it for anything. Here's a little explanation of using SD to calculate your probability of making money by counting cards:

http://www.blackjackinfo.com/bb/showthread.php?t=4891

Snyder has a nice article too:

http://www.blackjackforumonline.com/content/Blackjack_Basic_Strategy_Betting_And_Risk.htm

-Sonny-
 
#7
Sonny said:
Correct. In this case the variance per hand is about 1.33 so the variance of 100M rounds at $100 per round will be about 13.3B.



That ain't so big. For every $1 you bet, you expect to have a $1.15 swing most of the time. That's pretty close to an even money game. It could creep up to $2-$3.50, but that's nothing to worry about. Look at the variance of some other casino games and you will see much higher numbers. Blackjack is pretty tame in terms of variance.



Variance is just a number. You calculate it but you can't really do much with it. You can't apply it directly to your situation. That's what SD is for. You can apply SD directly to your bet size, use it to calculate your range of results for a given number of hands, find the probability of being ahead after a given time, your risk of ruin, and some other cool stuff. You calculate variance but you have to convert it to SD in order to use it for anything. Here's a little explanation of using SD to calculate your probability of making money by counting cards:

http://www.blackjackinfo.com/bb/showthread.php?t=4891

Snyder has a nice article too:

http://www.blackjackforumonline.com/content/Blackjack_Basic_Strategy_Betting_And_Risk.htm

-Sonny-
thanks Sonny,

Much appreciated!
 
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