How to figure out Covariance

[Unanamis]

Alright, so long story short, I want to be able to figure out my Kelly (optimal) bet using the Simulation Tables in DS's Blackjack Attack when playing more than 1 hand. In order to figure that out, I need to figure out the Covarience, which (from reading Katarina Walker's book on Spanish 21) can be figured out by multiplying the variance (the Standard Deviation Squared) by the correlation coefficient (in other words, rv=c).

The problem is, I don't know how to figure out the correlation coefficient and the closest thing that I found to answering this quandary was from this thread: https://www.blackjackinfo.com/commu...ing-bc-ic-pe-of-multiparameter-systems.24398/.

I believe what that provides me with, however, is the Betting Correlation rather than the correlation coefficient. Why else would it give the covarience of being around 1.2 (which is way too high from my limited understanding)?

I also don't entirely understand how Peter Griffin got his numbers for each card's EoR (effect of Removal), but I am curious if it could be possible to get similar numbers from DS's tables on EoR somehow.

I know it doesn't really matter too much in the grand scheme of things and that I could easily just throw ~55% into my Kelly calculation for two hands and whatnot, but that doesn't help me a whole bunch when I'm figuring out my standard deviation with 2+ hands, as well as my shift in risk.

 

[DSchles]

The formula at the bottom of page 20 of BJA3 tells you how to figure s.d. for any number of hands. Correlation coefficient for two hands of blackjack can be assumed to be 0.5, with reasonable amount of accuracy. Finally, correlation coefficient, in this case, is covariance/variance, which would be about 0.375.

You already know that the two-hand optimal bets are about 0.73% each times the one-hand optimal bet, so that should be no problem. If you want to go beyond two hands at a time, see Wong's Professional Blackjack, pp. 203-204.

Don

 

[Unanamis]

Would it be okay to assume that your .5 Correlation coefficient will be relatively consistent no matter how many decks one is playing? Or what type of game one is playing (H17/S17)? Or is the correlation coefficient not based on the count system that one is using as I had come to believe with the link to the previous post?

 

[DSchles]

"Would it be okay to assume that your .5 Correlation coefficient will be relatively consistent no matter how many decks one is playing? Or what type of game one is playing (H17/S17)?"

Yes, about 0.48 to 0.50.

"Or is the correlation coefficient not based on the count system that one is using as I had come to believe with the link to the previous post?"

Not based on the counting system.

Don

 

[Unanamis]

I think this is my last question. When you said,

"Correlation coefficient for two hands of blackjack can be assumed to be 0.5, with reasonable amount of accuracy. Finally, correlation coefficient, in this case, is covariance/variance, which would be about 0.375."

Is the Correlation Coefficient 0.5 or 0.375? And if it is the later, how did you get "r" to go from 0.5 to 0.375?

I'm assuming the actual CC is the later because it seems to collaborate with the data on page 20 of BJA3 more accurately (if using the standard deviation on the simulation charts in chapter 10, [say table 10.7 on pg 217] and having r=0.5, the Covariance would be around 0.64 at TC 0 [{1.133^2}*r=0.641], but if r=0.375, the Covariance would be about 0.481), but please let me know if I'm assuming wrongly.

 

[DSchles]

"I think this is my last question. When you said,

'Correlation coefficient for two hands of blackjack can be assumed to be 0.5, with reasonable amount of accuracy. Finally, correlation coefficient, in this case, is covariance/variance, which would be about 0.375.'"

"Is the Correlation Coefficient 0.5 or 0.375? And if it is the latter, how did you get "r" to go from 0.5 to 0.375?"

I apologize for the typo. VERY uncharacteristic for me. Please excuse the error. It should read: "Covariance for two hands of blackjack can be assumed to be 0.5, with reasonable amount of accuracy. Finally, correlation coefficient, in this case, is covariance/variance, which would be about 0.375."

"I'm assuming the actual CC is the latter because it seems to collaborate with the data on page 20 of BJA3 more accurately (if using the standard deviation on the simulation charts in chapter 10, [say table 10.7 on pg 217] and having r=0.5, the Covariance would be around 0.64 at TC 0 [{1.133^2}*r=0.641], but if r=0.375, the Covariance would be about 0.481), but please let me know if I'm assuming wrongly."

The latter calculation is correct; r = 0.375, which makes the covariance about 0.48, which I mentioned in the previous post.

Don