Sonny: How do I determine co-variance?

[Sonny]

I am trying to recreate table 2.1 "Standard Deviation By Number of Decks" from BJA (p 23 in the 2nd Ed). Everything is pretty straightforward except for the "Var+(h-1)*Cov" column. The "Var" and "h-1" parts are pretty simple, but how do I determine the co-variance?

From the examples it seems to be roughly 0.5, but I was hoping for a more accurate answer.

-Sonny-

[Don Schlesinger]

> I am trying to recreate table 2.1
> "Standard Deviation By Number of
> Decks" from BJA (p 23 in the 2nd Ed).
> Everything is pretty straightforward except
> for the "Var+(h-1)*Cov" column.
> The "Var" and "h-1"
> parts are pretty simple, but how do I
> determine the co-variance?

> From the examples it seems to be roughly
> 0.5, but I was hoping for a more accurate
> answer.

Here's the best I can do for you, directly from Griffin, p. 142: "From simulated hands I estimate the covariance of two blackjack hands played at the same table to be .50."

Wong, on pp. 202-203 of "Pro BJ," discusses covariance and gives 0.47 for his benchmark game and 0.48, when DAS is permitted.

I'm reasonably certain he used simulation as well.

Don

[Sonny]

[covariance]

> I'm reasonably certain he used simulation as
> well.
> Don
Maybe but... how can we use simulation for covariance? How can we get the result?
Thanks

[Don Schlesinger]

> Maybe but... how can we use simulation for
> covariance? How can we get the result?

You play two hands at a time vs. the same dealer's upcard and catalog the results: How many times do the results of the two hands wind up being identical? How many times are they different?

Don