bv21: Confused about SD calcuations in BJA

[bv21]

I know this should be basic but I can't reproduce the SD/100 hands column in the Chapter 10 tables of BJA. I'd like to modify the bet schedule and produce the new SD (understanding the math would be nice too). Could someone explain the formula please, I've been beating my head against a wall on this for quite a while tring to figure it out for myself.

Thanks much.

[bv21]

> I know this should be basic but I can't
> reproduce the SD/100 hands column in the
> Chapter 10 tables of BJA. I'd like to modify
> the bet schedule and produce the new SD
> (understanding the math would be nice too).
> Could someone explain the formula please,
> I've been beating my head against a wall on
> this for quite a while tring to figure it
> out for myself.

Maybe two simpler questions that would help me answer my original query is: why is the one-round s.d. given as 3.12 units for 4-deck play all game on page 19 of the 3rd edition? I figure this has to do with bet spreads, but how? Also, how is betting unit defined? Is it the same definition for play-all and backcounting?

> Thanks much.

[Don Schlesinger]

> Maybe two simpler questions that would help
> me answer my original query is: why is the
> one-round s.d. given as 3.12 units for
> 4-deck play all game on page 19 of the 3rd
> edition?

See p. 20 and the top of p. 21 for the explanation.

> I figure this has to do with bet
> spreads, but how?

See the p. 20 charts.

> Also, how is betting unit
> defined?

Smallest bet you make.

> Is it the same definition for
> play-all and backcounting?

Not in the chapter 10 charts. With optimal betting, your unit size will be larger for back-counting than for playing all.

Suggestion: Reread the text carefully and slowly!

Don

[bv21]

Thank you Don, very helpful.

I think I have the calculation down. I was using bet size and s.d. in my horizontal calculations instead of variance and bet^2. Can you refer me to an explanation of why you have to use the latter?

> See p. 20 and the top of p. 21 for the
> explanation.

> See the p. 20 charts.
OK, that did it. How is variance calculated for h not equal to 1. Also what is Cov?

> Smallest bet you make.

> Not in the chapter 10 charts. With optimal
> betting, your unit size will be larger for
> back-counting than for playing all.

> Suggestion: Reread the text carefully and
> slowly!

ADHD is a b@!$#

> Don

[Don Schlesinger]

> I think I have the calculation down. I was
> using bet size and s.d. in my horizontal
> calculations instead of variance and bet^2.
> Can you refer me to an explanation of why
> you have to use the latter?

Because it's the standard mathematical way to make the calculation. :-)

> OK, that did it. How is variance calculated
> for h not equal to 1. Also what is Cov?

See the formula given at the top of the variance column. Just plug in, say, 2, for when you play two hands. You have to know that the covariance for two hands is about 0.50 (actually about 0.48, I believe).

Covariance is a measure of how frequently the results of the two hands tend to behave in similar manner. Since both hands play against the same dealer upcard, the results often tend to be similar -- for example, both losing vs. dealer's ace or winning vs. dealer's 6. In other words, there is a kind of "linkage" between the results of the two hands; they don't behave totally independently of each other.

Hope this helps.

Don