Frank Smith: Question for Don on Standard Deviation

[Frank Smith]

Don,

What effect does the decision to play 2,3,4,5,6, or 7 hands have upon the standard deviation using the same betting scheme for each hand played under the same conditions, that is, basic strategy play in a six-deck using Atlantic City rules - dealer stands on soft seventeen, double after split. For example, playing two hands with a 1 to 4 unit bet spread on each hand with one unit being bet 25% of the time on each hand, 2 units being bet on each hand 25% of the time, 3 units being bet on each hand 25% of the time, and 4 units being bet 25% of the time on each hand. Does the 1.30 figure cited in your previously mentioned formula for 1 hand under the same conditions change appreciably as one moves from 2 hands to 7 hands using the same betting scheme? What would be the S.D. for each case 2 through 7 hands?

[Don Schlesinger]

> Don,

> What effect does the decision to play 2,3,4,5,6, or 7
> hands have upon the standard deviation using the same
> betting scheme for each hand played under the same
> conditions, that is, basic strategy play in a six-deck
> using Atlantic City rules - dealer stands on soft
> seventeen, double after split. For example, playing
> two hands with a 1 to 4 unit bet spread on each hand
> with one unit being bet 25% of the time on each hand,
> 2 units being bet on each hand 25% of the time, 3
> units being bet on each hand 25% of the time, and 4
> units being bet 25% of the time on each hand. Does the
> 1.30 figure cited in your previously mentioned formula
> for 1 hand under the same conditions change
> appreciably as one moves from 2 hands to 7 hands using
> the same betting scheme? What would be the S.D. for
> each case 2 through 7 hands?

Do you have BJA3? The answer to all of your questions can be derived from the methodology on p. 20. As you play multiple hands, the covariance between, or among, the hands comes into play according to the formula documented there.

So, you would multiply each squared bet size by its frequency (25%), times the number of simultaneous hands, times [1.3 + (h-1)*covariance], where h is the number of simultaneous hands, sum over all bet sizes, then take the square root of the sum. Note that the bottom of page 142 of Griffin gives the variance for any number of hands.

Don

[Frank Smith]

> Do you have BJA3? The answer to all of your questions
> can be derived from the methodology on p. 20. As you
> play multiple hands, the covariance between, or among,
> the hands comes into play according to the formula
> documented there.

> So, you would multiply each squared bet size by its
> frequency (25%), times the number of simultaneous
> hands, times [1.3 + (h-1)*covariance], where h is the
> number of simultaneous hands, sum over all bet sizes,
> then take the square root of the sum. Note that the
> bottom of page 142 of Griffin gives the variance for
> any number of hands.

> Don

Don,

I have BJA3 and have followed the formulas on page 20, but I do not see a formula to determine the covariance. I have also looked at page 142 of Griffin to no avail with respect to the covariance, any suggestions?

[Don Schlesinger]

> Don,

> I have BJA3 and have followed the formulas on page 20,
> but I do not see a formula to determine the
> covariance. I have also looked at page 142 of Griffin
> to no avail with respect to the covariance, any
> suggestions?

Griffin's formula works for any number of spots, n.

Don