Calculating SD per hand with TC frequencies

A simple SD calculation looks like this:

SD= Bet*Sqrt(1.33)

However I'm asking about when calculating SD while accounting for TC frequencies. Say my spread is 1-2u and 70% of the time I bet 1u and 30% of the time I bet 2u. Would my SD per hand calculation look like this?


.7(1*sqrt(1.33))=.8072
.3(2*sqrt(1.33))=.69195

.8072 + .69195 = 1.49915

My SD = 1.49915

Can someone please explain if I'm totally wrong and why?

If the variance per hand is always 1.33 then those numbers look fine to me. I posted a spreadsheet a while ago that goes into more detail. You can input the TC frequencies, TC advantages, bet spread and the number of hands you play and it will calculate the EV, SD and some other stuff.

http://www.blackjackinfo.com/bb/showthread.php?p=15578

It's based on the charts in Blackjack Attack, which has some great information on calculating and using SD. There is also a good article on Snyder's website:

http://www.blackjackforumonline.com/content/6DeckText.htm

-Sonny-

Thanks Sonny, that helps a ton.

Question about your spreadsheet

Say I have a max bet of $80 on one hand and I wanted to spread my bet over 2 hands, would I enter $80 in the bet column and 2 in the hands column or would I enter $40 in the bet column and 2 in the hands column?

You would enter $40 in the Bet column and 2 in the Hands column. The Bet column is your bet per hand, not per round. You might also consider betting 2 hands of $60.

-Sonny-

I haven't looked at Sonny's spreadsheet, but does it agree with this result? I thought it would be like this:

variance = 0.7 * (1^2) * 1.33 + 0.3 * (2^2) * 1.33
variance = 2.527
SD = sqrt(variance)
SD = 1.5897

Am I missing something here?

I don't think so. Sonny's spreadsheet agrees with you.

I don't know - would not NYnefingers calc above be correct?

Just asking because I know I struggle with this stuff all the time with no math background and if you say something I can't figure out I have to know where I'm going wrong lol.

It just seems to me the OP maybe should have squared his bet unit?

Ordinarily yes, but not the way it was written in the original post. The unit size was outside of the sqrt function so it did not need to be sqaured. It can be simplified like this:

var = sqrt(2^2 * 1.33)
var = sqrt(4) * sqrt(1.33)
var = 2 * sqrt(1.33)

which is what was in the OP. However, the mistake that I did not notice (which Nynefingers picked up on) is that you have to apply the 70%/30% weighting to the variance, not the SD. SD is not additive so you cannot add 70% of one SD to 30% of another. You must always convert them to variance before you try to scale them or do any other operations to them. That is the correction that needs to be made in the OP.

-Sonny-

Thanks again Sonny

In the charts of Blackjack Attack, the variances for the same number of hands are slightly different depending on the TC, why is it?

Mike

Because they are different.

Norm,

Good one! But I was expecting a more mathematical explanation.

Splits, double downs, insurance, pushes and blackjacks all vary by count. All of these affect variance. But the difference is not large. On average, sqrt 3 is probably closer. Griffin used 1.26 for the average squared result using BS. But it was a rough calc.

Add bonuses and side bets and the numbers can change significantly.

OK now.
Is BJ SD roughly equal to the SD of betting Odd-Even in roulette?