# Thread: hey math friends...SD question

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## hey math friends...SD question

I've been playing with an excel sheet I put together to look at various relations. I have cribbed the count frequencies and SDs from CVCX for my count. Is it correct to use a weighted average of the SDs by frequency to generate an overall SD for the specific game? I get 1.162 when I do it that way. Thanks, RG.

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No, that will distort the overall variance because your bets are likely different sizes at each true count.

Using a weighted average (and a weighted average bet) will give you a reasonable answer unless you have some wide ranging bet spread.

I believe 1.15 is the general SD number for blackjack.

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Here is an article on the Law of Total Variance: https://en.wikipedia.org/wiki/Law_of_total_variance

Of note, the special case at the end applies to this situation. If you have the EV, variance (standard deviation squared) and frequency at each true count, then you can get the total variance. The square root of the Total Variance is then the total standard deviation. This formula is difficult to use on a spreadsheet unless you create a function for it.

The method you are proposing is the first term of the formula below. The results of the additional 2 terms are small in comparison, so you might consider your method as a reasonable approximation.

From the article:
"One special case, (similar to the law of total expectation) states that if is a partition of the whole outcome space, i.e. these events are mutually exclusive and exhaustive, then

In this formula, the first component is the expectation of the conditional variance; the other two rows are the variance of the conditional expectation."

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Thank you both for your answers. This will take some further study!

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