Standard devation ques

I just went out and bought Blackjack Attack and a few of the Beat the X-Deck game books. My main question is on the second part of the chapter where Don explains standard devation. Suppose I know what my exact average bet will be for a certian number of hands how do I figure ount what my sd will be? I know that the regular formula is {1.1 * (sqrt)N} where N = number of hands played, but that doesn't seem to explain the sd numbers Snyder gave in his books. Also really stumped ove the sd per hand. Isn't the square root of 1 still 1? What am I missing here?

ed

Yes it is still 1.0 The problem and confusion stems from the concept of the standard blackjack hour or 100 hands. The standard deviation per hour is 10 times the standard deviation per hand, while the expected value per hour is 100 times that per hand.

So what if this is easy to understand and convert to the measure SCORE. Watch the chaos that happens when you try to find the equivalent for a table hopper. Then the stuttering begins such as you describe, where you are wondering: "do I multiply by ten, divide by 100?"

Just go back to per hand numbers and things will work out fine.

The standard deviation is the SQR of the total of the probability of each outcome multiplied by the payout of each outcome squared, term by term. An aceptable result can be found by inserting instead of each outcome the average variance per hand, which usually revolves around the way the rules change according to your double down rules, and the square of the amount bet. That is what I did in my Blackjack Therapy in free scaled down version on bjrnet.com, in the free counting systems board there (I would include the Url, but search for "zombie" and you should still find the url link he put up in a post here about 1 month ago).

That is where I show how to reduce down resonable estimates of the standard deviation to just the frequency of each betting level in your spread.

I just wanted to point out where the confusion comes from so often. It is not a knock on BJA so much as pointing out a missing explanation. You want to go to the 4th chapter of BJT.

I hope this helps!

Adapting from BJT
start with the probability of your high bet or pr

Sources for such information would have to start with Snyder�s book series on Beating the _decks, where a separate book was written for 1,2,4,6 and 8 deck games, or a simulator that can give you a probability of a given true count, given the number or decks in the pack and conventional shuffle point.

If you are jumping your bets between a high bet and low bet, your average bet is:

AB=pr*(H-1)+1

If you are using a proportional betting schedule that calls for different bets at each true count you expand out and:

AB=pr1*H1+pr2*H2��prn*Hn

A similar set of formulas is derived from Wong�s Proffesional Blackjack for calculating standard deviation per hand. Once G (gain per hand see the rest of BJT) and sd are found for one hand approximations can be used from the same book, or similar mentions in Theory of Blackjack by Peter Griffin, to adjust for math measures such as variance and covariance between hands, if you typically play more than 2 hands (you might notice that these formulas are in terms of variance and covariance ONLY meaning that they give the fraction of one unit to bet on each hand that results in the same variance per round that betting one unit on one hand does).

The simple formula for sd is�

..sd=SQR[FBV*((H^2-1)*pr+1)]

In the formula for proportional betting schedules the H and pr terms expand as:

H1^2*pr1+H2^2*pr2�..,+H^2*prn; we take the sum, multiply by the FBV and take the SQR.

Fortunately FBV, or flat bet variance is mostly tied to the probability of your double downs and for virtually any game is:

1.2 for d10 games where you can double on 10 and 11 only,

1.28 for DOA games, and

1.32 for DA$ games,

As pointed out by posters on Yahoo's Card Counter's Cafe I omitted the FBV for early surrender and late surrender games.