# Blackjack - Standard Deviation

#### Overkill

##### New Member
Hello all,

I am brand new to this forum. Thank you for having me.

I've been researching online the answers to my questions.

For about 10 years, I have been developing ways to beat casino blackjack. As some of you know, some interesting research has been done in terms of ensuring a random shuffle.

My strategies, which seem to hold some promise, operate under the premise of the nonrandom shuffle. As such, the strategies will not work with a machine shuffle.

Anyway, in a small sample of 163 hands, I am ahead 45 units. Using a double deck standard deviation of 1.15802, I find that my outcome of being ahead by that much is just over 3 standard deviations. (1.15802 X square root of 163 = 1 standard deviation = about 14.78. Also, the mean we would expect after playing 163 hands is, I believe, about a loss of 1 unit.). So, my outcome of being ahead 45 units is more than 3 standard deviations to the right of the mean, approximately.

My question: because the standard deviation TAKES INTO ACCOUNT sample size, cant I say that, even though my sample size is small, a finding of +45 units in 163 hands is really, really unusual (like more rare than 1/100)? (My fellow posters on the blackjack website insist that "anything can happen" with such a small sample and that any finding with 163 hands is embarrassingly meaningless, but I consistently see people on the internet drawing conclusions from standard deviation findings using samples much smaller, like n = 24.).

I keep seeing on the internet the number 30 as a minimum 'rule of thumb' sample size.

Also, the experts on the blackjack website are heavily, heavily into running computer simulations with extremely large numbers. Perhaps the most respected blackjack computer guy in the world would claim, for instance, that 400 million rounds of blackjack is insufficient to test a hypothesis. Instead, he would argue that 2 billion rounds are needed!

Obviously, because my strategies only seem to work with manually shuffled (not randomly or machine shuffled) cards, I wont live long enough to deal myself more than, say, 100,000 rounds of blackjack.

So, assuming 163 is a large enough sample to draw standard deviation conclusions (e.g., "there is only about a 1% chance that my finding was due to chance and not something systematic") from, how can I know that with billions of hands I will get the same result (i.e., more than 3 standard deviations to the right)?

I realize more is better when it comes to sample size, but why when it comes to interpretation of standard deviation? Like I said, sample size is 'built into' standard deviation. Does a finding of 3 standard deviations to the right of the mean with a sample of 163 have less significance than a finding of 3 standard deviations to the right of the mean with a sample of, say, 10,000? If so, why?

Ive been researching on You Tube, etc. the STANDARD ERROR and how it always goes down with increasing sample size. Is standard eror more appropriate than standard deviation in my case?

Again, I want to have confidence (confidence intervals via standard error?) that my smaller sample size findings will generalize to samples much bigger, like the population, so I can be more confident I will make, and not lose, money in any long-run scenario.

Thank you.

#### staassis

##### Active Member
I did not understand everything and, frankly, did not read every paragraph. Yours is a very long message. However, this I can say. If you are serious about blackjack to the extent of developing your on strategies and going to Las Vegas, you have to run Monte Carlo simulations. 30 data points are not sufficient for accurate inference in almost any estimation problem. But your problem does not even seem to be an estimation one. How the decks are shuffled and how the bias towards "10s" or "faces" is slowly aggravated through the game sequence is more or less clear. What you are trying to do is test the optimality of your decisions in more or less known environment. So simulate.

If you decide to improve on your know-how and polish the strategies a bit, methods of stochastic optimization may help.

#### Overkill

##### New Member
Thanks, staassis, but I still have questions unanswered. Thank you for the suggestions, but can you guys address my questions:

Does a finding of 3 standard deviations to the right of the mean with a sample of 163 have less significance than a finding of 3 standard deviations to the right of the mean with a sample of, say, 10,000? If so, why?

I've been researching on You Tube, etc. the STANDARD ERROR and how it always goes down with increasing sample size. Is standard error more appropriate than standard deviation in my case?

Again, I want to have confidence (confidence intervals via standard error?) that my smaller sample size findings will generalize to samples much bigger, like the population, so I can be more confident I will make, and not lose, money in any long-run scenario.

With all due respect, if you don't have the time to read the entire original post carefully, you inevitably end up answering questions that weren't asked, and then I am left asking the same questions again. Also, another unintended consequence of not reading the post is that the subsequent posts go way off the mark. We end up somewhere in Canada when I was hoping to go to Florida.

Yes, my post was long. But as you can tell from experience, what inevitably happens with many posts is that an original poster asks a question without providing enough details. Then, the next few exchanges are wasted clearing up what could have been included in the original post.

My original post is rich with details. This seems to be an efficient way of posting, as long as folks can take time to read the post. If someone doesn't have adequate time to address a post, please wait until you can.

I hope I am not coming across 'too strong.' It's just that I was really hoping for some specific answers to my questions. But perhaps I should just be grateful to get any help I can get.

Thanks again!

#### Overkill

##### New Member
Sorry for the confusion, Dason. Double deck refers to 2 decks of cards. 1.15802 units is the standard deviation for a single hand of double deck blackjack. For a single hand, a player can win or lose a maximum of 8 units, but usually it is much less.