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.