Thanks so much, Dog Hand. I appreciate the time you put into your response. And thank you for showing your work. The answer and interpretation you arrived at were what I thought.

I used an online sim (I think it was bjsim) a few years back to investigate one of my strategies. (By the way, when I last checked, bjsim had changed some.). Anyway, as I recall it would only let me do sims with small numbers of rounds. When checking one of my strategies. the sim said my E.V. was 5.00% (actually 4.98%) for 5,000 rounds.

Regarding interpretation: I believe you will all say that the 0.036% probability (please see Dog Hand's post) is meaningless as only 5,000 hands were run in the sim. I no longer have Norm's nice sim that I purchased, so maybe I will ask one of you to run a billion or so rounds if you don't mind.

But in the meantime, what is the value of all that calculating that Dog Hand did if it is "meaningless." I was under the impression that the z score calculations ALREADY TOOK INTO ACCOUNT the (small) sample size.

Is it perhaps true that using z scores, etc. for the game of blackjack is an inappropriate use of z scores. etc., unless one is working with, say, 100 million rounds or so or more? But again, though we are only using 5,000 rounds in the above example, standard deviation, etc. is indeed BUILT IN to the calculations, no?, thereby obviating the need for millions of rounds?

If you believe the 5,000 round probability result (0.036%) is meaningless, does that also mean that you would predict that a sim of one billion rounds with my flat betting, non-progression strategy is no more likely to result in a positive player E.V. than just 'regular' (i.e., no 'strategy' or system) flat-betting, basic strategy Blackjack?