# Thread: Distribution of SCOREs at different number of rounds

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## Distribution of SCOREs at different number of rounds

Background:

I have always been fascinated with visual distributions of a property under different conditions and thanks to Norm's wizardry I was able to use CVData to that end where I ran 6 different groups of sims each consisting of 500 different sims as detailed below:

500 — 10 million round sims || 500 — 25 million round sims || 500 — 50 million round sims || 500 — 100 million round sims || 500 — 250 million round sims || 500 — 500 million round sims

All sims consisted of 6D shoe at 75% penetration, play-all 1-15 bet spread using Hi-Lo full index for playing.

The distribution of SCORES from all 500 sims per group are summarized in the graph below.

A "True SCORE" for the game was calculated by running a 250 billion round sims (assumed to be THE answer).

Discussion:

As expected, the distribution of SCOREs gets narrower as more rounds are included in a sim which is just a visual corollary of the fact that expectation value is proportional to the number of rounds, while standard deviation is proportional to the square root of the number of rounds.

The distributions also support the known fact that a sim using less than 500M rounds cannot really be trusted to give an accurate number (with modern computers 10 billion round is really fast). I had run a 40 million round sim of perfect play using a combinatorial analyzer so this proves my sim results are not really accurate (need more computing power!)

Lastly, a few words about the 10 million round sims SCOREs distribution. 10 million rounds is a large number of rounds, even a large and disciplined BJ team cannot really pull more than 2 million rounds per year which will have an even larger distribution of SCOREs that's why serious BJ teams look for much stronger with higher SCOREs.

Acknowledgment: : Special thanks to Norm again, I had forgotten how fast CVData is! !!

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Very nice post!

I had run a 40 billion round sim of perfect play using a combinatorial analyzer so this proves my sim results are not really accurate (need more computing power!)
Didn't you mean "million" instead of "billion"? Because 40 billion rounds is quite accurate especially for a combinatorial analysis.

Sincerely,
Cac

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Originally Posted by Cacarulo
Very nice post!

Didn't you mean "million" instead of "billion"? Because 40 billion rounds is quite accurate especially for a combinatorial analysis.

Sincerely,
Cac
Yep thanks for catching this Cac!!

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