You seem to like to use a lot of mathematical terminology. You're explanations aren't clear and I not even sure if they are relevant.
Have a look at this Poker Variance Calculator.
http://pokerdope.com/poker-variance-calculator/
It shows that your winrate is more reliable over larger number of hands played because variance has less effect on your winrate the more hands you play.
These are my results. Have a play yourself.
If your winrate is 5BB/100 over 100 hands the probability that you are a losing player (below 0BB/100) is 48%.
If your winrate is 5BB/100 over 1000 hands the probability that you are a losing player (below 0BB/100) is 44%
If your winrate is 5BB/100 over 10,000 hands the probability that you are a losing player (below 0BB/100) is 31%.
(Currently my winrate is 6BB/100 over 19,000 hands so there is still a 20% chance that due to variance, I am a losing player (below 0BBs/100) at 2nl atm)
If your winrate is 5BB/100 over 100,000 hands the probability that you are a losing player (below 0BB/100) is 6%.
If your winrate is 5BB/100 over 1,000,000 hands the probability that you are a losing player (below 0BB/100) is 0% (negligible).
In conclusion. the more hands you play, the more reliable your winrate becomes as variance tends towards zero as the number of hands you play tends towards infinity.
This was the main point of my first post in this thread.
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