Assuming if you've a valid point and your theories are very accurate why would you say "it all depends on luck".If it all depends on luck it dissolves the entire point of your mathematical notations.However you can't live a life with double standards as Einstein says "Live life like everything is a miracle or nothing is a miracle".You just did that by saying its based on mathematical expression in one of your posts and not supporting it by saying "it all depends on luck".
That is not how probability works. Probability follows a pattern, and luck is only the outcome of 1 variable, or a random pattern in the distribution that is unique to your situation.
https://en.wikipedia.org/wiki/Central_limit_theoremhttps://en.wikipedia.org/wiki/Law_of_large_numbers