"Statistical Propensity" and "Diminishing Probability"

Are we simply guessing that a specific random event will occur? If so, are we nothing more than victims (or benefactors) of the fickle finger of lady luck?

I believe that some betting opportunities are "better" than others. In Roulette, betting that a series of 7 black decisions in a row will end within the next 5 decisions seems to be a "good" bet. It seems to me that it is a "better" wager than to bet that a series of 2 black decisions in a row will end within the next 5 decisions. Betting that 7 won't continue to 12 "seems like" a "better" wagering opportunity than betting that 2 won;t go to 7 BUT the mathematicians will tell us otherwise, the odds are exactly the same.

So why does it feel better? I think it feels better because we find ourselves encountering runs of 7 much more often than runs of 12. (But we also find ourselves encountering runs of 2 much much more often than runs of 7). Perhaps it is because of what Barstow calls the Law of Diminishing Probability and/or what R. D. Ellison calls the Law of Statistical Propensity. Although spins of the wheel and dice decisions are random events not related to previous decisions, it appears that over time the decisions tend to conform to or at least gravitate toward their mathematically expectations.

Ellison says:

"Taking all 38 numbers into consideration, the least number of times any number showed up was 16, and the most number of times was 50. This is a wider range, which accounts for the greater possibility of unconventional trends in a larger sampling, but not one of the 38 numbers tried to escape from the corral. Meaning, each one was compelled to show up a minimum number of times, but not too many times."

From: "American Roulette Is Now Mathematically Beatable" - by R.D. Ellison
See: http://www.thegamblersedge.com/propensity.htm

I believe that perhaps we can discover ideal betting opportunities. These would be bets that we would win more often than we'd lose AND (here is the tricky part) when we lose it is less than our winnings for that session or period of time. For example: suppose we should win this bet 7 out of ten times and with each win we'd gain one unit and with each loss we'd lose 2 units. For every 10 decisions, we should average a net of 3 units.

Eillison is promoting his 3Q/A Roulette system (which I have not tried) and arguing Statistical Propensity in support of it. I'm not sure (because I have not done the math) but if Ellsion is saying that the mathematical expectation is such that his wagering plan wins more often than it loses and wins more money than it loses, then it passes my test (and I imagine everyone else's) for a "good" bet.