Monday, August 25, 2008

"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.

BACCARAT - Barstow, Zumma and Excel


In Frank Barstow's excellent treatise on gambling systems, "Beat the Casino" (1979 Carlyle) the author makes some pretty strong claims about expected success using his pet systems. He claims on page 216, for example, that his "Barstow System" "can" average 12 units per hour profit. His conclusions are the result of a combination of reasoning, simulated trials and "real" Casino play.

It strikes me that with today's technology and information we can "test" Barstows claims in a way that he could not have easily accomplished.

Erick St. Germain's "72 Days at the Baccarat Table" (1995 Zumma) lists the outcomes of each decision in 600 "real casino" Baccarat shoes (about 40,000 decisions). Using a simple Excel spreadsheet, I have been able to test some of the the Zumma shoes against several systems in Barstow's book. Although I do not expect to discover the keys to the kingdom, I firmly believe that this time-consuming task will help illustrate the strengths and weaknesses of certain systems and be helpful in identifying trends within the shoes.

I'm curious if any of YOU have tried a similar approach and might be willing to share the results or are you aware of where this information may be obtained. Also, would you be interested in testing some of these 600 shoes yourself?

I plan on making some of my research available on this blog to give you all a better idea of what I'm talking about.

In the meantime "happy number crunching."