I like to consider myself an open-minded person.
Although often dismissed as Gambler's fallacy
, I find Ellison's arguments about the relation between past present and future spins
Recently I stumbled upon the following paper, about the Law of the third
in random games by Don A. R. Colonne B.Sc., MBA, M.A.(Econ)
What differentiates this essay from other similar arguments is that it is presented with scientific formality (ie. "research", "findings" etc.)
To tell you the truth it did not convince me more than Ellison's arguments, but I think it might be an interesting read.
- - - - - - - - - - - - - - - - - - - - -THE LAW OF THE THIRD
A FUNDAMENTAL RESEARCH DISCOVERING THE
MATHEMATICAL EQUATION REGULATING
RANDOMNESS WITH REPLACEMENT
Every Random numerical activity With Replacement such as Roulette and Dice Games in the gaming industry, Lotteries etc. which have multiple equally probable outcomes that could occur is believed to be Mutually Exclusive and Independent that two outcomes cannot occur simultaneously and the next outcome does not depend on what occurred in the past.
This Fundamental Research clearly reveals the fact that such activities are regulated by a Generic Linear Mathematical Equation. Depending on the number of equally likely outcomes (N) that could occur, the nature approximately hides one third of N.
The Roulette Players and Casinos have visually observed this phenomenon for decades and termed it as the Law of the Third. In the event of European Roulette, there are 37 equally likely outcomes that could occur and it had been observed that within any 37 consecutive outcomes, there are only 23-24 distinct numbers (DNs) and the other 13-14 numbers are not present. In other words there are 13-14 numbers among the 37 that have repeated.
The First Phase of this research firmly established the fact that this observation made by the Roulette Players is valid by analyzing 30 data sets comprising 37 consecutive spins each, randomly obtained from the Live Spinning Mode in a Real Casino
, Live Spinning Mode in an Internet Casino, Auto Spin Mode in an Internet Casino and Random Numbers Generated by the computer in an Internet Casino. All four modes firmly established compliance with the Law of the Third.
Based on such observation, the Second Phase of the research was commenced. The individual numbers from 1 to 50 were tested; each individual number 30 times by drawing them from a bin with replacement and the average number of DNs across the 30 samples were tabulated. Through a Regression Analysis, the Best Fit Line was established and the Liner Mathematical Equation Y = 0.6291X + 0.2402 was derived. When X was equated to 37 for the data samples used in the first phase, Y became a value between 23-24, which proved the fact that the Law of the Third is not specific to Roulette but it is generic to any random numerical activity with replacement. The Y value therefore is termed as Colonne’s Value.
The Third Phase of the research analyzed 200 consecutive draws of the most popular lottery in Sri Lanka which draws an alpha-numeric number from a machine comprising 7 compartments, one character of the alphabet except the letter “I” and a six-digit number (e.g. E225175), each letter drawn from a compartment containing 25 letters and each number drawn from six different compartments containing the individual numbers 0-9. The analysis revealed that the alphabetic character (1/25 probability), the first two numbers, the middle two numbers and the last two numbers (1/100 probability), are in strict compliance with the Law of The Third.
In summary, the probability
of occurrence of a particular number as the next outcome is not 1/N and it varies and
depends on whether it had already occurred within the immediate past outcomes equal to the Colonne’s Value (23-24 in the event of Roulette). Thus, the Old Hypothesis of Independent Events needs to be replaced with the New Hypothesis of Dependent Events based on immediate Past Outcomes