### Author Topic: Crazy (?) Theory about the law of the third and independent events.  (Read 5498 times)

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#### kav

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##### Crazy (?) Theory about the law of the third and independent events.
« on: July 20, 2016, 08:59:57 AM »
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 quite interesting.
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

ABSTRACT

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.
http://www.filefactory.com/file/312kn604xr2z/law-of-the-third-research-report.rar
« Last Edit: July 20, 2016, 10:02:17 AM by kav »

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#### scepticus

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #1 on: July 20, 2016, 09:53:47 AM »
Does anyone know if there have  been rejections of this work ?

#### Sheridan44

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #2 on: July 20, 2016, 10:26:44 AM »

#### BlueAngel

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##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #3 on: July 20, 2016, 10:26:58 AM »
Does anyone know if there have  been rejections of this work ?

You simply cannot reject a fact, or you decide to live in denial!

Law of thirds is the law of chance/gambling!

#### scepticus

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #4 on: July 20, 2016, 10:31:57 AM »
Does anyone know if there have  been rejections of this work ?

You simply cannot reject a fact, or you decide to live in denial!

Law of thirds is the law of chance/gambling!
I wasn't talking about The Law of the Third BA but his analysis - his WORK .
Get it ?

#### BlueAngel

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##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #5 on: July 20, 2016, 11:46:58 AM »
Quote
Get it ?

No

#### Bayes

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #6 on: July 20, 2016, 12:11:59 PM »
Does anyone know if there have  been rejections of this work ?

I for one reject it. There's no disputing the law of the third, and his empirical formula is interesting, but you can't then make the leap of concluding (as he does), that it implies that outcomes aren't independent.

He concludes that:

Quote
5.1.3 In view of 5.1.1 & 5.1.2, it is implied that that after reaching the availability of Y past outcomes, the
probability of occurrence of a number which is not included in N distinct numbers as the next spin outcome
is (Y – N) / ((X – N)(X – Y)) and the probability of occurrence of a number which is among the N distinct
numbers as the next spin outcome event is (X – 2Y + N) /((N(X – Y)), against the conventional wisdom of 1/X.

So he reckons that the probability of a number which is among the last 20 distinct numbers, given that X = 37 and Y = 24, is

(X - 2Y + N) / N(X - Y) = (37 - 2 * 24 + 20) / 20 * 13 = 3.46% as opposed to 2.7%.

Anyone's welcome to confirm for themselves that this isn't true, sadly.

What he's done is to apply linear regression to find the empirical formula for the law of the third, which is ok. But he then goes on to "predict" the probability of the next outcome or group of outcomes from that formula. The trouble is that the formula describes the relationship between X and Y, which can't give the probability of the next outcome assuming a fixed X and Y. The next "outcome" is the next value of X, not the probability of the corresponding Y given a value of X.

The relationship shows that the "Law of the Third" is a true relationship which applies for all values of X, but it can't turn independent events into dependent ones.

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#### Dane

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #7 on: July 20, 2016, 02:29:23 PM »
Crazy, yes!

In an old German roulette book I once read about "ZWEI DRITTEL GESETZ" (Law of the thirds).
As far as I remember, TWO numbers (average) ought to be sleeping  still right after 3X37 spins.
The author also analyzed the appearances of the six double streets.
One cycle in this context = Six spins.
He mentioned that all parts, say all six six lines
ought to come within only 2½ cycles.

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#### BlueAngel

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##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #8 on: July 20, 2016, 08:30:16 PM »

Something else about the law of thirds, if you had 2 options, which one would you choose?

1) 6 out of 9 chances to win

2) 24 out of 36 chances to win

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#### kav

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##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #9 on: July 20, 2016, 08:43:00 PM »

Something else about the law of thirds, if you had 2 options, which one would you choose?
1) 6 out of 9 chances to win
2) 24 out of 36 chances to win
What do you mean "chances to win"? Probability to win?
If you are talking about probability 6/9 = 24/36 = 2/3  - doesn't make any difference.

#### BlueAngel

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##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #10 on: July 20, 2016, 10:05:33 PM »

Something else about the law of thirds, if you had 2 options, which one would you choose?
1) 6 out of 9 chances to win
2) 24 out of 36 chances to win
What do you mean "chances to win"? Probability to win?
If you are talking about probability 6/9 = 24/36 = 2/3  - doesn't make any difference.

Ok, let me put it another way, if there was no zero, would you prefer to bet on Red/Black or on a coin with 2 sides?

#### slpcorner

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #11 on: July 20, 2016, 11:54:40 PM »

In the Original Post... that last link sent me to a "warning your computer has been hacked" window that was made to look like it was from microsoft --- had to reboot.
« Last Edit: July 21, 2016, 12:04:45 AM by slpcorner »

#### kav

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##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #12 on: July 21, 2016, 01:51:03 AM »
Hi slp,
What you saw was possibly an ad.

#### slpcorner

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #13 on: July 21, 2016, 07:50:57 AM »
hmmm that's weird -- just my luck I suppose. Carry on, Gentlemen!

#### ybot

##### Re: Crazy (?) Theory about the law of the third and independent events.
« Reply #14 on: August 21, 2016, 02:24:29 AM »
It was a law of the third related system.
How dooes it play?