This is a concise summary of the history of the development of Probability Theory. If you dig deeper, especially into the work of Bernoulli, you will understand why I made the comment [somewhere] in the Fooled By Randomness Thread that Bernoulli would roll over in his grave if he could read some of the posts here. Why not seek the TRUTH?

From Calculus, Volume II by Tom M. Apostol (2^{nd} edition, John Wiley & Sons, 1969 ):

"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite.

This problem and others posed by de Méré led to an exchange of letters between Pascal and Fermat in which the fundamental principles of probability theory were formulated for the first time. Although a few special problems on games of chance had been solved by some Italian mathematicians in the 15th and 16th centuries, no general theory was developed before this famous correspondence.

The Dutch scientist Christian Huygens, a teacher of Leibniz, learned of this correspondence and shortly thereafter (in 1657) published the first book on probability; entitled De Ratiociniis in Ludo Aleae, it was a treatise on problems associated with gambling. Because of the inherent appeal of games of chance, probability theory soon became popular, and the subject developed rapidly during the 18th century. The major contributors during this period were Jakob Bernoulli (1654-1705) and Abraham de Moivre (1667-1754).

In 1812 Pierre de Laplace (1749-1827) introduced a host of new ideas and mathematical techniques in his book, Théorie Analytique des Probabilités. Before Laplace, probability theory was solely concerned with developing a mathematical analysis of games of chance. Laplace applied probabilistic ideas to many scientific and practical problems. The theory of errors, actuarial mathematics, and statistical mechanics are examples of some of the important applications of probability theory developed in the l9th century.

Like so many other branches of mathematics, the development of probability theory has been stimulated by the variety of its applications. Conversely, each advance in the theory has enlarged the scope of its influence. Mathematical statistics is one important branch of applied probability; other applications occur in such widely different fields as genetics, psychology, economics, and engineering. Many workers have contributed to the theory since Laplace's time; among the most important are Chebyshev, Markov, von Mises, and Kolmogorov.

One of the difficulties in developing a mathematical theory of probability has been to arrive at a definition of probability that is precise enough for use in mathematics, yet comprehensive enough to be applicable to a wide range of phenomena. The search for a widely acceptable definition took nearly three centuries and was marked by much controversy. The matter was finally resolved in the 20th century by treating probability theory on an axiomatic basis. In 1933 a monograph by a Russian mathematician A. Kolmogorov outlined an axiomatic approach that forms the basis for the modern theory. (Kolmogorov's monograph is available in English translation as Foundations of Probability Theory, Chelsea, New York, 1950.) Since then the ideas have been refined somewhat and probability theory is now part of a more general discipline known as measure theory."

NASHVILLE, TENN United States Member #33372 February 20, 2006 1044 Posts Offline

Posted: October 14, 2010, 8:40 pm - IP Logged

I do not think anyone on this site believes it is possible to mathematicqlly predict the outcome of each and every draw at any given time or place. Mathemantics deals only wwith repeatable results.

What we are looking for is an algorithym which will make playing the lottory profitable. We fully expect to "not win" most of the time but hope, when the "win" does come, the reward far exceeds the cost.

Statistics only help us to see the problem we face; not a solution to the problem. So we try our best, searching, experimenting, backtesting, thinking, and talking with others who share our passions.

To date, I know of no algorithym which does what we wish. That is not to say one does not exist. We do not allow the fact that a successful algorithym has not been found to deter us from our crusade. We will plod along. We will succeed.

mid-Ohio United States Member #9 March 24, 2001 19823 Posts Offline

Posted: October 14, 2010, 9:38 pm - IP Logged

As GASMETERGUY says, no reasonable player would believes it's possible to mathematically predict the outcomes of each drawing every time but I believe it's possible to come up with a system that improves the odds of winning. I doubt if playing lotteries can ever be profitable without winning a few second prizes or eventually a jackpot. If such a system or algorithm is ever developed we'll probably read about one person or group winning several lottery jackpots within a year, I doubt if they would be selling or sharing it.

* you don't need to buy more tickets, just buy a winning ticket *

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: October 14, 2010, 11:51 pm - IP Logged

Quote: Originally posted by GASMETERGUY on October 14, 2010

I do not think anyone on this site believes it is possible to mathematicqlly predict the outcome of each and every draw at any given time or place. Mathemantics deals only wwith repeatable results.

What we are looking for is an algorithym which will make playing the lottory profitable. We fully expect to "not win" most of the time but hope, when the "win" does come, the reward far exceeds the cost.

Statistics only help us to see the problem we face; not a solution to the problem. So we try our best, searching, experimenting, backtesting, thinking, and talking with others who share our passions.

To date, I know of no algorithym which does what we wish. That is not to say one does not exist. We do not allow the fact that a successful algorithym has not been found to deter us from our crusade. We will plod along. We will succeed.

GASMETERGUY,

"I do not think anyone on this site believes it is possible to mathematicqlly predict the outcome of each and every draw at any given time or place."

Although you must admit there are some here who are not as realistic as you, I don't think anyone has ever claimed that such a feat is possible! I have never ascribed that belief to anyone. What I have noticed, and dissented on, is the belief of many that, "an algorithym which will make playing the lottory profitable" exists. For the reasons given in the discussion above of Laplace's metaphysical statement, I don't think you are going to find one. In one of my earlier posts I compared the chances of succeeding to the chances of winning a prize playing a Tchaikovsky Piano Concerto wearing boxing gloves! This becomes more meaningful when you close your eyes and contemplate the chaotic movements of ping pong balls in their respective machines. Of course, as Laplace asserted, there are laws of physics at play that could possibly, not plausibly, in some excrutiatingly complex way, be used to predict ball movements microseconds in advance. But will this allow you to buy the right ticket before the draw? As for using number theory, or pattern observations, or eliminating Pick-5 sets that contain certain numbers of specific digits, there are simple computer simulation techniques that can be used to prove or disprove these kinds of claims. All these tests require is sufficient specification to allow a programmer to write the code. System proponents have been quite reticent in this regard. I have shown here how several different methods of choosing numbers to bet on Pick-3 games are no better than playing QPs, but people have unending ways of convincing themselves that there is something lacking in my analysis, most of them illogical, and they continue to believe in their systems. I am currently building a database of Powerball predictions and results. We shall see what the result of that is.

You sound reasonable, and several of your reasons above are why I play, and enjoy playing the lottery.

United States Member #93947 July 10, 2010 2180 Posts Offline

Posted: October 14, 2010, 11:57 pm - IP Logged

Quote: Originally posted by RJOh on October 14, 2010

As GASMETERGUY says, no reasonable player would believes it's possible to mathematically predict the outcomes of each drawing every time but I believe it's possible to come up with a system that improves the odds of winning. I doubt if playing lotteries can ever be profitable without winning a few second prizes or eventually a jackpot. If such a system or algorithm is ever developed we'll probably read about one person or group winning several lottery jackpots within a year, I doubt if they would be selling or sharing it.

RJOh,

"I believe it's possible to come up with a system that improves the odds of winning."

If you're referring to winning money over the long haul, I disagree.

If you mean increasing the NUMBER of WINNING TICKETS, I agree!

"I doubt if playing lotteries can ever be profitable without winning a few second prizes or eventually a jackpot."