United States Member #59354 March 13, 2008 4051 Posts Offline

Posted: April 29, 2011, 2:48 am - IP Logged

Quote: Originally posted by toeplitz on April 27, 2011

I wonder what Paul Erdos thought about lottery games.

Also as for Monte Carlo Methods I wonder how many here know that the term itself was coined by Stanislaw Ulam and John von Neumann?

von Neumann was after all the father of Game Theory beginning with his publication of the Minimax theorem in 1928 which states that in matrix zero-sum games with perfect information, there exists a pair of strategies for both players that allows each to minimize his maximum losses --- applicable to our position.

Persons blocking discourse here should go back to the beginning and read "Zur Theorie der Gesellschaftsspiele" and also the volume which von Neumann co-authored with Oskar Morgenstern as 'hobby project' while running a section of the Manhattan Project in '44 "Theory of Games and Economic Behavior".

Besides the afore-mentioned Monte Carlo Methods we should also be thinking about such terms as 'Random Walk' and Markov chains. Also MCMC (Markov chain Monte Carlo methods). I've seen many interesting methods in computational biology and mathematical biology which would be applicable to our situation.

Also the term NOISE as in unwanted data. And one eliminates Noise through use of a Filter. Usage of Kalman filters may be of use to us in our situation.

In 1992 Stefan Klincewicz deftly showed how the Irish Lottery (6/36 at that time) was vunerable to a brute force attack. Also the Romanian born Australian accountant Stefan Mandel did the same a few times in several countries. He also reportedly spent several hudred hours learning Hungarian so as to carry on a correspondence through much of the 1980's with Paul Paul Erdos about the 'Law of Large Numbers' and Combinatorics.

In general there seems to be far too many nestbeschmutzers on here.

toeplitz

Don't take this the wrong way but I really, really, really like you. Markov chains, this is first time I have ever heard

the term but unless I have misunderstood the basic idea then it would describe exactly how I view random lottery

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

Posted: April 29, 2011, 10:08 pm - IP Logged

Since this is a Poll Thread on Interest inBacktesting and Simulation, perhaps it would make sense to start a new thread for this discussion. How about "Markov Chains and the Lottery" in the Mathematics Forum?

Here is some information to get you started...

Here you can find multiple sources on Markov Chains and their applications:

A Markov chain is a sequence of random values whose probabilities at a time interval depends upon the value of the number at theprevious time. A simple example is the nonreturning random walk, where the walkers are restricted to not go back to the location just previously visited."

I know of no such restrictions on Lottery Draws.

Here is a "Must Read" for anyone interested in these matters. You can read it at Google Books:

If you can't give up this idea and are willing to ignore the mainstream science, you can check this out. There is even lottery software available here, some free, some not. http://www.saliu.com/Markov_Chains.html (Markov Chain in Gambling, Game Theory, Lotto and Lottery, Ion Saliu, 2003)

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

Posted: May 2, 2011, 10:17 am - IP Logged

Quote: Originally posted by RL-RANDOMLOGIC on May 2, 2011

Jimmy

I don't know the ends or outs of Markov chains but if you thought of the lottery in terms of the lexigraphic indexed

Big Wheel senario then it would be impossible. While the same set could be drawn it would require a foward

movement in time/distance. The time/distance from the last draw would equal 100% or 360 degrees for this to happen.

PS. I checked out the link to Markov chains and the book ended in the 490's, could not find page 517

RL

RL-RANDOMLOGIC,

Sorry, but when you told toeplitz, "this is first time I have ever heard the term but unless I have misunderstood the basic idea then it would describe exactly how I view random lottery draws," I thought that you would really, really, be interested in the topic. I guess I was wrong.

"PS. I checked out the link to Markov chains and the book ended in the 490's, could not find page 517"

This is understandable. Many people find Google Books tricky to navigate. Maybe you'll do better viewing it at Amazon.com.

United States Member #13130 March 30, 2005 2171 Posts Offline

Posted: May 2, 2011, 12:21 pm - IP Logged

I checked out the link Jimmy posted. It seems the pages take a while to load, so at first you'll get a message saying you can't view some/many pages. After a while, they do show up. Pages that actually aren't included will have a message like Page 510 to 514 not shown in this preview.

In neo-conned Amerika, bank robs you. Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

United States Member #59354 March 13, 2008 4051 Posts Offline

Posted: May 5, 2011, 7:35 am - IP Logged

Quote: Originally posted by time*treat on May 2, 2011

I checked out the link Jimmy posted. It seems the pages take a while to load, so at first you'll get a message saying you can't view some/many pages. After a while, they do show up. Pages that actually aren't included will have a message like Page 510 to 514 not shown in this preview.

bgonÃ§alves Brasil Member #92564 June 9, 2010 2133 Posts Offline

Posted: May 5, 2011, 12:58 pm - IP Logged

A Markov Chain in Discrete Time is a stochastic process in which the variable "t" represents time intervals, {X (t), t = 0, 1, 2, 3, ...}, and which enjoys the Markov property,ie, the probability of X (t) transition from state "i" to state "j" in the next period depends only on the present state and not the states visited in past periods.

In our study we only consider Markov chains with the following characteristics:

• The state space X is finite or countable (discrete states).The present state is defined by the delay or recent success in a row suffered by a group of dozens of the universe;

• Transition probabilities between states are constant in time (stationary Markov chain), ie, the probability of a dozen happen depends on how many consecutive hits in this state or its recent delay.

A Markov chain in discrete time is completely defined if we know the states X = {0, 1, 2, ..., s} and transition probabilities between states in a period.

The characteristic property of a Markov chain is that his memory reaches back only to the most recent state.The knowledge of its current state is sufficient to describe the future development of the process.The Markov model is a simple model for random systems evolved over time when the successive states of a system are not independent.

A Markov Chain in Discrete Time is a stochastic process in which the variable "t" represents time intervals, {X (t), t = 0, 1, 2, 3, ...}, and which enjoys the Markov property,ie, the probability of X (t) transition from state "i" to state "j" in the next period depends only on the present state and not the states visited in past periods.

In our study we only consider Markov chains with the following characteristics:

• The state space X is finite or countable (discrete states).The present state is defined by the delay or recent success in a row suffered by a group of dozens of the universe;

• Transition probabilities between states are constant in time (stationary Markov chain), ie, the probability of a dozen happen depends on how many consecutive hits in this state or its recent delay.

A Markov chain in discrete time is completely defined if we know the states X = {0, 1, 2, ..., s} and transition probabilities between states in a period.

The characteristic property of a Markov chain is that his memory reaches back only to the most recent state.The knowledge of its current state is sufficient to describe the future development of the process.The Markov model is a simple model for random systems evolved over time when the successive states of a system are not independent.

"The Markov model is a simple model for random systems evolved over time when the successive states of a system are not independent."

Some models look back further than 1 transition state, but generally, this is an informative simplification. The important thing for lottery players to remember is the key phrase, "NOT independent."

OkJimmy,thenyou mightconsiderdevelopingasystemora50/50sitema Topredictthathalfthe numbersare goingto repeat,orsequencesofpatternsto peerswhohavePossibilityof repeating, astherepetitionofaneventisthe likelysecret,alotteryexampleof49 / 6,tryto seethe repetitionofpairsandtriplets,rather thanprovidenumbers Randomly,andtheother 50%(system2)to seeforthreetypesofoutputfrequencies,hot,cold andmédios.emNUMCgamewecanprovide100%,reachingup to 75to 80%ofmathematical prediction,there is always arandom factor,a game of49 / 6ifwe hitfourpairsofnumbersbythe union,will onlymisstwomorenumbers, tohit100%.Astandard Replayshows thefrequency ofrepetitionofthetwonumbersfrom alotteryof49 / 6 We can thinkoffournumberspredict!

"We can thinkoffournumberspredict!"

This sounds like a system that someone could program a backtest for which could remove any doubts that obviously remain that previous draws are independent of today's draw.

mid-Ohio United States Member #9 March 24, 2001 19891 Posts Online

Posted: May 6, 2011, 4:38 pm - IP Logged

Quote: Originally posted by jimmy4164 on May 6, 2011

"We can thinkoffournumberspredict!"

This sounds like a system that someone could program a backtest for which could remove any doubts that obviously remain that previous draws are independent of today's draw.

If one observed certain relations between present drawings and previous drawings, how will back testing disprove what they observed?

Observations such as half the time a drawing in a 5/39 game will have at least one number from the previous drawing is supported by calculating the odds and those of all 5 winning numbers hitting in the previous 15 drawings at least half the time even though only 70% of the numbers may be covered are more likely to be proved by back testing.

The only things back testing will disprove are things we already know aren't true.

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

If one observed certain relations between present drawings and previous drawings, how will back testing disprove what they observed?

Observations such as half the time a drawing in a 5/39 game will have at least one number from the previous drawing is supported by calculating the odds and those of all 5 winning numbers hitting in the previous 15 drawings at least half the time even though only 70% of the numbers may be covered are more likely to be proved by back testing.

The only things back testing will disprove are things we already know aren't true.

"The only things back testing will disprove are things we already know aren't true."

Using universal quantifiers like "only" in math and logic can get you in trouble. Other problems arise when you talk about "disproving" things. If you believe statistics of the frequency of numbers repeating over 15 draws can be used to provide an edge selecting for the next draw, why not write a backtest or simulation and see what happens?

mid-Ohio United States Member #9 March 24, 2001 19891 Posts Online

Posted: May 6, 2011, 9:48 pm - IP Logged

Quote: Originally posted by jimmy4164 on May 6, 2011

"The only things back testing will disprove are things we already know aren't true."

Using universal quantifiers like "only" in math and logic can get you in trouble. Other problems arise when you talk about "disproving" things. If you believe statistics of the frequency of numbers repeating over 15 draws can be used to provide an edge selecting for the next draw, why not write a backtest or simulation and see what happens?

I didn't say I believed, I said I observed.

Using a lottery program I can check any/all winning numbers with any amount of previous drawings. I checked 2251 of 2266 drawings of Ohio Rolling Cash5 and found the following number of times the 5 winning numbers had been in the previous 15 drawings at least 1 time:

5/5 = 1135 4/5 = 828 3/5 = 256 2/5 = 30 1/5 = 1 number pool size of 15 drawings = 28-29 (28/39 = 70% 1135/2251 = 50%)

When I checked the previous drawing of 2265 of 2266 drawings, I got the following:

MATCH 0 = 1084 MATCH 1 = 930 MATCH 2 = 218 MATCH 3 = 32 MATCH 4 = 1 MATCH 5 = 0 (1181/2265 = 52%)

The above are statistics/observations not beliefs.

Note: these figures only apply to Ohio Rolling Cash5 (5/39) and I can't say if knowing only these statistics have any advantage because they're probably normal for all 5/39 games but with other statistics I believe one may be able to develop profiles of combinations that are more likely to win. Only by winning more than normal would one know for sure. All any back testing would show is if any past winning numbers had one the profiles used but we already that if we used that data to develop them.

*that match 4 in a previous drawing happened back in '04. 12/14/04 - 03 11 20 29 35 12/13/04 - 11 20 29 35 37

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