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How do I prove my state lottery's CGNs are fixed?

Topic closed. 147 replies. Last post 8 years ago by Greg.

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January 20, 2009
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Posted: January 20, 2009, 12:19 pm - IP Logged

i think that anytime a person is involved wheather it be a computer programmer or the person who makes the balls used for some lottery drawing that there is a chance for someone to try to cheat. im not saying that it is happening im just saying that i think it is possible. do you agree????

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    New Member

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    January 21, 2009
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    Posted: January 22, 2009, 12:09 am - IP Logged

    Not necessarily.  In fact, I would say that for the person who makes the balls, it's in their best interest to make them function as perfectly and randomly as possible; that's the service they're selling.  Especially in the cases of large state lotteries, where the number of rules and regulations surrounding them is huge.

     

    Now, if we're talking about smaller operations, like casinos, then yes, it's certainly in their interest to cheat (like the video poker machines that were set to never pay out a Royal Flush).  Partly this is because they can get away with it, but mostly because the casino is a private, profit-driven endeavor.

     

    Just my thoughts.

      JADELottery's avatar - MeAtWork 03.PNG
      The Quantum Master
      West Concord, MN
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      Posted: January 24, 2009, 3:57 pm - IP Logged

      Thanks needawinner and TechBox,

      It's great thinking about the possibilities and theories about gambling establishments, state or private. This post is about the detection of those activities; if any exists. There can be any number of reasons why and how number fixing is done. This post deals with the way we can quantify it, represent it and see it. As we continue, this will become more evident as the data is collected and analyzed.

      Keep up the Great work.

      Presented 'AS IS' and for Entertainment Purposes Only.
      Any gain or loss is your responsibility.
      Use at your own risk.

      Order is a Subset of Chaos
      Knowledge is Beyond Belief
      Wisdom is Not Censored
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      Jehocifer

        bigato1010's avatar - army

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        February 22, 2006
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        Posted: January 31, 2009, 7:20 pm - IP Logged

        Thanks needawinner and TechBox,

        It's great thinking about the possibilities and theories about gambling establishments, state or private. This post is about the detection of those activities; if any exists. There can be any number of reasons why and how number fixing is done. This post deals with the way we can quantify it, represent it and see it. As we continue, this will become more evident as the data is collected and analyzed.

        Keep up the Great work.

        Hey JADE. execellent graphs . Do you think Michigan lottrey is fixed in your opinion ?

          JADELottery's avatar - MeAtWork 03.PNG
          The Quantum Master
          West Concord, MN
          United States
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          December 7, 2001
          3675 Posts
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          Posted: January 31, 2009, 7:49 pm - IP Logged

          Hey JADE. execellent graphs . Do you think Michigan lottrey is fixed in your opinion ?

          That remains to be seen.

          Although, there may be some interesting findings coming up that are not necessarily restricted to just Badger 5 or the Wisconsin Lottery.

          Wink

          Presented 'AS IS' and for Entertainment Purposes Only.
          Any gain or loss is your responsibility.
          Use at your own risk.

          Order is a Subset of Chaos
          Knowledge is Beyond Belief
          Wisdom is Not Censored
          Douglas Paul Smallish
          Jehocifer

            JADELottery's avatar - MeAtWork 03.PNG
            The Quantum Master
            West Concord, MN
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            Posted: February 7, 2009, 10:46 am - IP Logged

            Those of you watching and playing the Pick 3 should take notice of the numbers for the past year.

            There is a reason why I released JADE's Pick 3 Pick 4 Selector on my Birthday (2008-04-27); so it would be a memorable date.

            However, as a matter of reference, it's a good date to establish a beginning.

            Presented 'AS IS' and for Entertainment Purposes Only.
            Any gain or loss is your responsibility.
            Use at your own risk.

            Order is a Subset of Chaos
            Knowledge is Beyond Belief
            Wisdom is Not Censored
            Douglas Paul Smallish
            Jehocifer

              JADELottery's avatar - MeAtWork 03.PNG
              The Quantum Master
              West Concord, MN
              United States
              Member #21
              December 7, 2001
              3675 Posts
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              Posted: February 24, 2009, 11:02 am - IP Logged

              Those of you watching and playing the Pick 3 should take notice of the numbers for the past year.

              There is a reason why I released JADE's Pick 3 Pick 4 Selector on my Birthday (2008-04-27); so it would be a memorable date.

              However, as a matter of reference, it's a good date to establish a beginning.

              Those of you paying attention should be seeing some interesting numbers being selected.

              Regardless if the lottery is CGN or NOT, the kind of feedback that is generated from a Quantum Selection has some very Unusual Effects in a system of selection that is being controlled.

              Only in a truely Random selection will Qauntum Selection have no Unusual Side Effects.

              Look for it, it's happening right now in at least one of the Pick 3 Looteries we have been monitoring.

              Red Eyes

              Presented 'AS IS' and for Entertainment Purposes Only.
              Any gain or loss is your responsibility.
              Use at your own risk.

              Order is a Subset of Chaos
              Knowledge is Beyond Belief
              Wisdom is Not Censored
              Douglas Paul Smallish
              Jehocifer

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                Posted: March 11, 2009, 5:13 pm - IP Logged

                How do I prove my state lottery's Computer Generated Numbers are fixed? This is a perplexing and difficult task, but it's not beyond a reasonable plausibility. The task becomes an experiment with a number of steps to follow. Following this opening is a header outline of what can be expected in general; after that, each header is presented in more detail and may have data, graphs, explanations in logic and process, theories, etc. The contents in each header will not get too technical unless it is needed to help support a current or following idea, process, data, graph, computation or theory.

                Next is a list of each header and a brief explanation:

                • Pretext
                      Setup information.
                • Correlation
                      Simple explanation and graphs in the presentation.
                • Computations for Analysis
                      Draw mean and span, the Simplified Bidirectional Mean Averaging.
                • Wheel Application
                      Using the draw mean to derive wheel numbers.
                • Distributions and Analysis
                      Lottery and Wheel Pool distributions and draw span distribution.
                • The Pretest, Experiment 0
                      The 60 draw sample data for analysis and correlation from 2007-08-06 to 2007-10-04.
                • The Setup and Cost Effective Approach
                      If they're watching the Lottery Post Predictions, use it to an advantage.
                • The Test, Experiment 1
                      Draw and wheel data for the 60 day sample from 2007-10-05 to 2007-12-03.
                • The Conclusion, Experiment 1
                      Possible proof the Computer Generated Numbers are fixed?
                • The Posttest, Experiment 2
                      A 90 draw sample and wheel posting to play on current draw number deficiencies started 2007-12-04.

                 

                Pretext

                Prerequisites: Understanding of lotteries, lottery wheels, analysis and systems; graph reading and table reading skills; math operations, statistics, averages, line equations.

                In going through this, I ask that anyone reading this please keep this basic understanding in mind. This is not an attempt to try and predict any particular combination. This has more to do with reasonable expectation. I have stated in my blog and defined the difference between the two. The following is from my blog on 2007-02-23:

                "Reasonable Expectation and Prediction are often thought of as being the same; they are not. Prediction has a level of precision that is greater than Reasonable Expectation and Prediction can be derived from Reasonable Expectation. Reasonable Expectation has a level of accuracy that is greater than Prediction, however, Reasonable Expectation can only be derived from many different Predictions."

                Understanding this difference between reasonable expectation and prediction is important for this topic. There is a tendency to think this topic is about predicting exact combinations. It is about what would be reasonably expected from a lottery selection and the playing of a wheeled set of numbers in a combinatorial set.

                The lottery chosen to work with is the Wisconsin Lottery Badger 5. It is a pick 5 of 31 numbers game and is a completely Computer Generated Number game. It has been a Computer Generated Numbers game since its implementation back on 2003-02-17. The numbers selected will be analyzed based on their individual total frequency for the numbers 1 to 31. This creates a distribution and the distribution can be analyzed using a computational method called the Simplified Bidirectional Mean Averaging to show the average fluctuations in the data throughout the numbers  1 to 31. The span of numbers between the largest and the smallest numbers is also analyzed by distribution.

                The selected numbers from the previous day's draw are averaged to get a mean value and that mean value is used to create pool of 12 numbers. Those 12 numbers are then inserted into a set of combinations called a wheel. The wheel is then posted on the Lottery Post's prediction board and recorded for further analysis. The 12 numbers derived are also analyzed based on their individual total frequency relative to the 1 to 31 numbers. Here too, the analysis produces a distribution of numbers 1 to 31 and the Simplified Bidirectional Mean Averaging is applied to find the average fluctuations in the distribution.

                Both of these analysis procedures are applied to a set of 60 draws before the posting of the wheels and 60 draws during the posting of the wheels; they are experiment 0 (before) and 1 (during). Both experiments will produce a graph of distributions that can be compared to each other and between the drawn numbers and wheeled numbers. From that, it can be visually inspected to see if there is a correlation between the drawn numbers and the wheeled numbers.

                In any means of proving that something is influenced by something else, there needs to be a means of correlating the data in to the data out. The statistical information is provided via a link, however, it's easier to present the data in a graphical form for easy reading. If there are questions about the graphs, refer to the data links provided first. The data can be downloaded to perform additional analysis.

                 

                Correlation

                This is an over simplified description, correlation is the relationship between to different sets of data relative to the same event. Typically, it's thought of as degree of relationship between the Data A (in) to the Data B (out). It's like the heat put into a flask of water and the temperature measured or the electrical current put into a light bulb and the light emitted out. The level of correlation can be expressed as a value from 0 to 1. Later in the topic, this value will be referred to as the R-squared value. The closer to 0 the R-squared value is means there is low correlation between the Data A (in) and the Data B (out). A value closer to 1 means there is a high correlation between the Data A (in) and the Data B (out). Also, there are negative, neutral and positive relationships between the Data A (in) and the Data B (out). The more negative a correlation is means Data A goes in one direction and Data B goes in the opposite direction. The more positive a correlation is means Data A goes in one direction and Data B goes in the same direction. A neutral correlation means Data A changes, but Data B does not change in relationship to Data A. Below are some simple animated graphs to show how this would look.

                The animated graphs can be also shown as a line graph to display all the data values at once. The following are the same animated graphs as a non-animated line graphs.

                The data can also be graphed as an XY plot with Data A (in) on the horizontal X axis and Data B (out) on the vertical Y axis . The green line on the graph is the general trend line for each. A negative correlation will slant from upper left to lower right and the data will be fairly close to the line, a positive correlation will slant from the lower left to the upper right and the data will be fairly close to the line. A neutral correlation may be slanted or horizontal, but the data will not be very close to the line.

                Understanding these last two sets of line graphs is going to be important in showing the relationship between the wheel distributions (Data A) and the draw distributions (Data B). As the distribution data is presented, it will begin as a bar graph and then the Simplified Bidirectional Mean Averaging will be applied to give a line graph showing the average fluctuations in the distributions. The fluctuation distributions will be shown in both formats, line graphs and XY plots.

                 

                Computations for Analysis

                In order to get the wheel numbers and the average fluctuations in the distributions, a few math operations need to be done. First the mean value of the previously selected draw is needed to derive the wheel numbers. If the previous days draw is represented by these set of values for each column, {A, B, C, D, E}, then the mean is the sum of those numbers divided by the pick size, r. The equation is as follows:

                Dm = (A + B + C + D + E) / r

                Example, if the previous days draw is {1, 2, 3, 4, 5}, then the mean is Dm = (1 + 2 + 3 + 4 + 5) / 5, Dm  = 15 / 5 or Dm = 3. The mean will be applied to find the wheel numbers later.

                Next is the Simplified Bidirectional Mean Averaging and is similar to the posted topic Bidirectional Mean Averaging and the Wave Matrix. As the name suggests, it a simplified version of the bidirectional mean averaging process. It involves a few steps: up mean averaging, down mean averaging, the average between the up an down processes. The process is as follows:

                By example, if the sample data is {X1, X2, X3, X4, X5, X6, X7, X8, X9, X10}, then the up mean averaging is

                U1 = X1
                U2 = (U1 + X2) / 2
                U3 = (U2 + X3) / 2
                U4 = (U3 + X4) / 2
                U5 = (U4 + X5) / 2
                U6 = (U5 + X6) / 2
                U7 = (U6 + X7) / 2
                U8 = (U7 + X8) / 2
                U9 = (U8 + X9) / 2
                U10 = (U9 + X10) / 2

                The up mean averaging data is {U1, U2, U3, U4, U5, U6, U7, U8, U9, U10}. The down mean averaging is

                D10 = X10
                D9 = (D10 + X9) / 2
                D8 = (D9 + X8) / 2
                D7 = (D8 + X7) / 2
                D6 = (D7 + X6) / 2
                D5 = (D6 + X5) / 2
                D4 = (D5 + X4) / 2
                D3 = (D4 + X3) / 2
                D2 = (D3 + X2) / 2
                D1 = (D2 + X1) / 2

                The down mean averaging data is {D1, D2, D3, D4, D5, D6, D7, D8, D9, D10}. The simplified bidirectional mean averaging is

                B1 = (U1 + D1) / 2
                B2 = (U2 + D2) / 2
                B3 = (U3 + D3) / 2
                B4 = (U4 + D4) / 2
                B5 = (U5 + D5) / 2
                B6 = (U6 + D6) / 2
                B7 = (U7 + D7) / 2
                B8 = (U8 + D8) / 2
                B9 = (U9 + D9) / 2
                B10 = (U10 + D10) / 2

                The simplified bidirectional mean averaging data is {B1, B2, B3, B4, B5, B6, B7, B8, B9, B10} for this sample set of 10 numbers. A different quantity set of numbers will follow the same basic process where X1 is set equal to U1 and then the following mean averaging; also, Xn is set equal to Dn and then the following mean averaging, where n is the quantity of numbers in the set.

                Another step is needed to make the averaging results more smooth; to work out any big differences in the data. This process is called iteration and it is simply the reapplication of the bidirectional mean averaging method to the data derived by the bidirectional mean averaging. If the data from the bidirectional mean averaging is {B1, B2, B3, B4, B5, B6, B7, B8, B9, B10}, then the bidirectional mean averaging data is set equal to the original variables {X1, X2, X3, X4, X5, X6, X7, X8, X9, X10} and the bidirectional mean averaging process is repeated. The new data is said to have been reiterated in the bidirectional mean averaging process, hence the term, iteration. The first iteration is the first application of the method, the second iteration is the reapplication of the method and so on. An example of the method and the following iterations are shown in the graph below. From the graph, Iteration 8 shows the average fluctuations in the distribution. Below the example are a few more graphs.

                This graph shows Iteration 8 plotted against a second axis on the right, Average Fluctuation.

                An additional calculation is needed for a distribution discussed later in the post. It is the draw span and it's the difference between the largest number and the smallest number in an individual draw. If the draw data is {A, B, C, D, E} and the draw data is in ascending order, then the draw span is

                Ds = E - A, where E > A

                Example, if the draw is {1, 2, 3, 4, 5}, then the draw span is Ds = 5 - 1 or Ds = 4.

                 

                Wheel Application

                The draw mean is used to derive the 12 numbers that will be inserted in a wheel for posting on the Lottery Post's prediction board. First, the Integer part of the draw mean is found; it is Di = Int(Dm). The Di value is then used to add and subtract incremental values above and below the Di value to get a set of 12 numbers. Below are the equations for finding Wn values 1 to 12, where n is 1 to 12.

                W1 = Di - 5
                W2 = Di - 4
                W3 = Di - 3
                W4 = Di - 2
                W5 = Di - 1
                W6 = Di
                W7 = Di + 1
                W8 = Di + 2
                W9 = Di + 3
                W10 = Di + 4
                W11 = Di + 5
                W12 = Di + 6

                The wheel numbers are then {W1, W2, W3, W4, W5, W6, W7, W8, W9, W10, W11, W12}.

                The wheel used is as follows:

                IndexABCDE
                112357
                2123512
                312478
                4125612
                5125710
                6126711
                7126910
                8134611
                913489
                10135612
                1113678
                12145711
                1314589
                14145810
                15145912
                16146911
                171461012
                181481012
                191571011
                20158911
                211581012
                2223469
                23234910
                24235911
                25236910
                26237810
                27237911
                28238912
                292471011
                30256711
                312671012
                322681011
                332681012
                342781112
                353461112
                36347912
                37348910
                3835689
                39356811
                40357812
                413671012
                4238101112
                4345789
                444591112
                45467810
                464791011
                474791112
                4856101112
                495891012
                506791112

                If the previous day's lottery numbers are {10, 13, 20, 22, 28}, then the draw mean is Dm = (10 + 13 + 20 + 22 + 28) / 5, Dm = 93 / 5 or Dm = 18.6 and the Integer value is then Di = Int(18.6) or Di = 18. The the wheel numbers then become {18 - 5, 18 - 4, 18 - 3, 18 - 2, 18 - 1, 18, 18 + 1, 18 + 2, 18 + 3, 18 + 4, 18 + 5, 18 + 6} or {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24} and when applied to the list of combinations, the wheel becomes the play or prediction post lines as follows:

                IndexABCDE
                11314151719
                21314151724
                31314161920
                41314171824
                51314171922
                61314181923
                71314182122
                81315161823
                91315162021
                101315171824
                111315181920
                121316171923
                131316172021
                141316172022
                151316172124
                161316182123
                171316182224
                181316202224
                191317192223
                201317202123
                211317202224
                221415161821
                231415162122
                241415172123
                251415182122
                261415192022
                271415192123
                281415202124
                291416192223
                301417181923
                311418192224
                321418202223
                331418202224
                341419202324
                351516182324
                361516192124
                371516202122
                381517182021
                391517182023
                401517192024
                411518192224
                421520222324
                431617192021
                441617212324
                451618192022
                461619212223
                471619212324
                481718222324
                491720212224
                501819212324

                This process is done for each days drawing and posting.

                 

                Distributions and Analysis

                There are three distributions that will be looked at and analyzed. They are the lottery and wheel numbers distributions and the draw span distribution. The table below shows a 60 draw example of lottery numbers, wheel numbers and draw span for each draw.

                IndexLottery NumbersDraw SpanWheel Numbers
                ABCDE123456789101112
                0113192024-------------
                1235152220101112131415161718192021
                221020222624456789101112131415
                31610212726111213141516171819202122
                42351220188910111213141516171819
                5241617252334567891011121314
                6131719273017789101112131415161718
                731223293027161718192021222324252627
                8162022252812141516171819202122232425
                971118192316171819202122232425262728
                104513233026101112131415161718192021
                11131720222613101112131415161718192021
                1292224293021141516171819202122232425
                1322242627308171819202122232425262728
                1451018262924202122232425262728293031
                1531012161916121314151617181920212223
                162820252826789101112131415161718
                1721920252624111213141516171819202122
                18569132116131415161718192021222324
                19512192124195678910111213141516
                2021422263129111213141516171819202122
                21489132622141516171819202122232425
                22101317193020789101112131415161718
                2346911128121314151617181920212223
                241102129302934567891011121314
                251212212625131415161718192021222324
                261715162019789101112131415161718
                2727813252367891011121314151617
                28571718211667891011121314151617
                29118252729288910111213141516171819
                304515172925151617181920212223242526
                311192026282791011121314151617181920
                328913162416131415161718192021222324
                33471820302691011121314151617181920
                343410141714101112131415161718192021
                35239112422456789101112131415
                363719202623456789101112131415
                3721222326287101112131415161718192021
                38101224252717192021222324252627282930
                394914182420141516171819202122232425
                4035172329268910111213141516171819
                41236122826101112131415161718192021
                42811151821135678910111213141516
                437151623272091011121314151617181920
                4491516172819121314151617181920212223
                4526792422121314151617181920212223
                4611920252726456789101112131415
                4711415212625131415161718192021222324
                48356121310101112131415161718192021
                4927101218162345678910111213
                504817192824456789101112131415
                513911142219101112131415161718192021
                52171012292867891011121314151617
                537131430312467891011121314151617
                541411141716141516171819202122232425
                551810222524456789101112131415
                56314162429268910111213141516171819
                5718192325268121314151617181920212223
                582921222321171819202122232425262728
                5945891410101112131415161718192021
                60581115201534567891011121314

                The numbers in each column heading of Lottery Numbers, Draw Span and Wheel Numbers can be tallied to find each headings distribution of numbers. For this example, the following tables show their respective distributions.

                NumberFrequencies
                WheelDraw
                1011
                2114
                3412
                41011
                51212
                6166
                72011
                8249
                92712
                103611
                11397
                124411
                134810
                14529
                15508
                16458
                174611
                18429
                193911
                203612
                213310
                222411
                23218
                24169
                251210
                26713
                2767
                2857
                2929
                3029
                3112

                 

                ValueSpan Frequency
                10
                20
                30
                40
                50
                60
                71
                83
                90
                102
                110
                121
                132
                141
                151
                167
                172
                181
                194
                204
                212
                223
                233
                246
                253
                268
                272
                282
                292
                300

                The bar graphs of these can be seen next.

                The draw span will be referred to later in the post. The wheel and draw distributions will have the Simplified Bidirectional Mean Averaging applied to get the average fluctuations for each data set. The Bidirectional Mean Averaging will be carried out to 8 Iterations for analysis. The next table shows the average fluctuations for each wheel and draw distribution.

                NumberFrequenciesFluctuations
                WheelDrawWheelDraw
                10118.29622111.20978
                21149.45570511.12575
                341211.1496311.00038
                4101113.3109510.84371
                5121215.8558710.67092
                616618.6942210.498
                7201121.7272810.34132
                824924.847410.20175
                9271227.9363210.07813
                10361130.864729.965723
                1139733.492749.866072
                12441135.688619.785218
                13481037.335929.723592
                1452938.347119.684897
                1550838.674179.672521
                1645838.316539.685291
                17461137.311689.713629
                1842935.718199.739883
                19391133.615979.747519
                20361231.098819.718874
                21331028.272439.641936
                22241125.253369.513316
                2321822.167099.332396
                2416919.130699.102002
                25121016.250058.820878
                2671313.613148.488693
                276711.287148.112503
                28579.314647.717087
                29297.7207327.331684
                30296.5201186.99004
                31125.7181666.733356

                Here is a graph of the data.

                Now the fluctuations only.

                The fluctuation data then can be applied to an XY plot to show the relationship between the wheel and draw average fluctuation. In the XY plot there will be a green line showing the trend line and some additional information about the line and correlation of the data. The R-square value is the degree of correlation between the wheel and draw fluctuations and the equation of the line is given by y = 8.77 + 0.0326x. The R-square value is close to 0, meaning the data in (wheel fluctuation) has a low influence on the data out (draw fluctuation) and can be visually verified by the points and their respective distances from the line.

                Next, these basic processes of finding fluctuations and correlation will be applied to some actual draw data in a pretest, Experiment 0.

                 

                The Pretest, Experiment 0

                For this part, the data can be accessed through the following link for reference, Experiment 0 Data. Experiment 0 never posted any wheels to the Lottery Post's prediction board and was never played in the Badger 5 game. It is the 60 draw data from 2007-08-06 to 2007-10-04. The following graphs are the wheel and draw distributions, their fluctuations and the XY Plot and correlation.

                From the graphs, an inference can be made based on the R-square value and the XY Plot. The low R-square value shows there is a low relationship between the wheel numbers (data in) to the draw numbers (data out). Also, from the visual inspection of the plot, the data points are fairly far from the trend line, meaning this tends to suggest there is a low relationship between the wheel and the draw. This is what would be reasonably expected for a random event where no wheel was played or posted. In a truly random setting, it is also reasonable to expect a low correlation if the wheel is played or posted. In the next step, there needs to be a setup for attention grabbing to get those who could possibly be involved to play along. Then Experiment 1 can be tested to see if there is a relationship between data in (wheel) and data out (draw).

                 

                The Setup and Cost Effective Approach

                Ever had that feeling you're being watched? The feeling goes something like this: You work out a really great system for analyzing and playing numbers in a specific lottery game. You've done all the research, worked all the loose ends and then comes the time to either play or post your find. It works great and then like someone switching off a light, it goes cold.

                Well, in the case of posting on the Lottery Post, I think there might be a reason. It's described in one word, discredit. One of the most effective ways of discouraging many people from playing a proven method is to show it doesn't work. I think this is what could be happening at the Lottery Post.

                Unfortunately for the ones watching, this can prove to be a very cost effective way of proving the opening sentence in this post. If a $50.00 wheel were played for 60 draws, that would be a $3000.00 cost to play. Far beyond my ability to afford. So, basically I needed a way to attract attention and get the eye of those who would be watching. Loud mouthing, posting wheels and systems seems to have worked. Instead of actually playing the $50.00 wheel, I've used the watchful eye as an advantage.

                Next is the heart of this post, Experiment 1.

                 

                The Test, Experiment 1

                The Excel Sheet for the data and graphs can be found here, Experiment 1 Data. Experiment 1 posted wheels on the Lottery Post's prediction board during the period 2007-10-05 to 2007-12-03, a total of 60 draws. The following are the distributions, fluctuations and correlation graphs for the data.

                In the fluctuations graph, there is an obvious visual correlation between the data in (wheel) and the data out (draw). As the wheel number fluctuation increases, the draw number fluctuation decreases and the same is true in the opposite, as the wheel number fluctuation decreases, the draw number fluctuation increases. This would tend to suggest there may be a negative correlation between the two. Following this graph is the XY plot that can help in determining the correlation.

                Next is the XY plot of the fluctuations and shows the plotted data points and tend line. In the lower right are the R-square value and line equation based on 31 data points.

                From the graphs, it visually shows there is a possible correlation between the data in (wheel) to the data out (draw), the points are very close to the line. From the the R-square value of 0.957, it's very close to 1 and suggests there is a close correlation between the wheel and draw data, numerically. The -0.0526 value in the line equation suggests there is a negative correlation between the data in (wheel) and the data out (draw). As a comparison between the before and after, examine the XY plots of both Experiment 0 and 1. There is a dramatic difference between the two. Below is the XY plot for Experiment 0.

                Going back to the distributions graph, looking at just the wheel data, there appears to be something like a normal distribution curve. Below is a bar graph of just the wheel distribution data; this data can be analyzed to find a mean wheel number and standard deviation. The mean and standard deviation can then be used to find what are the 50% of the highest frequently posted wheel numbers. In other words, where does the bulk of the wheel numbers lay?  The mean value is just the average of all the wheel numbers that are to be inserted into the combinations of the wheel and the standard deviation is the value related to those numbers, also.

                To find the wheel number mean, add up all the numbers that are to be inserted in the wheel combinations and divided by the total set of numbers. The wheel number mean is then equal to 16.11667. The standard deviation value for the wheel numbers is 5.24639. This operation can be found in the Experiment 1 Data Excel file by click on the bottom tab, Wheel # Analysis. These values can then be used to create a normal distribution curve and find the 50% bulk of the wheel numbers. Below is a graph of the wheel distribution and normal distribution.

                The graph shows there is a peak at the number 16; this is consistent with the mean value of 16.11667. Also, looking at the graph there appears to be a bulk of the data centered around the mean. To find the 50% bulk of the data that is closest to the mean and is 25% above and 25% below the mean can be determined by multiplying the standard deviation by 0.674489524681121 and then adding and subtracting it from the mean. This will produce a lower limit and upper limit of where the 50% bulk of the data is falling. The lower limit is

                Lb = 16.11667 - (0.674489524681121 * 5.24639)
                Lb = 16.11667 - 3.53864
                Lb = 12.57803

                Lu = 16.11667 + (0.674489524681121 * 5.24639)
                Lu = 16.11667 + 3.53864
                Lu = 19.65530

                The Lb and Lu values can now establish a set of high work bulk numbers that represent the highest frequency numbers where the work is being done by the wheel. The set of numbers are going to be the integer values that are greater than Lb and less than Lu; these are {13, 14, 15, 16, 17, 18, 19}. In addition to the high work bulk of numbers, there is a counter part that shows the low work bulk of numbers where the least amount of work is being done. It is also 50% of the numbers and is the remaining set of numbers not covered by the high work bulk numbers of {13, 14, 15, 16, 17, 18, 19}; they are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}.

                It's important to understand these as what numbers are doing the most work and how this relates to the numbers being drawn by the lottery. Below is a distribution table of the drawn lottery numbers. From this table it can be shown what are the highest frequency numbers and lowest frequency numbers by finding the mean or average frequency of the table.

                NumberDraw
                111
                211
                39
                410
                58
                613
                712
                812
                910
                1011
                1111
                126
                136
                149
                159
                167
                1710
                188
                194
                2014
                215
                2214
                2310
                246
                2514
                266
                2710
                2813
                297
                3012
                3112

                From this an average frequency can be found by summing the frequencies and dividing by the total numbers in the set. The average frequency is 9.67742 and can be used to setup a table that shows the numbers below average and above average.

                Experiment 1
                Draw Number Frequencies
                Below averageAbove average
                31
                52
                124
                136
                147
                158
                169
                1810
                1911
                2117
                2420
                2622
                2923
                 25
                 27
                 28
                 30
                 31

                The table shows the high work bulk wheel numbers in gray. It also shows that almost half of the below average draw number frequencies are the high work bulk wheel numbers. The same was applied to Experiment 0. The data can be accessed in this link, Experiment 0 Data. The following is the table for Experiment 0 showing the below average and above average draw number frequencies. As it turns out, the high work bulk wheel numbers have the same set of numbers in Experiment 0, {13, 14, 15, 16, 17, 18, 19}.

                Experiment 0
                Draw Number Frequencies
                Below averageAbove average
                21
                63
                74
                85
                910
                1112
                1513
                1614
                1817
                2119
                2520
                2622
                2823
                3024
                27
                29
                31

                Notice the high work bulk numbers are fairly evenly distributed between the below average and above average draw number frequencies and there is actually more by count in the above average column.

                The draw span also changed slightly between Experiment 0 and 1. Below are some graphs showing the change. The shift can be seen where the peek of each fluctuation line is. In Experiment 0 the peek is at 23. The peek in Experiment 1 is at 25, meaning there was a slight shift in the span of drawn numbers. This shows the draw span increased slightly during Experiment 1 as compared to Experiment 0.

                All this data will play an important role in the next part, the conclusion.

                 

                The Conclusion, Experiment 1

                Is this possible proof the Wisconsin Lottery Badger 5 Computer Generated Numbers are fixed? Well, looking at just small slice of the possible data that could be derived for this topic, it appears to be fixed. There is the direct relationship between the data in (wheel) and data out (draw) in Experiment 1. Also, the high work bulk wheel numbers are clustered in the low frequency drawn numbers. In addition, the draw span shifted slightly to higher span values.

                Some might say, "Well, this is a small sample and the data can interpreted in may ways. Don't think much of it." This is true if it were not for Experiment 2 running currently. The next part will address the implications of the posttest, Experiment 2.

                 

                The Posttest, Experiment 2

                Experiment 2 is designed to pick up on the low frequency or deficient draw numbers established in Experiment 1. The deficient draw numbers contain almost all the high work bulk wheel numbers established in Experiment 1. To play on these deficient draw number, a wheel with a fixed set of numbers is used to be inserted in a wheel for posting. The numbers are {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22} and is a total set of 13 numbers. This also contains the high work bulk wheel numbers from Experiment 1, {13, 14, 15, 16, 17, 18, 19}.

                This setup creates a paradox for the would be wheel watchers. On one hand, if they stop trying to discredit the wheel by returning to a truly random state, the wheel begins to look good. However, on the other hand, if the continue to try and discredit the wheel by randomly manipulating the draw numbers, they will continue the current deficiencies and possibly increase the deficiencies which would go against the very notion of a truly random setting.

                There is one other possible choice, but that would lead to something of an admission of guilt, change the play matrix or discontinue the game. The basis is covered, all we have to is watch them watching us.

                To be continued... with Experiment 2...

                Hi Jade:

                 

                I'm afraid your sample set of 90 past draws is really insufficient to make a quality statistic, and hence, a solid conclusion about the fairness of the computer drawn lottery in your state. If you are talking about a 5 or 6 ball lottery, I'm sure I don't have to remind you of the total number of possibilities that there are, so 60 or 90 past draws constitue a drop in the bucket.  I'm reminded of a statement that Gail Howard has made in several of her publications. It's about the 1,2,3,4,5 draw that never seems to occur in the P5 lottery, so, "because the probablility of this draw occurring is very low, prefer the balanced wheel". What a fallacious statement! In a (fair)1-39 ball lottery any one combination of 5 has an equal shot in the barrel(1/575757).   Consider this now:

                IN THE ABOVE SCENARIO, IT WOULD TAKE APPROXIMATELY 1578 YEARS TO GENERATE  575757 P5 DRAWS, ASSUMING ONE DAILY DRAW. 

                Even if you were to find a bias within these 90 draws, the finding would be inconclusive because, in a random selection process there are always "hot spots" that do occur, and in a fair draw they iron out in the long run.

                I think you should concentrate your efforts on the P3 or P4(if it they are computer generated). There are far less possibilities in these games and hence valid statistics to be obtained from the past results. Another thing to remember is that the state always makes a daily trip to the bank to make a deposit, and thus, it would be in their best interest to keep the games fair. This assures maximum profits for them.

                 

                Good luck in your work,

                 

                jayemmar

                  MillionsWanted's avatar - 24Qa6LT

                  Norway
                  Member #9517
                  December 10, 2004
                  1272 Posts
                  Online
                  Posted: March 11, 2009, 8:12 pm - IP Logged

                  Regarding Gail Howard's statement about the 1-2-3-4-5(-6) scenario. She has also pointed out that one of the reason to avoid the combination was that it was purchased by several thousand ticket buyers each draw. You will only win a few hundred dollars if that combination occurred.

                    RJOh's avatar - chipmunk
                    mid-Ohio
                    United States
                    Member #9
                    March 24, 2001
                    19825 Posts
                    Offline
                    Posted: March 11, 2009, 9:09 pm - IP Logged

                    Hi Jade:

                     

                    I'm afraid your sample set of 90 past draws is really insufficient to make a quality statistic, and hence, a solid conclusion about the fairness of the computer drawn lottery in your state. If you are talking about a 5 or 6 ball lottery, I'm sure I don't have to remind you of the total number of possibilities that there are, so 60 or 90 past draws constitue a drop in the bucket.  I'm reminded of a statement that Gail Howard has made in several of her publications. It's about the 1,2,3,4,5 draw that never seems to occur in the P5 lottery, so, "because the probablility of this draw occurring is very low, prefer the balanced wheel". What a fallacious statement! In a (fair)1-39 ball lottery any one combination of 5 has an equal shot in the barrel(1/575757).   Consider this now:

                    IN THE ABOVE SCENARIO, IT WOULD TAKE APPROXIMATELY 1578 YEARS TO GENERATE  575757 P5 DRAWS, ASSUMING ONE DAILY DRAW. 

                    Even if you were to find a bias within these 90 draws, the finding would be inconclusive because, in a random selection process there are always "hot spots" that do occur, and in a fair draw they iron out in the long run.

                    I think you should concentrate your efforts on the P3 or P4(if it they are computer generated). There are far less possibilities in these games and hence valid statistics to be obtained from the past results. Another thing to remember is that the state always makes a daily trip to the bank to make a deposit, and thus, it would be in their best interest to keep the games fair. This assures maximum profits for them.

                     

                    Good luck in your work,

                     

                    jayemmar

                    Even if you were to find a bias within these 90 draws, the finding would be inconclusive because, in a random selection process there are always "hot spots" that do occur, and in a fair draw they iron out in the long run.

                    Systems designers and players are looking for bias in lottery drawings all the time to take advantage of, if such bias could be found someone would probably have won several jackpots in the same game by now.  In fact if someone was interested in proving a systems was bias, the best thing they could do to bring attention to it would be to win the top prize several times.

                    Instead most players who are complaining about those systems being bias are basing their suspicions on the fact that they have never won a decent prize.

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

                      Avatar

                      United States
                      Member #7437
                      October 3, 2004
                      383 Posts
                      Offline
                      Posted: March 12, 2009, 11:59 am - IP Logged

                      Hi RJOh:

                       

                      I agree with you 100%. The point I'm trying to make is that if we see a bias over a short period of time, it's no reason to conclude that the lottery itself is unfair because of this short term bias. Indeed, we should exploit this opportunity and generate our selections based on the current trend or bias.

                       

                      jayemmar

                        RJOh's avatar - chipmunk
                        mid-Ohio
                        United States
                        Member #9
                        March 24, 2001
                        19825 Posts
                        Offline
                        Posted: March 12, 2009, 3:08 pm - IP Logged

                        Being a system player, I assume all random drawings for jackpot style games have certain bias and I play accordingly.  I assume:

                        Once a combination of numbers hit, they won't hit again.

                        Future combinations will match 0-3 about the same amount as previous winning combinations had in the same number of previous drawings.

                        75% of winning numbers distributing patterns are a third of the possible patterns.

                        80% of the time no one will win the jackpot.

                        I assume much more but this gives you an idea of the types of assumptions I make and I'm right 95% of the time and with most jackpot style games I only have to be 100% right once in a life time.

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

                          Avatar

                          United States
                          Member #119
                          February 19, 2002
                          527 Posts
                          Offline
                          Posted: March 23, 2009, 10:47 pm - IP Logged

                          Hi,

                          1- How about first proving the Null Hypothesis: that they are not fixed?  Can you sooner prove (mathematically) that they are not fixed?  If you cannot, then you have proven that they are indeed "fixed".

                          2- I can give you a non-mathematical way: find an ethical way to examine the software packages of states who purchase these.  I believe you would probably discover that states with computerized lotteries use "super computers" to run software that can run a set of pre-determined combinations against those chosen by ticket buyers in less time than the few minutes between completion of sales and the time of the "computerized "drawing" (if you can truly call it a drawing-- it's actually more a "predetermination".

                          Why do I say this?  In PA, the game "Treasure Hunt" is computerized.  It rarely exceeds a certain amount.  This would not occur in a truly random environment.  A truly random environment and computerized lotteries are mutually exclusive.  Computerized lotteries only exist to unfairly/unjustly enhance the state's profitability at the expense, of course, of "unsuspecting" ticket buyers. 

                          But LP readers here are not the unsuspecting but suspecting.

                          If you can prove that these drawings are indeed fixed, and I sincerely hope you can, a faster way would be to teach ethics courses or mandate them to all state lottery employees.

                          But of course given the current climate of the business world and its lack of ethics, why am I not surprised that some state governments also lack the type of people whose sense of fair play, decency, and integrity have been undermined, indeed corrupted and resulted in the very reason for this thread?

                           

                          Outlaw Computerized Lotteries: Restore Randomness to Its True Place In Every State Lottery.

                          - me

                             
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