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5th Degree Polynomial Wave Projection

Topic closed. 18 replies. Last post 9 years ago by JADELottery.

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The Quantum Master
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Posted: July 22, 2007, 6:33 pm - IP Logged

5th Degree Polynomial Wave Projection

Reference - Bidirectional Mean Averaging and The Wave Matrix

1 - 6 Point Set of y Wave Values

    {y0, y1, y2, y3, y4, y5}

2 - Variable Coefficient Equations

    a0 =  720y0 - 1800y1 + 2400y2 - 1800y3 +  720y4 - 120y5
    a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
    a2 =  580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
    a3 =  -155y0 +  685y1 - 1210y2 + 1070y3 -  475y4 +  85y5
    a4 =    20y0 -  95y1 +  180y2 -  170y3 +  80y4 -  15y5
    a5 =    -1y0 +    5y1 -  10y2 +  10y3 -    5y4 +  1y5

3 - 7th Point Wave Projection y Value

    y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120

 

These 3 basic steps are derived from a polynomial curve fitting process called Least Squares Fitting (Wikipedia, Wolfram MathWorld). There is a long and involved process to arrive at the last 2 steps. It is the fitting for a 5th degree polynomial with 6 points on the curve. A 5th Degree Polynomial is y = a0 x0 + a1 x1 + a2 x2 + a3 x3 + a4 x4 + a5 x5; {a0, a1, a2, a3, a4, a5} are the variable coefficients. The projection is designed to find the approximate 7th point for the curve, y6.

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    hennybogan's avatar - DiscoBallGlowing
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    Posted: July 22, 2007, 6:52 pm - IP Logged

    Fractals is the final ultimate frontier. When one of you youngsters discovers how ro apply it to games of chance, ALL and I do mean ALL,  casinos and state lotteries will be no more.

      Ephesians 3:20


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      The Quantum Master
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      Posted: July 22, 2007, 9:29 pm - IP Logged

      Deviation from The Wave for 5th Degree Wave Projection

      Using the basic 3 steps, we can apply it to a long history of a wave to find a mean difference and standard deviation of the mean difference for the approximate projection. The standard deviation is used to Quantumly Project a point or a range for the final y6 value. Within a set of y wave values a subset of 6 points can be created starting at the beginning and then the 6 point move along the wave by 1 to 1 less than the final y values. At each successive change an approximate projection can be calculated and compared to the actual y6 value for the wave. The first wave projection at the beginning of the wave has an approximate y6 value and an actual y6 value. The difference between the actual and approximate are used to calculate a mean difference and a standard deviation.

      Presented 'AS IS' and for Entertainment Purposes Only.
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        The Quantum Master
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        Posted: July 22, 2007, 11:55 pm - IP Logged

        Mean Difference and Standard Deviation

        1 - Set of Wave Values

            {W0, W1, W2, ... Wn-2, Wn-1, Wn}

         

        2 - Approximate Projection Set

            First difference calculation.

            S0 = {y0, y1, y2, y3, y4, y5} = {W0, W1, W2, W3, W4, W5}

            Plug values into following equations.

            a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
            a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
            a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
            a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
            a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
            a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

            y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

            Dy0 = y6 - W6  First difference between approximate and actual.

         

            Second difference calculation.

            S1 = {y0, y1, y2, y3, y4, y5} = {W1, W2, W3, W4, W5, W6}

            Plug values into following equations.

            a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
            a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
            a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
            a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
            a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
            a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

            y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

            Dy1 = y6 - W7  Second difference between approximate and actual.

         

            Third difference calculation.

            S2 = {y0, y1, y2, y3, y4, y5} = {W2, W3, W4, W5, W6, W7}

            Plug values into following equations.

            a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
            a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
            a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
            a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
            a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
            a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

            y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

            Dy2 = y6 - W8  Third difference between approximate and actual.

            .

            .

            .

            Continue advancing subset through the set of Wave Values.

            .

            .

            .

         

            Second to last difference calculation.

            Sn-8 = {y0, y1, y2, y3, y4, y5} = {Wn-8, Wn-7, Wn-6, Wn-5, Wn-4, Wn-3}

            Plug values into following equations.

            a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
            a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
            a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
            a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
            a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
            a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

            y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

            Dyn-8 = y6 - Wn-2  Second to last difference between approximate and actual.

         

            Next to last difference calculation.

            Sn-7 = {y0, y1, y2, y3, y4, y5} = {Wn-7, Wn-6, Wn-5, Wn-4, Wn-3, Wn-2}

            Plug values into following equations.

            a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
            a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
            a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
            a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
            a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
            a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

            y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

            Dyn-7 = y6 - Wn-1  Next to last difference between approximate and actual.

         

            Last difference calculation.

            Sn-6 = {y0, y1, y2, y3, y4, y5} = {Wn-6, Wn-5, Wn-4, Wn-3, Wn-2, Wn-1}

            Plug values into following equations.

            a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
            a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
            a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
            a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
            a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
            a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

            y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

            Dyn-6 = y6 - Wn  Next to last difference between approximate and actual.

         

            Dy = {Dy0, Dy1, Dy2, ... Dyn-8, Dyn-7, Dyn-6}  Set of differences between approximate and actual

            The set of differences will always be 6 less than the number of the Wave Data set count. For that reason, there needs to be at least 10 or more points in the Wave to calculate the mean and standard deviation.

         

        3 - Mean Difference

            m = ( [0 to n - 6] å Dyi ) / (n - 6)

            m = (Dy0 + Dy1 + Dy2 + ... + Dyn-8 + Dyn-7 + Dyn-6) / (n - 6)

         

        4 - Standard Deviation of Difference

         

                                                                                           
            s = Ö( [0 to n - 6] å (Dyi - m)²) / (n - 6)

         

                                                                                                                                                                                             
            s = Ö((Dy0 - m)² + (Dy1 - m)² + (Dy2 - m)² + ... + (Dyn-8 - m)² + (Dyn-7 - m)² + (Dyn-6 - m)²) / (n - 6)

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        Jehocifer

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          Posted: July 23, 2007, 1:06 am - IP Logged

          The last equation should look like this.

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            hennybogan's avatar - DiscoBallGlowing
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            Posted: July 23, 2007, 1:21 am - IP Logged

            So, are you going to plug some drawing numbers into these equations and see if they produce a hit in any state, or is this just meaningless dribble?

              Ephesians 3:20


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              The Quantum Master
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              Posted: July 23, 2007, 1:30 pm - IP Logged

              So, are you going to plug some drawing numbers into these equations and see if they produce a hit in any state, or is this just meaningless dribble?

              Thank you for your useless comments.

              Yes, it is meaningless dribble, specially made for you.

              Please feel free to add more pseudo psycho babble.

              Presented 'AS IS' and for Entertainment Purposes Only.
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              Jehocifer

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                Posted: July 23, 2007, 3:00 pm - IP Logged

                Mean Difference and Standard Deviation Quantum Projection

                reference - Random Number Transforms - Normal Distribution

                After calculating the Mean Difference and Standard Deviation, the Standard Deviation can be used to induce a Quantum Projection of the Wave using the Random Number Transforms - Normal Distribution. The projection can be a single point, a set of points or a range above and below the mean difference.

                The Normal Distribution line shows the level of probability above and below the Mean Difference in the Yô direction. The probability is based on the Difference Standard Deviation and can be used to randomly estimate the above/below the Mean Difference. The Standard Deviation is used with the Random Number Transforms - Normal Distribution; with the Standard Deviation function. 

                1 - Last set of 6 Wave Values

                    {Wn-5, Wn-4, Wn-3, Wn-2, Wn-1, Wn}

                2 - Future Wave Projection

                    {y0, y1, y2, y3, y4, y5} = {Wn-5, Wn-4, Wn-3, Wn-2, Wn-1, Wn}

                    Plug values into following equations.

                    a0 = 720y0 - 1800y1 + 2400y2 - 1800y3 + 720y4 - 120y5
                    a1 = -1044y0 + 3510y1 - 5080y2 + 3960y3 - 1620y4 + 274y5
                    a2 = 580y0 - 2305y1 + 3720y2 - 3070y3 + 1300y4 - 225y5
                    a3 = -155y0 + 685y1 - 1210y2 + 1070y3 - 475y4 + 85y5
                    a4 = 20y0 - 95y1 + 180y2 - 170y3 + 80y4 - 15y5
                    a5 = -1y0 + 5y1 - 10y2 + 10y3 - 5y4 + 1y5

                    y6 = (1a0 + 7a1 + 49a2 + 343a3 + 2401a4 + 16807a5) / 120   

                    y6 is the approximate future value.

                3 - Offset y6 by the Mean Difference

                    Yoff = y6 + m

                    m is the mean difference calculated first from the earlier post.

                4 - Randomly Vary the Offset with Random Normal Distribution - Standard Deviation

                    Y = Yoff + Rand_SD(s)

                    s is the standard deviation calculated from the earlier post

                    Y is a single Quantumly Selected Y value.

                    Rand_SD( ) is a function defined in Random Number Transforms - Normal Distribution

                    Yrand = ABS( Rand_SD(s) )

                    Y- = Yoff - Yrand, Y+ = Yoff + Yrand

                    Y- to Y+ is a Quantum range of possible points where y6 might be.

                 

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                  Posted: July 23, 2007, 3:49 pm - IP Logged

                  Typo correction:

                  Presented 'AS IS' and for Entertainment Purposes Only.
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                  Order is a Subset of Chaos
                  Knowledge is Beyond Belief
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                  Jehocifer

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                    Posted: July 24, 2007, 5:41 pm - IP Logged

                    You can go to this link to see the process for finding the equations.

                    Process for Finding Variable Coefficients and Polynomial Equations

                    The LP editor can't handle the formating.

                    Enjoy.

                    Presented 'AS IS' and for Entertainment Purposes Only.
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                    Use at your own risk.

                    Order is a Subset of Chaos
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                      Posted: July 27, 2007, 9:38 pm - IP Logged

                      kind of makes sense if your data plots with a nice sine wave...

                      red balls in powerball have a range of 1 to 42 every draw, a graph of that is a jagged sawtooth that appears to have no rhyme or reason....

                      you can limit sorted order whiteballs to observed range and cut the choices, but the red ones are as noisy as plotting DRAW ORDER data.

                      all we have to go on is past history, which is supposedly random (looks random to me, except how they always manage to avoid drawing the numbers on my ticket).

                      I was trying to apply some sort of "weight" to the possible outcomes based on observed history... such as

                      Higer/Lower... works ok near the range boundaries, less so in the middle

                      odd/even... proved useless

                      hot follower... covered less than 10% for each case

                      on white balls, my "weights" would put 3 of the 6 numbers I picked in the range most of the time... but a range still leaves ambiguity... my goal is always "one pick-DONE"

                      is there some other method or adaptation of this method that can focus more closely on a point rather than a range?

                      Playing more than one ticket per game is betting against yourself.

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                        The Quantum Master
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                        Posted: July 28, 2007, 3:37 pm - IP Logged

                        kind of makes sense if your data plots with a nice sine wave...

                        red balls in powerball have a range of 1 to 42 every draw, a graph of that is a jagged sawtooth that appears to have no rhyme or reason....

                        you can limit sorted order whiteballs to observed range and cut the choices, but the red ones are as noisy as plotting DRAW ORDER data.

                        all we have to go on is past history, which is supposedly random (looks random to me, except how they always manage to avoid drawing the numbers on my ticket).

                        I was trying to apply some sort of "weight" to the possible outcomes based on observed history... such as

                        Higer/Lower... works ok near the range boundaries, less so in the middle

                        odd/even... proved useless

                        hot follower... covered less than 10% for each case

                        on white balls, my "weights" would put 3 of the 6 numbers I picked in the range most of the time... but a range still leaves ambiguity... my goal is always "one pick-DONE"

                        is there some other method or adaptation of this method that can focus more closely on a point rather than a range?

                        Have you tried to apply the Bidirectional Mean Averaging to find The Wave Matrix for the Powerball number?

                        There are a few techniques to using the BMA to arrive at a particular Wave Matrix.

                        One is with the RMS adjustment and one is without the RMS adjustment.

                        Also, play around with the Degree of Weighting Data value in the BMA.

                        I'll get back to this later tonight.

                        We are having my son's birthday party today and I'll be busy most of the day.

                        Presented 'AS IS' and for Entertainment Purposes Only.
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                        Use at your own risk.

                        Order is a Subset of Chaos
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                        Wisdom is Not Censored
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                        Jehocifer

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                          Posted: July 28, 2007, 7:51 pm - IP Logged

                          I am curious, how the coefficients are chosen? Thanks.

                          P.S. Just for grins I wonder if differentiating the equations and plotting against the original may give any valuable data from the intersects? Or possibly shifting the phase by introducing a sine, cosine, or cotangent function into the lower degrees of the polynomials.  I say this because the plot shown looks like 2.5 cycles of a dinged decay.  Just a thought.

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                            The Quantum Master
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                            Posted: July 28, 2007, 9:32 pm - IP Logged

                            I am curious, how the coefficients are chosen? Thanks.

                            P.S. Just for grins I wonder if differentiating the equations and plotting against the original may give any valuable data from the intersects? Or possibly shifting the phase by introducing a sine, cosine, or cotangent function into the lower degrees of the polynomials.  I say this because the plot shown looks like 2.5 cycles of a dinged decay.  Just a thought.

                            Posted earlier:

                            You can go to this link to see the process for finding the equations.

                            Process for Finding Variable Coefficients and Polynomial Equations

                            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

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                              Posted: July 28, 2007, 11:28 pm - IP Logged

                              Posted earlier:

                              You can go to this link to see the process for finding the equations.

                              Process for Finding Variable Coefficients and Polynomial Equations

                              Thanks.