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Mega Millions Full Distribution

Topic closed. 81 replies. Last post 2 months ago by wander73.

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Somerset
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December 17, 2004
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Posted: September 11, 2016, 7:39 pm - IP Logged

I was reading the post here https://www.lotterypost.com/thread/289726 and found it very interesting so I thought this might be of use.

The full distribution for the MegaMillions

I don't know why people would play a pick 5/75 game, OK the rewards are great but the odds are so bad, 18.5 million to 1 to hit 5 and a crazy 259 million to one for the jackpot, why do people play this?

Normal_Distribution-75-5-1

Normal_Distribution-75-5-2Normal_Distribution-75-5-3Normal_Distribution-75-5-4Normal_Distribution-75-5-5

It has been said every software has a bug in it, it has also been said that every program can be reduced by one line of code.

There for any program can be reduced to 1 line that dont work.

    MoneyMike$'s avatar - Lottery-050.jpg
    Ny
    United States
    Member #167314
    July 5, 2015
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    Posted: September 11, 2016, 7:53 pm - IP Logged

    What if I picked numbers like this: 

    0_ 3_ 4_ 4_ 6_

    2_ 3_ 5_ 6_ 7_

    2_ 2_ 4_ 4_ 6_

     

    In my experience Mega and Powerball numbers land in between 3-5 groups.. powerball having 1 less group.. 

    But there are 7 groups

    0_ 1_ 2_ 3_ 4_ 5_ 6_ 7_ 

     

    Could choosing the first digit of the sets of groups and leaving the second digit to fate, luck or some calculation give a better chance than showed in these graphs?

    Creativity..

    " What's more likely to happen will happen.. "

    Million dollar operation 

    Wink

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      Somerset
      United Kingdom
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      Posted: September 11, 2016, 8:36 pm - IP Logged

      The best approach is this.

      The draw as with any draw follows a fixed set of rules based upon the rules in this case 5/75, these never change, the graphs show this.

      What I would do if I were to play this draw is do the math to find when each number should appear.

      So graph 1 show ball 1 appears in 1,150,626 combinations of the 17,259,390 different possible combinations found in 5/75

      So 17,259,390 / 1,150,626 = 15

      So ball one should appear in ticket position one on average once every 15 draws.

      do the same for the others

      Ball 2 Ticket position 1 = 15.85 draws

      B3 T1 = 16.77 draws

      B4 T1 = 17.76 draws

      B5 T1 = 18.82 draws

      B6 T1 = 19.96 draws

      And so on, do this for all 5 graphs

      Once you have the data

       

      Position 1 2 3 4 5

      Ball 1 : 15 0 0 0 0

      Ball 2 : 16 278 0 0 0

      Ball 3 : 17 145 6,753 0 0

      Ball 4 : 18 101 2,315 243,090 0

      Ball 5 : 19 79 1,191 61,641 17,259,390

      Ball 6 : 20 66 736 25,014 3,451,878

      Ball 7 : 21 57 505 12,691 1,150,626

      Ball 8 : 23 51 372 7,360 493,125

      Ball 9 : 24 47 287 4,670 246,563

      Ball 10 : 25 44 230 3,161 136,979

      Ball 11 : 27 41 190 2,247 82,188

      Ball 12 : 29 40 161 1,660 52,301

      Ball 13 : 31 38 138 1,265 34,867

      Ball 14 : 33 37 121 989 24,139

      Ball 15 : 35 36 107 790 17,242

      Ball 16 : 38 35 96 643 12,644

      Ball 17 : 41 35 87 531 9,483

      Ball 18 : 44 35 80 445 7,252

      Ball 19 : 47 35 73 378 5,640

      Ball 20 : 51 35 68 324 4,453

      Ball 21 : 55 35 63 280 3,562

      Ball 22 : 59 35 60 245 2,884

      Ball 23 : 64 35 56 216 2,359

      Ball 24 : 69 36 54 191 1,949

      Ball 25 : 75 37 51 171 1,624

      Ball 26 : 81 37 49 153 1,364

      Ball 27 : 89 38 47 138 1,154

      Ball 28 : 97 39 45 126 983

      Ball 29 : 106 41 44 115 843

      Ball 30 : 116 42 43 105 727

      Ball 31 : 127 43 42 97 630

      Ball 32 : 140 45 41 89 549

      Ball 33 : 154 47 40 83 480

      Ball 34 : 170 49 40 77 422

      Ball 35 : 189 51 39 72 372

      Ball 36 : 210 54 39 68 330

      Ball 37 : 234 57 39 64 293

      Ball 38 : 261 60 39 60 261

      Ball 39 : 293 64 39 57 234

      Ball 40 : 330 68 39 54 210

      Ball 41 : 372 72 39 51 189

      Ball 42 : 422 77 40 49 170

      Ball 43 : 480 83 40 47 154

      Ball 44 : 549 89 41 45 140

      Ball 45 : 630 97 42 43 127

      Ball 46 : 727 105 43 42 116

      Ball 47 : 843 115 44 41 106

      Ball 48 : 983 126 45 39 97

      Ball 49 : 1,154 138 47 38 89

      Ball 50 : 1,364 153 49 37 81

      Ball 51 : 1,624 171 51 37 75

      Ball 52 : 1,949 191 54 36 69

      Ball 53 : 2,359 216 56 35 64

      Ball 54 : 2,884 245 60 35 59

      Ball 55 : 3,562 280 63 35 55

      Ball 56 : 4,453 324 68 35 51

      Ball 57 : 5,640 378 73 35 47

      Ball 58 : 7,252 445 80 35 44

      Ball 59 : 9,483 531 87 35 41

      Ball 60 : 12,644 643 96 35 38

      Ball 61 : 17,242 790 107 36 35

      Ball 62 : 24,139 989 121 37 33

      Ball 63 : 34,867 1,265 138 38 31

      Ball 64 : 52,301 1,660 161 40 29

      Ball 65 : 82,188 2,247 190 41 27

      Ball 66 : 136,979 3,161 230 44 25

      Ball 67 : 246,563 4,670 287 47 24

      Ball 68 : 493,125 7,360 372 51 23

      Ball 69 : 1,150,626 12,691 505 57 21

      Ball 70 : 3,451,878 25,014 736 66 20

      Ball 71 : 17,259,390 61,641 1,191 79 19

      Ball 72 : 0 243,090 2,315 101 18

      Ball 73 : 0 0 6,753 145 17

      Ball 74 : 0 0 0 278 16

      Ball 75 : 0 0 0 0 15

      Look to the past 100 draws and start applying this math

      So if the 3rd draw has the number one in ticket position 1 then set the a counter to 15, expect to see this ball in 15 draws time.

      If after 9 draws ball one occurs then it does not reset to 15, remember this math is based on fixed data based upon the rules of the draw, it still remains on average every 15 draws ball one must appear in ticket position 1 so the fact that after 9 + 3 draws its appeared twice means you adjust the average to maintain the rule.

      So

      Draw 1 No Hit : Odds 15 to 1

      Draw 2 No Hit : Odds 14 to 1

      Draw 3 Hit : Odds 15 to 1

      Draw 4 No Hit : Odds 14 to 1

      Draw 5 No Hit : Odds 13 to 1

      Draw 6 No Hit : Odds 12 to 1

      Draw 7 No Hit : Odds 11 to 1

      Draw 8 No Hit : Odds 10 to 1

      Draw 9 hit :      Odds 9 to 1 : (15 - 9 = 6 remains)  the rules say on average every 15 draws, we must obey these rules so expand 15 + 6 = 21

      Draw 10 No Hit : Odds 21 to 1

      Draw 11 No Hit : Odds 20 to 1

      and so on

      Do this for all balls in all ticket positions and eventually you will see things failing in line, by the math it has to.

      Jamie

      It has been said every software has a bug in it, it has also been said that every program can be reduced by one line of code.

      There for any program can be reduced to 1 line that dont work.

        lottoburg's avatar - wiggle
        NYC
        United States
        Member #54483
        August 20, 2007
        886 Posts
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        Posted: September 11, 2016, 10:07 pm - IP Logged

        The best approach is this.

        The draw as with any draw follows a fixed set of rules based upon the rules in this case 5/75, these never change, the graphs show this.

        What I would do if I were to play this draw is do the math to find when each number should appear.

        So graph 1 show ball 1 appears in 1,150,626 combinations of the 17,259,390 different possible combinations found in 5/75

        So 17,259,390 / 1,150,626 = 15

        So ball one should appear in ticket position one on average once every 15 draws.

        do the same for the others

        Ball 2 Ticket position 1 = 15.85 draws

        B3 T1 = 16.77 draws

        B4 T1 = 17.76 draws

        B5 T1 = 18.82 draws

        B6 T1 = 19.96 draws

        And so on, do this for all 5 graphs

        Once you have the data

         

        Position 1 2 3 4 5

        Ball 1 : 15 0 0 0 0

        Ball 2 : 16 278 0 0 0

        Ball 3 : 17 145 6,753 0 0

        Ball 4 : 18 101 2,315 243,090 0

        Ball 5 : 19 79 1,191 61,641 17,259,390

        Ball 6 : 20 66 736 25,014 3,451,878

        Ball 7 : 21 57 505 12,691 1,150,626

        Ball 8 : 23 51 372 7,360 493,125

        Ball 9 : 24 47 287 4,670 246,563

        Ball 10 : 25 44 230 3,161 136,979

        Ball 11 : 27 41 190 2,247 82,188

        Ball 12 : 29 40 161 1,660 52,301

        Ball 13 : 31 38 138 1,265 34,867

        Ball 14 : 33 37 121 989 24,139

        Ball 15 : 35 36 107 790 17,242

        Ball 16 : 38 35 96 643 12,644

        Ball 17 : 41 35 87 531 9,483

        Ball 18 : 44 35 80 445 7,252

        Ball 19 : 47 35 73 378 5,640

        Ball 20 : 51 35 68 324 4,453

        Ball 21 : 55 35 63 280 3,562

        Ball 22 : 59 35 60 245 2,884

        Ball 23 : 64 35 56 216 2,359

        Ball 24 : 69 36 54 191 1,949

        Ball 25 : 75 37 51 171 1,624

        Ball 26 : 81 37 49 153 1,364

        Ball 27 : 89 38 47 138 1,154

        Ball 28 : 97 39 45 126 983

        Ball 29 : 106 41 44 115 843

        Ball 30 : 116 42 43 105 727

        Ball 31 : 127 43 42 97 630

        Ball 32 : 140 45 41 89 549

        Ball 33 : 154 47 40 83 480

        Ball 34 : 170 49 40 77 422

        Ball 35 : 189 51 39 72 372

        Ball 36 : 210 54 39 68 330

        Ball 37 : 234 57 39 64 293

        Ball 38 : 261 60 39 60 261

        Ball 39 : 293 64 39 57 234

        Ball 40 : 330 68 39 54 210

        Ball 41 : 372 72 39 51 189

        Ball 42 : 422 77 40 49 170

        Ball 43 : 480 83 40 47 154

        Ball 44 : 549 89 41 45 140

        Ball 45 : 630 97 42 43 127

        Ball 46 : 727 105 43 42 116

        Ball 47 : 843 115 44 41 106

        Ball 48 : 983 126 45 39 97

        Ball 49 : 1,154 138 47 38 89

        Ball 50 : 1,364 153 49 37 81

        Ball 51 : 1,624 171 51 37 75

        Ball 52 : 1,949 191 54 36 69

        Ball 53 : 2,359 216 56 35 64

        Ball 54 : 2,884 245 60 35 59

        Ball 55 : 3,562 280 63 35 55

        Ball 56 : 4,453 324 68 35 51

        Ball 57 : 5,640 378 73 35 47

        Ball 58 : 7,252 445 80 35 44

        Ball 59 : 9,483 531 87 35 41

        Ball 60 : 12,644 643 96 35 38

        Ball 61 : 17,242 790 107 36 35

        Ball 62 : 24,139 989 121 37 33

        Ball 63 : 34,867 1,265 138 38 31

        Ball 64 : 52,301 1,660 161 40 29

        Ball 65 : 82,188 2,247 190 41 27

        Ball 66 : 136,979 3,161 230 44 25

        Ball 67 : 246,563 4,670 287 47 24

        Ball 68 : 493,125 7,360 372 51 23

        Ball 69 : 1,150,626 12,691 505 57 21

        Ball 70 : 3,451,878 25,014 736 66 20

        Ball 71 : 17,259,390 61,641 1,191 79 19

        Ball 72 : 0 243,090 2,315 101 18

        Ball 73 : 0 0 6,753 145 17

        Ball 74 : 0 0 0 278 16

        Ball 75 : 0 0 0 0 15

        Look to the past 100 draws and start applying this math

        So if the 3rd draw has the number one in ticket position 1 then set the a counter to 15, expect to see this ball in 15 draws time.

        If after 9 draws ball one occurs then it does not reset to 15, remember this math is based on fixed data based upon the rules of the draw, it still remains on average every 15 draws ball one must appear in ticket position 1 so the fact that after 9 + 3 draws its appeared twice means you adjust the average to maintain the rule.

        So

        Draw 1 No Hit : Odds 15 to 1

        Draw 2 No Hit : Odds 14 to 1

        Draw 3 Hit : Odds 15 to 1

        Draw 4 No Hit : Odds 14 to 1

        Draw 5 No Hit : Odds 13 to 1

        Draw 6 No Hit : Odds 12 to 1

        Draw 7 No Hit : Odds 11 to 1

        Draw 8 No Hit : Odds 10 to 1

        Draw 9 hit :      Odds 9 to 1 : (15 - 9 = 6 remains)  the rules say on average every 15 draws, we must obey these rules so expand 15 + 6 = 21

        Draw 10 No Hit : Odds 21 to 1

        Draw 11 No Hit : Odds 20 to 1

        and so on

        Do this for all balls in all ticket positions and eventually you will see things failing in line, by the math it has to.

        Jamie

        Hi, Jamie:

        I like your LSA.

        But could you tell us when do you finish your V7 of LSA?

        Best regards,

        lb

        • Saying Lotto #s Can be Predicted means that Lotto's ODD can be reduced down  to an economical level by a system.
        • Saying a Lotto System Works means that we can win constantly (not each draw)  and economically (get a real profit) by using the System.
        • Practice is the only criterion for testing truth.
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          Somerset
          United Kingdom
          Member #9710
          December 17, 2004
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          Posted: September 12, 2016, 5:10 am - IP Logged

          Thanks

          LSAv7, I have put so many hours to this yet it still won’t be available until next year, I code LSA myself and simply cannot justify putting other developers on to this as they work on ‘bread and butter’ projects for me.

          LSA is a labour of love, over the years I have logged user suggestions and v7 is to implement many of them making a lot of work for myself.

          2017 some time.....

          It has been said every software has a bug in it, it has also been said that every program can be reduced by one line of code.

          There for any program can be reduced to 1 line that dont work.

            lottoburg's avatar - wiggle
            NYC
            United States
            Member #54483
            August 20, 2007
            886 Posts
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            Posted: September 12, 2016, 9:51 am - IP Logged

            Thanks

            LSAv7, I have put so many hours to this yet it still won’t be available until next year, I code LSA myself and simply cannot justify putting other developers on to this as they work on ‘bread and butter’ projects for me.

            LSA is a labour of love, over the years I have logged user suggestions and v7 is to implement many of them making a lot of work for myself.

            2017 some time.....

            Hi, Jamie:

            Thanks for your sincere reply!

            Could you give us some smart strategies for using LSA V6.08?

            And the best way is to explain them by using a living example such as Pick-5 (5/39).

            If so, I believe firmly that not only we can develop our winning chance but also you can get

            more useful suggestions for your V7 since there are more users  than your site. Isn't it?

            Best regards.

            lb

            • Saying Lotto #s Can be Predicted means that Lotto's ODD can be reduced down  to an economical level by a system.
            • Saying a Lotto System Works means that we can win constantly (not each draw)  and economically (get a real profit) by using the System.
            • Practice is the only criterion for testing truth.
              Sunglasses's avatar - nicebear
              Zaperlopopotam
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              Posted: September 14, 2016, 9:47 am - IP Logged

              Ball 1 = Lowest 1st
              Ball 2 = lowest 2nd
              ...

               

              Of course 1 2 3 4 5 has the same chance as 1 18 35 43 69

               

              Waffles, beer, fries, choc'lat's, cigarettes ... some more mayonaise?
              Sauna, massage ... ? 
              Halal koscher mouton?
              Professeur Mamadou vous prédit votre future!
              Drugs straight from Colombia?
              Coke with sugar and caffeine?
              Vodka Red Bull?
              Bet on the winning numbers and win the jackpot!
              Chi chi's, Mac Do, Starbucks, Apple ...

              .
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                Somerset
                United Kingdom
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                Posted: September 16, 2016, 7:56 pm - IP Logged

                Yes, correct.

                Ball placement probability among other things can provide a user with the information to locate their chosen numbers in the best possible positions on tickets.

                Looking at the chart above, the combination 13, 23, 29, 36, 37 would be a bad choice whereas the combination 1, 19, 38, 57, 75 has the highest hit probability you can choose for this draw.

                For those that don’t understand the importance of distributions take a look to the last distribution graph I posted above titled “05 75: Normal Distribution” and you will see this draw has 1,150,626 lines with ball 75 as the highest number, this fact is very significant when targeting smaller win combinations and very useful when building wheels.

                Some wheels look great but if you compare the numbers in each ticket line against these charts, it can be shocking how bad the probability of intercepting some combinations actually are.

                The distributions are an excellent way of determining you placements on tickets.

                It has been said every software has a bug in it, it has also been said that every program can be reduced by one line of code.

                There for any program can be reduced to 1 line that dont work.

                  JADELottery's avatar - MeAtWork 03.PNG
                  The Quantum Master
                  West Concord, MN
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                  Posted: September 17, 2016, 8:52 am - IP Logged

                  The formula for finding any Combinatorial Distribution is as follows:

                  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: September 17, 2016, 9:00 am - IP Logged

                    You can find the Average Hit Frequency for any given draw using the following:

                    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
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                      Online
                      Posted: September 17, 2016, 9:06 am - IP Logged

                      The Average Rate at which a number will recur in a given column is a follows:

                      Please note, this is on a draw to draw recurrence.

                      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

                        Sunglasses's avatar - nicebear
                        Zaperlopopotam
                        Belgium
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                        Posted: September 17, 2016, 10:35 am - IP Logged

                        C(x,y) = V(x,y)/y!

                        .
                          JADELottery's avatar - MeAtWork 03.PNG
                          The Quantum Master
                          West Concord, MN
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                          Member #21
                          December 7, 2001
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                          Posted: September 17, 2016, 11:06 am - IP Logged

                          Combinatorial Distribution

                              Factorial - n! = n * (n -1) * (n - 2) * ... * 3 * 2 * 1 , and 0! = 1

                              Permutation - P(n,r) = n! / (n - r)!

                              Combination - C(n,r) = P(n,r) / r!

                              Combinatorial Distribution - D(n,r,c,z) = C(z - 1, c - 1) * C(n - z, r - c)

                                n - total number of items
                                r - number of items in a combinatorial or permutational set
                                c - column number of the distribution
                                z - item number of the distribution

                          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

                            Sunglasses's avatar - nicebear
                            Zaperlopopotam
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                            March 26, 2016
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                            Posted: September 17, 2016, 11:09 am - IP Logged

                            C(70,20) = 393849377343759797528386895216640000 / 2432902008176640000 = 161884603662657876

                            .
                              Sunglasses's avatar - nicebear
                              Zaperlopopotam
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                              Posted: September 17, 2016, 11:12 am - IP Logged

                              p(n, r) = M(i=0;i<r): (n-i)/(r-i)

                              n = h - l + 1

                              .