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6/49 number % question.

Topic closed. 11 replies. Last post 1 year ago by JADELottery.

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paul762's avatar - lion

United Kingdom
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December 11, 2003
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Posted: July 4, 2015, 9:01 am - IP Logged

How many numbers would I need to use to guarantee that I have the 6 winning numbers in my selections 85% of the time? What would be the best way to select those numbers?

Life's Tragedy is that we get old to soon and wise too late - Benjamin Franklin.
    SergeM's avatar - slow icon.png
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    Posted: July 4, 2015, 1:20 pm - IP Logged

    Do a random test, that should be close to the mathematical answer.

      JADELottery's avatar - MeAtWork 03.PNG
      The Quantum Master
      West Concord, MN
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      Posted: July 4, 2015, 4:14 pm - IP Logged
      Quantity of Numbers you usePercent of time 6 drawn numbers match your numbers.
      Q100% · Comb(Q, 6) / Comb(49, 6)
      60.000007%
      70.000050%
      80.000200%
      90.000601%
      100.001502%
      110.003304%
      120.006608%
      130.012271%
      140.021475%
      150.035791%
      160.057266%
      170.088502%
      180.132753%
      190.194024%
      200.277178%
      210.388049%
      220.533567%
      230.721884%
      240.962513%
      251.266464%
      261.646403%
      272.116804%
      282.694114%
      293.396927%
      304.246159%
      315.265237%
      326.480291%
      337.920356%
      349.617575%
      3511.607418%
      3613.928902%
      3716.624818%
      3819.741972%
      3923.331421%
      4027.448731%
      4132.154227%
      4237.513265%
      4343.596498%
      4450.480155%
      4558.246333%
      4666.983283%
      4776.785714%
      4887.755102%
      49100.000000%

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      Use at your own risk.

      Order is a Subset of Chaos
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      Jehocifer

        SergeM's avatar - slow icon.png
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        Posted: July 4, 2015, 5:59 pm - IP Logged

        I thought that it would be something like that without calculating.

          RJOh's avatar - chipmunk
          mid-Ohio
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          Posted: July 5, 2015, 12:12 pm - IP Logged

          How many numbers would I need to use to guarantee that I have the 6 winning numbers in my selections 85% of the time? What would be the best way to select those numbers?

          You would think having 85% of the 49 numbers or 42 would cover all six numbers 85% of the time but I checked that theory using the last 1323 drawings of Ohio's Classic Lotto(6/49) and it turns out it only covered all six numbers 40% of the time. You need to use 48 of the 49 numbers to cover all six number 85% of the time.  The following is a chart showing percentage of coverage for other groups sizes.

          *Looks like Jade's chart is right on.

          49/49 = 100%
          48/49 = 87%
          47/49 = 76%
          46/49 = 67%
          45/49 = 59%
          44/49 = 50%
          43/49 = 45%
          42/49 = 40%

           * you don't need to buy more tickets, just buy a winning ticket * 
             
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            JADELottery's avatar - MeAtWork 03.PNG
            The Quantum Master
            West Concord, MN
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            Posted: July 5, 2015, 3:20 pm - IP Logged

            For any N / R lottery and Q / R wheel the percent probability S drawn numbers are in Q wheel numbers.

            P(N, R, Q, S) = 100% · Comb(Q, S) · Comb(N - Q, R - S) / Comb(N, R)

            N - Lottery Pool Size

            R - Lottery Pick Size

            Q - Wheel Pool Size

            S - Quantity of Drawn Numbers Matching the Wheel Numbers

            Where Q ≤ N and S ≤ R; Comb(n, r) = n! / (r! · (n - r)!); n! = n · (n - 1) · (n - 2) ... 3 · 2 · 1 and 0! = 1.

            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

              SergeM's avatar - slow icon.png
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              Posted: July 5, 2015, 8:42 pm - IP Logged

              Lurking Combin(n,0) = 1, while truly = 0.

                paul762's avatar - lion

                United Kingdom
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                Posted: July 6, 2015, 10:06 am - IP Logged

                You would think having 85% of the 49 numbers or 42 would cover all six numbers 85% of the time but I checked that theory using the last 1323 drawings of Ohio's Classic Lotto(6/49) and it turns out it only covered all six numbers 40% of the time. You need to use 48 of the 49 numbers to cover all six number 85% of the time.  The following is a chart showing percentage of coverage for other groups sizes.

                *Looks like Jade's chart is right on.

                49/49 = 100%
                48/49 = 87%
                47/49 = 76%
                46/49 = 67%
                45/49 = 59%
                44/49 = 50%
                43/49 = 45%
                42/49 = 40%

                My initial thought was that it might be around 42 numbers RJOH, which is why I asked for confirmation, looks like I was a out a bit Embarassed

                Life's Tragedy is that we get old to soon and wise too late - Benjamin Franklin.
                  RJOh's avatar - chipmunk
                  mid-Ohio
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                  Posted: July 6, 2015, 11:03 am - IP Logged

                  My initial thought was that it might be around 42 numbers RJOH, which is why I asked for confirmation, looks like I was a out a bit Embarassed

                  I did my figuring the old fashion way, I took the 1323 Classic Lotto drawing results and checked the match6 I got with 49 and less numbers and then divided the results by 1323.

                  Problem is with my method you need a data file of a game with the appropriate matrix.  Jade's formula works with any matrix and can be plugged into your computer calculator with the scientific view.

                   * you don't need to buy more tickets, just buy a winning ticket * 
                     
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                    RJOh's avatar - chipmunk
                    mid-Ohio
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                    Posted: July 6, 2015, 9:40 pm - IP Logged

                    I did my figuring the old fashion way, I took the 1323 Classic Lotto drawing results and checked the match6 I got with 49 and less numbers and then divided the results by 1323.

                    Problem is with my method you need a data file of a game with the appropriate matrix.  Jade's formula works with any matrix and can be plugged into your computer calculator with the scientific view.

                    I no longer has to do my figuring the hard way thanks to Jade's formula. Comb(n, r) = n! / (r! · (n - r)!)

                    I wrote a 10 line program in QB64 that will give me the coverage percentage for any lottery matrix for every group size.

                    Thanks Jade.

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

                      RJOh's avatar - chipmunk
                      mid-Ohio
                      United States
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                      Posted: July 14, 2015, 10:07 am - IP Logged

                      I no longer has to do my figuring the hard way thanks to Jade's formula. Comb(n, r) = n! / (r! · (n - r)!)

                      I wrote a 10 line program in QB64 that will give me the coverage percentage for any lottery matrix for every group size.

                      Thanks Jade.

                      Works equally well for 5/39 games too

                                                 WHEEL COVERAGE AND PERCENT
                       LOTTERY POOL SIZE  39
                        COMBINATION SIZE  5
                       575757 POSSIBLE COMBOS - Wheel Size - Percent Cover - Possible Combinations
                       No.    %COVER        Combos             No.    %COVER        Combos 
                      ________________________________________________________________________________
                       39 = 100.000000%     575757             38 =  87.179313%     501941
                       37 =  75.708328%     435896             36 =  65.477623%     376992
                       35 =  56.383509%     324632             34 =  48.328722%     278256
                       33 =  41.221557%     237336             32 =  34.975867%     201376
                       31 =  29.510887%     169911             30 =  24.750893%     142505
                       29 =  20.625715%     118754             28 =  17.069528%     98279
                       27 =  14.021540%     80730              26 =  11.424959%     65780
                       25 =   9.227851%     53130              24 =   7.382281%     42504
                       23 =   5.844306%     33649              22 =   4.573805%     26334
                       21 =   3.534304%     20349              20 =   2.692803%     15504
                       19 =   2.019602%     11628              18 =   1.488128%     8568
                       17 =   1.074759%     6188               16 =   0.758653%     4368
                       15 =   0.521574%     3003               14 =   0.347716%     2002
                       13 =   0.223532%     1287               12 =   0.137558%     792
                       11 =   0.080242%     462                10 =   0.043768%     252
                        9 =   0.021884%     126                 8 =   0.009726%     56
                        7 =   0.003647%     21                  6 =   0.001042%     6
                        5 =   0.000174%     1 

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

                        JADELottery's avatar - MeAtWork 03.PNG
                        The Quantum Master
                        West Concord, MN
                        United States
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                        Posted: July 14, 2015, 10:37 am - IP Logged

                        I no longer has to do my figuring the hard way thanks to Jade's formula. Comb(n, r) = n! / (r! · (n - r)!)

                        I wrote a 10 line program in QB64 that will give me the coverage percentage for any lottery matrix for every group size.

                        Thanks Jade.

                        It's a well known combinatorial function.

                        You can learn more about combinations at https://en.wikipedia.org/wiki/Combination

                        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