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Repetition and skips explained

Topic closed. 13 replies. Last post 5 years ago by SergeM.

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SergeM's avatar - slow icon.png
Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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Posted: May 11, 2012, 7:02 pm - IP Logged

A repetition is a skip of 0 games.

For keno 20/70, 20 numbers are drawn, 50 numbers are not drawn. The chance is 20.

The chance for a repetition is 20/70 or 2/7. You can expect average 2/7*20 numbers to repeat.

Skip 0: average 20*(2/7)1 numbers.
Skip 1: average 20*(2/7)2 numbers.
Skip 2: average 20*(2/7)3 numbers.
Skip 3: average 20*(2/7)4 numbers.
...

With p = 20, n = 70: avg skip x = p*(p/n)1+x

Repetitions can vary from 0 to maximum 20 of 20 drawn numbers.
The average is 2/7*20 drawn numbers.

    frenchie's avatar - Lottery-041.jpg
    Los Angeles
    United States
    Member #75410
    June 2, 2009
    479 Posts
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    Posted: May 13, 2012, 3:21 pm - IP Logged

    Hi SergeM,

    Talking about Keno 20/70 do you have a system for it ? I would be interrested.

    Regards,

    Serge.

      SergeM's avatar - slow icon.png
      Economy class
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      Member #123700
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      Posted: May 13, 2012, 5:10 pm - IP Logged

      Hi SergeM,

      Talking about Keno 20/70 do you have a system for it ? I would be interrested.

      Regards,

      Serge.

      That's a hard nut!

      Picking the system to play and mixing the numbers is related to the payouts.
      I pick my numbers using my own "software". I will send you a few suggestions how you could play.

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        bgonçalves
        Brasil
        Member #92564
        June 9, 2010
        2122 Posts
        Offline
        Posted: May 13, 2012, 6:37 pm - IP Logged

        Hello sergem on this lottery 50/5 eurominlhao   If we divide the trio in a position to have 10 positions 1,2,3 1,2,4 1,2,5 2,3,4 2,3,5 ...... = 3,4,5 up the total are 10 position   Sergem, how you could make or assemble a formula of probability Or within 10 positions of the suit, suit or have greater likelihood of left in a certain position, ie its frequency in repeats determicada position. example Suit 02,08,45 = the best position to place this suit? Sergem if we use certain fixed positions within the greater probability! You can see this formula? It can serve many lotteries

          SergeM's avatar - slow icon.png
          Economy class
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          Member #123700
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          Posted: May 14, 2012, 10:41 am - IP Logged

          I am sure that a man with a doctor title can calculate this with paper and pencil.


            United States
            Member #124493
            March 14, 2012
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            Posted: May 15, 2012, 9:12 pm - IP Logged

            2/7=0.28

            Skip 0: average 20*(2/7)1 numbers.      20*0.28=5.6

            Skip 1: average 20*(2/7)2 numbers.       20*0.28=5.6 →  (5.6)^2= 31.36

            Skip 2: average 20*(2/7)3 numbers.                                             (5.6)^3= 175.61

             Skip 3: average 20*(2/7)4 numbers.                                               (5.6)^4= 983.41

             

            is this the correct calculation??

              SergeM's avatar - slow icon.png
              Economy class
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              Member #123700
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              Posted: May 17, 2012, 6:48 am - IP Logged

              If you wonder, how many repetitions do I expect? The average can be 1.2 for example, so you might expect one repetition.

              With integers, you wouldn't talk about an average, but you would sum up the amount of repetitions by their count.  Repetitions: 0:*1, 1:*10, 2:*2, 3:*0 ... . By calculating the weighted average, you should find a value close to the probability.

                SergeM's avatar - slow icon.png
                Economy class
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                Member #123700
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                Posted: May 17, 2012, 10:55 am - IP Logged

                For repetitions, you might go further into probabilities.

                For Keno 20/70, I calculated in Excel the odds for the count of numbers repeating.

                RepetitionsOdds
                00,000291128440738996
                10,003756496009535440
                20,021188985303785800
                30,069345770085117200
                40,147359761430874000
                50,215566279578879000
                60,224548207894665000
                70,169928373541909000
                80,094466760291390200
                90,038755593965698500
                100,011723567174623800
                110,002599460570870020
                120,000417770448889825
                130,000047830605955186
                140,000003804707291890
                150,000000202917722234
                160,000000006892585674
                170,000000000138024244
                180,000000000001437753
                190,000000000000006177
                200,000000000000000006

                 

                Repetition(s):
                0:3434,91
                1:266,21
                2:47,19
                3:14,42
                4:6,79
                5:4,64
                6:4,45
                7:5,88
                8:10,59
                9:25,8
                10:85,3
                11:384,7
                12:2393,66
                13:20907,12
                14:262832,31
                15:4928105,78
                16:145083434,19
                17:7245103994,93
                18:695529983513,03
                19:161884603662658
                20:1,61884603662658E+17

                  SergeM's avatar - slow icon.png
                  Economy class
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                  Member #123700
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                  Posted: May 21, 2012, 7:26 pm - IP Logged

                  Pick 3

                  For 1 digit, p = 1/10

                  Skip 0:  0.1         1 in 10
                  Skip 1:  0.01       1 in 100
                  Skip 2:  0.001     1 in 1000
                  Skip 3:  0.0001   1 in 10000
                  ...

                  For 2 digits, p = 1/100

                  Skip 0:  0.01         1 in 100
                  Skip 1:  0.0001     1 in 10 000
                  ...

                  For 3 digits, p = 1/1000

                  Skip 0: 0.001      1 in 1000
                  Skip 1: 0.000 001    ...

                    SergeM's avatar - slow icon.png
                    Economy class
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                    Member #123700
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                    Posted: May 21, 2012, 8:15 pm - IP Logged

                    This is different to the model. Third digit for 100 drawings.

                    Skips & count

                    -551
                    -361
                    -321
                    -261
                    -232
                    -223
                    -201
                    -192
                    -182
                    -175
                    -151
                    -144
                    -133
                    -126
                    -112
                    -107
                    -93
                    -82
                    -75
                    -65
                    -57
                    -49
                    -34
                    -23
                    -19
                    011

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                      Belgium
                      Member #128218
                      May 19, 2012
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                      Posted: May 22, 2012, 6:13 am - IP Logged

                      I am sure that a man with a doctor title can calculate this with paper and pencil.

                      Lol, nice reply... Smile

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                        Belgium
                        Member #128218
                        May 19, 2012
                        96 Posts
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                        Posted: May 22, 2012, 6:15 am - IP Logged

                        Thanks for the interesting topic SergeM, I will have a look at it...

                          SergeM's avatar - slow icon.png
                          Economy class
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                          Member #123700
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                          Posted: May 22, 2012, 1:06 pm - IP Logged

                          Pick 3 BE
                          History of 2963 drawings,
                          last 1000 drawings.

                          Skips before hit:

                          NOT = was not drawn before

                          NOT92
                          01
                          -12
                          -21
                          -31
                          -62
                          -72
                          -82
                          -92
                          -111
                          -141
                          -181
                          -191
                          -212
                          -222
                          -231
                          -241
                          -252
                          -272
                          -291
                          -301
                          -311
                          -322
                          -332
                          -341
                          -354
                          -381
                          -391
                          -401
                          -411
                          -421
                          -431
                          -451
                          -481
                          -511
                          -531
                          -562
                          -592
                          -601
                          -611
                          -621
                          -631
                          -651
                          -662
                          -671
                          -681
                          -701
                          -721
                          -731
                          -741
                          -761
                          -773
                          -812
                          -821
                          -832
                          -853
                          -863
                          -873
                          -901
                          -921
                          -931
                          -942
                          -952
                          -961
                          -972
                          -982
                          -991
                          -1031
                          -1041
                          -1061
                          -1102
                          -1141
                          -1151
                          -1162
                          -1182
                          -1191
                          -1212
                          -1221
                          -1231
                          -1241
                          -1252
                          -1261
                          -1271
                          -1291
                          -1302
                          -1311
                          -1341
                          -1352
                          -1361
                          -1372
                          -1381
                          -1401
                          -1422
                          -1432
                          -1441
                          -1462
                          -1481
                          -1491
                          -1501
                          -1511
                          -1531
                          -1541
                          -1551
                          -1561
                          -1592
                          -1601
                          -1623
                          -1631
                          -1641
                          -1663
                          -1672
                          -1683
                          -1701
                          -1732
                          -1743
                          -1751
                          -1762
                          -1771
                          -1782
                          -1801
                          -1813
                          -1821
                          -1832
                          -1862
                          -1872
                          -1882
                          -1891
                          -1902
                          -1931
                          -1961
                          -1971
                          -1981
                          -1992
                          -2001
                          -2011
                          -2032
                          -2063
                          -2082
                          -2091
                          -2121
                          -2151
                          -2171
                          -2211
                          -2231
                          -2242
                          -2251
                          -2271
                          -2291
                          -2311
                          -2321
                          -2332
                          -2352
                          -2371
                          -2381
                          -2391
                          -2421
                          -2433
                          -2451
                          -2462
                          -2471
                          -2481
                          -2501
                          -2531
                          -2551
                          -2571
                          -2581
                          -2591
                          -2602
                          -2611
                          -2621
                          -2631
                          -2672
                          -2711
                          -2743
                          -2782
                          -2801
                          -2823
                          -2832
                          -2841
                          -2853
                          -2861
                          -2882
                          -2922
                          -2931
                          -2971
                          -2981
                          -3041
                          -3061
                          -3081
                          -3091
                          -3113
                          -3121
                          -3131
                          -3141
                          -3161
                          -3172
                          -3182
                          -3192
                          -3211
                          -3241
                          -3282
                          -3303
                          -3331
                          -3341
                          -3361
                          -3382
                          -3421
                          -3431
                          -3461
                          -3482
                          -3512
                          -3561
                          -3581
                          -3592
                          -3602
                          -3621
                          -3631
                          -3641
                          -3652
                          -3681
                          -3701
                          -3711
                          -3742
                          -3751
                          -3781
                          -3792
                          -3812
                          -3821
                          -3831
                          -3842
                          -3891
                          -3911
                          -3921
                          -3931
                          -3951
                          -3992
                          -4001
                          -4021
                          -4031
                          -4062
                          -4071
                          -4091
                          -4101
                          -4121
                          -4141
                          -4152
                          -4192
                          -4202
                          -4221
                          -4241
                          -4251
                          -4261
                          -4271
                          -4281
                          -4302
                          -4341
                          -4352
                          -4361
                          -4381
                          -4401
                          -4411
                          -4472
                          -4491
                          -4501
                          -4521
                          -4552
                          -4571
                          -4591
                          -4622
                          -4631
                          -4651
                          -4661
                          -4701
                          -4713
                          -4721
                          -4751
                          -4761
                          -4771
                          -4781
                          -4811
                          -4851
                          -4921
                          -4932
                          -4951
                          -4961
                          -4982
                          -5011
                          -5022
                          -5053
                          -5061
                          -5081
                          -5102
                          -5111
                          -5121
                          -5132
                          -5142
                          -5181
                          -5211
                          -5291
                          -5311
                          -5321
                          -5343
                          -5361
                          -5391
                          -5402
                          -5411
                          -5422
                          -5461
                          -5481
                          -5561
                          -5621
                          -5631
                          -5652
                          -5662
                          -5671
                          -5741
                          -5751
                          -5771
                          -5791
                          -5822
                          -5841
                          -5861
                          -5871
                          -5881
                          -5911
                          -5941
                          -5951
                          -5961
                          -5972
                          -5982
                          -5991
                          -6001
                          -6011
                          -6021
                          -6051
                          -6081
                          -6111
                          -6142
                          -6151
                          -6191
                          -6202
                          -6211
                          -6251
                          -6261
                          -6281
                          -6291
                          -6311
                          -6341
                          -6381
                          -6391
                          -6401
                          -6441
                          -6451
                          -6462
                          -6471
                          -6491
                          -6511
                          -6561
                          -6631
                          -6651
                          -6672
                          -6731
                          -6771
                          -6781
                          -6821
                          -6861
                          -6922
                          -6931
                          -6952
                          -6971
                          -6991
                          -7031
                          -7041
                          -7071
                          -7091
                          -7141
                          -7161
                          -7171
                          -7191
                          -7221
                          -7231
                          -7291
                          -7311
                          -7341
                          -7362
                          -7411
                          -7421
                          -7481
                          -7491
                          -7511
                          -7611
                          -7621
                          -7642
                          -7673
                          -7731
                          -7771
                          -7782
                          -7801
                          -7811
                          -7871
                          -7881
                          -7892
                          -7902
                          -7921
                          -7931
                          -7951
                          -7992
                          -8011
                          -8022
                          -8042
                          -8051
                          -8061
                          -8121
                          -8191
                          -8211
                          -8291
                          -8351
                          -8361
                          -8371
                          -8381
                          -8431
                          -8471
                          -8493
                          -8592
                          -8611
                          -8621
                          -8734
                          -8761
                          -8821
                          -8831
                          -8841
                          -8861
                          -8871
                          -8892
                          -8902
                          -8941
                          -8951
                          -9011
                          -9042
                          -9081
                          -9101
                          -9121
                          -9131
                          -9141
                          -9151
                          -9162
                          -9171
                          -9191
                          -9232
                          -9261
                          -9271
                          -9321
                          -9331
                          -9351
                          -9371
                          -9381
                          -9411
                          -9431
                          -9501
                          -9511
                          -9571
                          -9581
                          -9611
                          -9621
                          -9631
                          -9653
                          -9661
                          -9742
                          -9751
                          -9771
                          -9791
                          -9811
                          -9831
                          -9851
                          -9892
                          -9911
                          -9971
                          -10001
                          -10071
                          -10081
                          -10092
                          -10151
                          -10161
                          -10181
                          -10191
                          -10281
                          -10291
                          -10331
                          -10351
                          -10371
                          -10382
                          -10422
                          -10521
                          -10551
                          -10691
                          -10701
                          -10711
                          -10751
                          -10771
                          -10801
                          -10841
                          -10861
                          -10891
                          -10931
                          -10941
                          -10952
                          -10991
                          -11012
                          -11021
                          -11051
                          -11081
                          -11102
                          -11121
                          -11161
                          -11191
                          -11311
                          -11383
                          -11441
                          -11501
                          -11511
                          -11621
                          -11651
                          -11661
                          -11681
                          -11691
                          -11701
                          -11721
                          -11801
                          -11882
                          -11902
                          -11921
                          -11971
                          -11991
                          -12031
                          -12131
                          -12191
                          -12201
                          -12251
                          -12321
                          -12401
                          -12411
                          -12441
                          -12461
                          -12471
                          -12501
                          -12531
                          -12591
                          -12642
                          -12711
                          -12722
                          -12781
                          -12791
                          -12811
                          -12831
                          -12871
                          -12921
                          -12931
                          -13061
                          -13102
                          -13111
                          -13151
                          -13191
                          -13301
                          -13341
                          -13371
                          -13391
                          -13421
                          -13481
                          -13511
                          -13551
                          -13561
                          -13581
                          -13591
                          -13601
                          -13621
                          -13641
                          -13661
                          -13711
                          -13731
                          -13751
                          -13841
                          -13871
                          -13901
                          -14011
                          -14061
                          -14091
                          -14141
                          -14151
                          -14171
                          -14201
                          -14232
                          -14351
                          -14461
                          -14511
                          -14601
                          -14633
                          -14661
                          -14741
                          -14781
                          -14831
                          -14981
                          -14991
                          -15081
                          -15111
                          -15121
                          -15131
                          -15161
                          -15201
                          -15251
                          -15271
                          -15281
                          -15352
                          -15361
                          -15411
                          -15431
                          -15441
                          -15471
                          -15551
                          -15651
                          -15682
                          -15831
                          -15921
                          -16191
                          -16201
                          -16281
                          -16391
                          -16461
                          -16621
                          -16732
                          -16781
                          -16801
                          -16811
                          -16832
                          -16922
                          -17061
                          -17151
                          -17181
                          -17201
                          -17211
                          -17331
                          -17461
                          -17471
                          -17551
                          -17581
                          -17641
                          -17771
                          -17811
                          -17831
                          -17841
                          -17911
                          -17951
                          -17961
                          -17971
                          -17981
                          -18011
                          -18031
                          -18261
                          -18321
                          -18401
                          -18411
                          -18531
                          -18591
                          -18611
                          -18621
                          -18721
                          -18851
                          -18951
                          -18971
                          -19071
                          -19141
                          -19281
                          -19561
                          -19571
                          -19581
                          -19691
                          -19701
                          -19951
                          -19991
                          -20021
                          -20041
                          -20101
                          -20111
                          -20271
                          -20301
                          -20381
                          -20391
                          -20471
                          -20611
                          -20661
                          -20921
                          -20931
                          -20942
                          -21111
                          -21131
                          -21141
                          -21321
                          -21351
                          -21411
                          -21611
                          -21971
                          -22071
                          -22121
                          -22531
                          -22601
                          -22651
                          -22681
                          -22801
                          -22981
                          -23161
                          -23221
                          -23361
                          -23431
                          -23471
                          -24081
                          -24571
                          -24881
                          -25781
                          -26041
                          -26061
                          -26221
                          -26261
                          -26961
                          -28171
                          -28721

                            SergeM's avatar - slow icon.png
                            Economy class
                            Belgium
                            Member #123700
                            February 27, 2012
                            4035 Posts
                            Offline
                            Posted: June 2, 2012, 11:08 am - IP Logged

                            Euromillions

                            Numbers:

                            3 skips 3 hits in x drawings?

                            Relative
                            frequency
                            FrequencyCount of
                            games
                            needed
                                     0,02483 to 7
                                     0,092068 to 12
                                     0,1329613 to 17
                                     0,1535718 to 22
                                     0,1433323 to 27
                                     0,1126228 to 32
                                     0,1024533 to 37
                                     0,0818538 to 42
                                     0,0511243 to 47
                                     0,038148 to 52
                                     0,024153 to 57
                                     0,036458 to 62
                                     0,013563 to 67
                                     0,011968 to 72
                                     0,012073 to 77
                                     0,001078 to 82
                                     0,00783 to 87
                                     0,00688 to 92
                                     0,00393 to 97
                                     0,00498 to 102
                                     0,002103 to 107