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Generalized Average Rate of Reoccurrence

Topic closed. 1 reply. Last post 10 years ago by JADELottery.

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JADELottery's avatar - RelativeChange 02.PNG
The Quantum Master
West Concord, MN
United States
Member #21
December 7, 2001
3579 Posts
Offline
Posted: November 7, 2006, 2:17 pm - IP Logged

Generalized Average Rate of Reoccurrence

    Reference - Combinatorial Distribution, Average Rate of Reoccurrence Distribution

    Generalized Average Rate of Reoccurrence - Ag = n / r

      n - number of items
      r - number of items in a combinatorial set

The generalized average rate of reoccurrence was derived from the combinatorial distribution function. The generalized average rate of reoccurrence is the same average rate for all items or numbers drawn in a combinatorial random selection. In example, the generalized average rate of reoccurrence for all numbers in a 6/49 lottery is about 49 / 6 = 8.167 draws. Looking at the column total in the combinatorial distribution, the total is the same for all items or numbers. Item/number 1 in column 1 for the combinatorial distribution function can be used to describe the column total for all items/numbers. Setting c = 1 and z = 1, the generalized average rate of reoccurrence can derive for all items/numbers.

    c = 1 and z = 1, also for reference  a! / (a - 1)! = a

    Ag = Ar(n,r,1,1)

    Ag = C(n,r) / D(n,r,1,1)

    Ag = C(n,r) / (C(1 - 1,1 - 1) * C(n - 1, r - 1))

    Ag = C(n,r) / ( 1 * C(n - 1, r - 1))

    Ag = C(n,r) / C(n - 1, r - 1)

    Ag = (n! / (r! * (n - r)!)) / ((n - 1)! / ((r - 1)! * ((n - 1) - (r - 1))!))

    Ag = (n! / (r! * (n - r)!)) / ((n - 1)! / ((r - 1)! * (n - 1 - r + 1)!))

    Ag = (n! / (r! * (n - r)!)) / ((n - 1)! / ((r - 1)! * (n - r)!))

    Ag = (n! / (r! * (n - r)!)) * ((r - 1)! * (n - r)! / (n - 1)!)

    Ag = (n! / (n - 1)!) * ((r - 1)! / r!) * ((n - r)! / (n - r)!)

    Ag = (n! / (n - 1)!) * ((r - 1)! / r!) * 1

    Ag = (n! / (n - 1)!) * (1 / (r! / (r - 1)!)

    Ag = n * (1 / r)

    Ag = n / r

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    JADELottery's avatar - RelativeChange 02.PNG
    The Quantum Master
    West Concord, MN
    United States
    Member #21
    December 7, 2001
    3579 Posts
    Offline
    Posted: November 28, 2006, 11:30 am - IP Logged

    Some various generalized average rates for Pick 5, Pick 6 and Pick 1 of Powerball and Mega Millions:

     

     

    n

    Pick 5

    Pick 6

    Pick 1

     

     

    30

    6.00

    5.00

     

     

     

    31

    6.20

    5.17

     

     

     

    32

    6.40

    5.33

     

     

     

    33

    6.60

    5.50

     

     

     

    34

    6.80

    5.67

     

     

     

    35

    7.00

    5.83

     

     

     

    36

    7.20

    6.00

     

     

     

    37

    7.40

    6.17

     

     

     

    38

    7.60

    6.33

     

     

     

    39

    7.80

    6.50

     

     

     

    40

    8.00

    6.67

     

     

     

    41

    8.20

    6.83

     

     

     

    42

    8.40

    7.00

    42

    <- Powerball

     

    43

    8.60

    7.17

     

     

     

    44

    8.80

    7.33

     

     

     

    45

    9.00

    7.50

     

     

     

    46

    9.20

    7.67

    46

    <- Mega Millions

     

    47

    9.40

    7.83

     

     

     

    48

    9.60

    8.00

     

     

     

    49

    9.80

    8.17

     

     

     

    50

    10.00

    8.33

     

     

     

    51

    10.20

    8.50

     

     

     

    52

    10.40

    8.67

     

     

     

    53

    10.60

    8.83

     

     

     

    54

    10.80

    9.00

     

     

    Powerball ->

    55

    11.00

    9.17

     

     

    Mega Millions ->

    56

    11.20

    9.33

     

     

    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
    US God plus Islam Allah
    Jehocifer