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Rollover Probabilities for Powerball's current jackpot.

Topic closed. 5 replies. Last post 4 years ago by KY Floyd.

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New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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Posted: August 12, 2012, 12:32 pm - IP Logged

The current Powerball jackpot is $203M Cash/$305 million annuity as of this writing.

Based on these figures the anticipated sales, according to the Lottery, should be around 102.6M, yielding 56.3 million tickets sold.

The Poisson probability distribution for this number of sales (purely randomized) suggests the following probabilities for this many tickets sold:

k,   number of winnersp(m,k)
074.62%
121.84%
23.20%
30.31%
4

0.02%

 

Anything can happen, but this suggests that the most likely outcome would be yet another rollover.

Another set of probabilities can be determined by considering what the last $2 powerball ticket drawing sold, which was the $325M (annuity) jackpot last February, a continuation of a $1 powerball ticket run.   This set sold $169.4M tickets.   Were this repeated, the distribution of winners would be as follows:

k,   number of winnersp(m,k)
061.68%
129.81%
27.20%
31.16%
40.14%
50.01%

This also suggests that a rollover is the most probable outcome although, again, anything can happen.


    United States
    Member #124493
    March 14, 2012
    7023 Posts
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    Posted: August 12, 2012, 6:17 pm - IP Logged

    The current Powerball jackpot is $203M Cash/$305 million annuity as of this writing.

    Based on these figures the anticipated sales, according to the Lottery, should be around 102.6M, yielding 56.3 million tickets sold.

    The Poisson probability distribution for this number of sales (purely randomized) suggests the following probabilities for this many tickets sold:

    k,   number of winnersp(m,k)
    074.62%
    121.84%
    23.20%
    30.31%
    4

    0.02%

     

    Anything can happen, but this suggests that the most likely outcome would be yet another rollover.

    Another set of probabilities can be determined by considering what the last $2 powerball ticket drawing sold, which was the $325M (annuity) jackpot last February, a continuation of a $1 powerball ticket run.   This set sold $169.4M tickets.   Were this repeated, the distribution of winners would be as follows:

    k,   number of winnersp(m,k)
    061.68%
    129.81%
    27.20%
    31.16%
    40.14%
    50.01%

    This also suggests that a rollover is the most probable outcome although, again, anything can happen.

    based on thrifty anlalysis that all Qp GENERATE jackpot winners...then i would assume the jackpot will not roll...

    somebody will win this draw...because duplicate Quick PIcks cannot happen thus making the probablity of a quick pick losing ticket infintesimal.

      weshar75's avatar - Lottery-042.jpg
      Mcminnville, Oregon
      United States
      Member #3013
      December 13, 2003
      3044 Posts
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      Posted: August 12, 2012, 8:07 pm - IP Logged

      The current Powerball jackpot is $203M Cash/$305 million annuity as of this writing.

      Based on these figures the anticipated sales, according to the Lottery, should be around 102.6M, yielding 56.3 million tickets sold.

      The Poisson probability distribution for this number of sales (purely randomized) suggests the following probabilities for this many tickets sold:

      k,   number of winnersp(m,k)
      074.62%
      121.84%
      23.20%
      30.31%
      4

      0.02%

       

      Anything can happen, but this suggests that the most likely outcome would be yet another rollover.

      Another set of probabilities can be determined by considering what the last $2 powerball ticket drawing sold, which was the $325M (annuity) jackpot last February, a continuation of a $1 powerball ticket run.   This set sold $169.4M tickets.   Were this repeated, the distribution of winners would be as follows:

      k,   number of winnersp(m,k)
      061.68%
      129.81%
      27.20%
      31.16%
      40.14%
      50.01%

      This also suggests that a rollover is the most probable outcome although, again, anything can happen.

      I am wondering if the cash value will increase before wednesday night since their is 4 days before the drawing.-weshar75

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        New Jersey
        United States
        Member #21206
        September 4, 2005
        949 Posts
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        Posted: August 13, 2012, 4:39 pm - IP Logged

        I am wondering if the cash value will increase before wednesday night since their is 4 days before the drawing.-weshar75

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        This is certainly possible.   If they sold the 169M tickets I spoke of above, the new jackpot would be approximately $225M cash/338M annuity.

        I would expect it to end up somewhere in that neighborhood, but even so the most probable outcome would still be a rollover.

          Avatar
          New Jersey
          United States
          Member #21206
          September 4, 2005
          949 Posts
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          Posted: August 15, 2012, 10:50 am - IP Logged

          The new probabilities of various numbers of winners, reflecting the new jackpot figures of $213.3M Cash/$320M Annuity are given in the following table:

           

          k,   number of winnersp(m,k)
          068.25%
          126.07%
          24.98%
          30.63%
          40.06%

           ...if anyone's interested.

           

          Also if anyone's interested, the pretax cash basis expectation value is 0.73.

           

          Anything can happen, but the Poisson distribution (randomized) would seem to suggest that the most probable outcome is yet another rollover.

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            NY
            United States
            Member #23835
            October 16, 2005
            3471 Posts
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            Posted: August 15, 2012, 6:53 pm - IP Logged

            based on thrifty anlalysis that all Qp GENERATE jackpot winners...then i would assume the jackpot will not roll...

            somebody will win this draw...because duplicate Quick PIcks cannot happen thus making the probablity of a quick pick losing ticket infintesimal.

            "because duplicate Quick PIcks cannot happen"

            First, what universe are you in where that's how it works?

            Second, the increase in the jackpot is based on selling about 70 million tickets. Even if there wasn't a single repeated combination that would leave about 105 million unplayed combinations, and about a 60% chance of a rollover.