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Probability of a Rollover in Powerball.

Topic closed. 310 replies. Last post 10 years ago by Prob988.

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United States
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June 2, 2005
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Posted: March 17, 2006, 1:50 pm - IP Logged

Higher interest rates and sales bigger than expected is causing the jackpots to reach new records. I hope it continues to roll. Lower interest rates and more jackpot winners will decrease the PB jackpot and won't set records.

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    New Jersey
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    Posted: March 19, 2006, 7:55 am - IP Logged

    The Powerball Jackpot has rolled again.  The cash value is $47.9M, the annuity is $101M.  (A comparably sized cash value would produce roughly an $81M annuity advertised value.)

    Lottoreport has not yet posted the sales for the last drawing, but as I've noted before, Powerball sales figures do not generally vary much through the first 10 draws, rising only slowly with jackpot increases.  The average sales of 9th draws is $17.3M, but for this run, sales have been running about $19M in this jackpot run.

    If the Powerball sells 19M tickets, the probability of various numbers of winners is as follows:

     

    087.81%
    111.42%
    20.74%
    30.03%

    Based on average sales figures from previous runs, I estimate that the series has a 7% chance of reaching a 19th draw, which will probably have an annuity value of more than to $300M, and a 2% chance of rolling beyond that, most likely triggering the cap again.

     

     

     

     


      United States
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      Posted: March 23, 2006, 12:36 am - IP Logged

      Prob988, PB Jackpot of 101.3 million for tonight 3/22 has rolled to an estimated 117 million for Saturday 3/25. I hope the PB jackpot continues to roll until it hits the cap again. Only 6 tickets hit 5 numbers for $200000 and one ticket multiplied by 2 for $400000.

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        New Jersey
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        Posted: March 23, 2006, 7:04 am - IP Logged

        The powerball jackpot has rolled.  The cash value is 55.3M and the annuity value is at $117M.  (The advertised annuity jackpot at MM would be about $94M for a cash value of this size.)

        The most recent powerball jackpot at this level sold about $24M in tickets.  If powerball sells $24M tickets for this jackpot the distribution of winners will be as follows:

         

        084.85%
        113.94%
        21.14%
        30.06%

        I'd estimate an 8% of a 19th draw and a 3% chance of a 20th draw.

         

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          New Jersey
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          Posted: March 27, 2006, 7:23 am - IP Logged

          The Powerball jackpot has rolled.    The cash jackpot is 63.8M, the annuity $135M.

          The last jackpot at this level sold 28.3M tickets.  If the same number is sold the probability of various numbers of winners will be:

           

          082.39%
          115.96%
          21.55%
          30.10%

          I estimate the probability of a 19th draw occurring as 9%, and of a 20th at 3%.


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            Posted: March 27, 2006, 2:05 pm - IP Logged

            I hope it contines to roll Prob988 until it hits the cap at 390 million. People are most interested when it reached the cap level. Most 5/5 winners (missing the PB) occur at the cap.

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              New Jersey
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              Posted: March 30, 2006, 6:25 am - IP Logged

              The Powerball jackpot has rolled.    The cash jackpot is 71.8M, the annuity $152M.

              The last jackpot at this jackpot level sold 28.8M tickets.  As is the case in MM, it is almost as if the powerball had skipped a drawing when one views average sales.  If the same number is sold the probability of various numbers of winners will be:

              082.11%
              116.19%
              21.60%
              30.10%
              40.01%

               

              I estimate that the probability of reaching a capped drawing is about 15%, of passing it about 5%.  There is a roughly 45% chance of a jackpot in excess of $250M annuity.  Keep in mind that the Powerball annuity is inflated via an accounting trick.  The equivalent jackpot in MM, based on cash value would be around $124M.  The actual value of the PB is very close to MM, although the odds of winning PB are better.

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                New Jersey
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                Posted: April 2, 2006, 8:18 am - IP Logged

                The Powerball jackpot has rolled.    The cash jackpot is 80.4M, the annuity $174M.

                The last jackpot at this jackpot prize level sold 32.5 M tickets.  As is the case in MM, it is almost as if the powerball had skipped a drawing when one views average sales, the sales figure, 29.9M would be characteristic of the average of one later draw.  If the same number is sold the probability of various numbers of winners will be:

                080.06%
                117.81%
                21.98%
                30.15%
                40.01%

                I estimate the probability of reaching a capped jackpot at around 19% based on previous PB sales.  (I have not successfully mathematically modeled the Powerball, which does not behave as classically exponential as MM does.)  I estimate that probability of going one draw beyond the cap as being around 6%.

                The graduated annuity that is used to inflate the advertised figure for Powerball now results in the cash value being only 46.21% of the advertised jackpot.  In this rollover, the cash value of the Powerball jackpot is only slightly higher than the MM jackpot, which is $78.9M.  The Powerball is still a better bet right now though, since the odds of winning are much better.

                 

                 

                 

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                  Morrison, IL
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                  Posted: April 3, 2006, 12:31 am - IP Logged

                  Yeah, if you think in terms of odds of winning, Mega Millions and Powerball are approximately equal bets when their annuity jackpots are equal.

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                    Posted: April 3, 2006, 1:58 am - IP Logged

                    By the time it hits the cap it might be as low as 45% cash value. Ouch. It had been at 47.2% until the current drawing. Powerball has a habit of dropping the cash payout percent as the pot grows.

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                      Morrison, IL
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                      Posted: April 3, 2006, 12:19 pm - IP Logged

                      I think the drop may be due to rising interest rates. Mega Millions dropped theirs to 57.1% from 58.3% as well.

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                        Mcminnville, Oregon
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                        Posted: April 3, 2006, 7:27 pm - IP Logged

                        In the Powerball FAQ section it says that when the interest rates climb the cash value percentage will decline.-weshar75

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                          Morrison, IL
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                          Posted: April 3, 2006, 8:13 pm - IP Logged

                          I wish Powerball would increase their maximum annuity rollovers to at least $40 million whenever it hits a record to accomodate the backloaded annuity.

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                            Posted: April 6, 2006, 8:53 am - IP Logged

                            The Powerball has rolled over.  The cash value is now $91 million and the annuity value is $195M.  The back loaded annuity means that the cash value is actually lower than the cash value for MM.

                            Sales for the last drawing did not rise appreciably with respect to the previous drawing.  Although up until now PB was running above average, sales were, at this time, very close to the average for a 13th drawing.

                            I am going to estimate that the 14th drawing will also be average, and calculate the rollover/winner probability for $32.6 million in sales, the average figure.  If this many tickets sell, the probability of various numbers of winners will be: 

                             

                            080.06%
                            117.81%
                            21.98%
                            30.15%
                            40.01%

                            These probabilities are the same as I gave for the 13th drawing, but I over-estimated sales at that time, based on the record breaking behavior of the run the held up until this drawing.

                            As I am treating the system differently, my long range probabilities for the long term are also the same as last time.  I estimate a 19% probability of reaching the cap and a 6% chance of exceeding it.    Again, my last assumptions were probably too optimistic. 

                             


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                              Posted: April 6, 2006, 2:35 pm - IP Logged

                              I hope PB continues to roll and set new records Prob988. I think higher interest rates actually lowers the cash value although it continues to set new records on rolls.

                                 
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