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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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New Jersey
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September 4, 2005
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Posted: February 15, 2007, 2:54 pm - IP Logged

The Powerball jackpot has rolled.  The cash value is 27.5M; the advertised annuity, $58M.  The average number of tickets sold on on sixth draws is 16.7M.

The average sales of this size produce a probability distribution for numbers of winners as follows:

 

089.14%
110.25%
20.59%
30.02%

 

The long term jackpot evolution has been pretty accurate of late in Powerball (not so good in MM - which I am still modeling as a pure exponential).  Here is what it suggests for the long term behavior for this run:

 

 

Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
$578,696,238.33$274,381,83727.19%0.34%
$353 $457,144,193.15$216,749,40237.72%1.23%
$300 $366,140,574.52$173,601,13448.19%3.27%
$245 $298,007,960.30$141,296,87857.90%6.79%
$218 $246,998,415.94$117,111,31866.42%11.73%
$196 $208,808,576.24$99,004,06673.61%17.66%
$180 $180,216,596.55$85,447,52479.51%23.99%
$158 $158,810,345.33$75,298,00983.84%30.17%
$132 $142,358,753.07$67,497,68584.48%35.98%
$119 $126,613,062.79$60,032,05685.12%42.60%
$104 $111,573,274.48$52,901,12285.76%50.05%
$92 $97,239,388.14$46,104,88286.41%58.35%
$79 $83,611,403.78$39,643,33887.07%67.53%
$67 $70,689,321.40$33,516,48987.73%77.55%
$57 $58,473,140.99$27,724,33488.40%88.40%
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    New Jersey
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    Member #21206
    September 4, 2005
    949 Posts
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    Posted: February 18, 2007, 11:41 am - IP Logged

    Powerball has rolled over.  The cash jackpot is $31.9 M, the advertised annuity value is $67M.  The average sales for 7th draws is 17.1M.

    Sales of 17.1M in this drawing would produce a probability distribution for numbers of winners as follows:

     

    088.93%
    110.43%
    20.61%
    30.02%

     

    The long term jackpot model suggests the following:

     

    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
    $576,368,847.15$274,420,39127.19%0.38%
    $353 $455,322,666.60$216,787,95637.72%1.40%
    $300 $364,697,778.85$173,639,68948.19%3.70%
    $245 $296,848,712.96$141,335,43257.90%7.68%
    $218 $246,051,455.65$117,149,87266.42%13.26%
    $196 $208,020,551.07$99,042,62173.61%19.97%
    $180 $179,547,562.97$85,486,07879.51%27.12%
    $158 $158,230,398.41$75,336,56383.84%34.12%
    $132 $141,842,645.74$67,534,03684.47%40.69%
    $119 $126,157,590.33$60,066,07785.11%48.17%
    $104 $111,175,232.19$52,932,68585.76%56.60%
    $92 $96,895,571.30$46,133,86286.41%66.00%
    $79 $83,318,607.67$39,669,60687.07%76.38%
    $67 $70,444,341.30$33,539,91887.73%87.73%
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      New Jersey
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      Posted: February 22, 2007, 7:45 am - IP Logged

      Powerball has rolled over.  The cash jackpot is $37.5M, the advertised annuity is $78M.  Average sales for 8th round drawings are 18.3M.  Average sales would provide the following probability distribution for numbers of winners:

       

      088.20%
      111.07%
      20.69%
      30.03%

       

      The long term probability distribution model suggests the following for jackpot evolution:

       

      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
      $570,972,780.08$274,506,14427.19%0.43%
      $353 $451,097,314.83$216,873,70937.72%1.59%
      $300 $361,348,918.54$173,725,44248.19%4.21%
      $245 $294,156,064.51$141,421,18557.90%8.74%
      $218 $243,850,100.07$117,235,62566.42%15.10%
      $196 $206,187,016.78$99,128,37373.61%22.74%
      $180 $177,989,409.22$85,571,83179.51%30.89%
      $158 $156,878,416.64$75,422,31683.82%38.85%
      $132 $140,632,056.86$67,611,56684.46%46.35%
      $119 $125,082,161.96$60,135,65585.10%54.88%
      $104 $110,228,731.94$52,994,58385.74%64.49%
      $92 $96,071,766.79$46,188,34986.40%75.21%
      $79 $82,611,266.52$39,716,95587.05%87.05%
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        New Jersey
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        Posted: February 25, 2007, 11:35 pm - IP Logged

        The powerball jackpot has rolled over.  The new cash prize is $43.2M; the advertised annuity is $90M.  The average sales for a 9th drawing are 21.1M.  Average sales would produce a winner distribuiton probability like this:

         

        k, number of winnersp(m,k)
        086.57%
        112.49%
        20.90%
        30.04%

         

         

        The long term models suggests the following:

         

        Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
        $571,990,745.54$274,555,55827.19%0.50%
        $353 $451,923,172.17$216,923,12337.72%1.82%
        $300 $362,030,948.32$173,774,85548.19%4.84%
        $245 $294,730,413.44$141,470,59857.90%10.04%
        $218 $244,343,830.47$117,285,03966.42%17.34%
        $196 $206,620,389.67$99,177,78773.61%26.10%
        $180 $178,377,593.64$85,621,24579.51%35.46%
        $158 $157,232,769.34$75,471,72983.81%44.60%
        $132 $140,946,828.33$67,654,47884.45%53.22%
        $119 $125,359,406.09$60,172,51585.09%63.02%
        $104 $110,470,502.62$53,025,84185.73%74.06%
        $92 $96,280,117.91$46,214,45786.39%86.39%

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          Posted: February 26, 2007, 7:41 pm - IP Logged

          I hope PB continues to roll and reaches between 365 and 390 million on this run.

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            New Jersey
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            Posted: March 1, 2007, 11:54 pm - IP Logged

            Powerball has rolled.  The cash jackpot is $50.2M, the advertised annuity is $105M.  Tenth round jackpots sell  21.9 M tickets.  If this is the nubmer that sell, the distribution of winners will be as follows:

             

            086.07%
            112.91%
            20.97%
            30.05%

             

             

            Here is the long term model of the run:

             

            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
            $574,228,336.77$274,535,83327.19%0.57%
            $353 $453,682,406.54$216,903,39837.72%2.11%
            $300 $363,432,046.34$173,755,13148.19%5.60%
            $245 $295,863,381.83$141,450,87457.90%11.62%
            $218 $245,276,055.51$117,265,31466.42%20.07%
            $196 $207,402,322.12$99,158,06373.61%30.22%
            $180 $179,047,004.98$85,601,52079.51%41.06%
            $158 $157,817,938.35$75,452,00583.81%51.64%
            $132 $141,473,902.14$67,637,99984.45%61.61%
            $119 $125,830,565.07$60,158,99485.09%72.96%
            $104 $110,887,927.12$53,014,99085.74%85.74%
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              New Jersey
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              Posted: March 4, 2007, 9:55 pm - IP Logged

              Not that anybody is noticing, Powerball has rolled and has quite an impressive jackpot.  The cash value is $57.6M, the advertised annuity is $120M.  Tenth draws average about 21.9M in sales.  This suggests the following probability distribution for numbers of winners:

               

              086.07%
              112.91%
              20.97%
              30.05%

               

              The long term model suggests the following:

               

              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
              $572,275,012.31$274,692,00627.19%0.67%
              $353 $452,207,438.95$217,059,57137.72%2.46%
              $300 $362,315,215.09$173,911,30348.19%6.52%
              $245 $295,014,680.21$141,607,04657.90%13.53%
              $218 $244,628,097.24$117,421,48766.42%23.38%
              $196 $206,904,656.44$99,314,23573.61%35.19%
              $180 $178,661,860.41$85,757,69379.51%47.81%
              $158 $157,517,036.11$75,608,17783.77%60.13%
              $132 $141,184,317.03$67,768,47284.41%71.79%
              $119 $125,554,268.61$60,266,04985.05%85.05%
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                New Jersey
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                Posted: March 11, 2007, 3:37 pm - IP Logged

                The powerball jackpot has rolled.  The cash value is $79.5M.  The advertised annuity is $165M.

                Average ticket sales for 12th drawings are 27.4M.  If this is the number of tickets that sell, the probability of various numbers of winners is:

                 

                082.90%
                115.55%
                21.46%
                30.09%
                  stephi's avatar - winifrid
                  rural lowcountry, south carolina
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                  Posted: March 11, 2007, 3:44 pm - IP Logged

                  I hope PB continues to roll and reaches between 365 and 390 million on this run.

                  Me too!

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                    New Jersey
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                    Posted: March 15, 2007, 10:35 am - IP Logged

                    The Powerball jackpot has rolled.  The cash value is $88.2M, the annuity is advertised at $183M.  Thirteen round draws sell on average 31.4M tickets.  (Recent draws have been above average though).

                    Here is the probability for various numbers of winners:

                     

                    080.66%
                    117.34%
                    21.86%
                    30.13%
                    40.01%

                     

                     

                    The long term model function suggests the following for jackpot evolution:

                     

                    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                    $571,390,249.50$275,391,36627.19%1.11%
                    $353 $451,812,747.87$217,758,93137.72%4.09%
                    $300 $362,287,431.05$174,610,66348.19%10.85%
                    $245 $295,261,592.23$142,306,40757.90%22.51%
                    $218 $245,080,668.78$118,120,84766.42%38.87%
                    $196 $207,511,201.21$100,013,59573.61%58.53%
                    $180 $179,383,681.90$86,457,05379.51%79.51%
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                      New Jersey
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                      Posted: March 30, 2007, 12:02 am - IP Logged

                      Powerball has rolled.  The cash jackpot is 19.1M, the advertised annuity is $41M.

                      Fourth round drawings sell 15.4M tickets on average.  The probabilities in an average run for various numbers of winners is as follows:

                       

                       

                      089.97%
                      19.51%
                      20.50%
                      30.02%

                       

                       

                      The long term model suggests the following:

                       

                      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                      $590,800,138.12$275,226,40627.19%0.26%
                      $353 $467,086,533.74$217,593,97137.72%0.96%
                      $300 $374,464,598.37$174,445,70348.19%2.56%
                      $245 $305,120,382.33$142,141,44657.90%5.30%
                      $218 $253,203,735.58$117,955,88766.42%9.16%
                      $196 $214,334,766.21$99,848,63573.61%13.79%
                      $180 $185,234,335.54$86,292,09379.51%18.73%
                      $158 $163,447,417.09$76,142,57783.43%23.56%
                      $132 $146,242,225.46$68,127,47684.11%28.24%
                      $119 $129,809,086.06$60,472,03884.80%33.58%
                      $104 $114,147,998.90$53,176,26385.49%39.60%
                      $92 $99,258,963.96$46,240,15286.19%46.31%
                      $79 $85,141,981.26$39,663,70386.89%53.73%
                      $67 $71,797,050.79$33,446,91987.60%61.84%
                      $57 $59,224,172.55$27,589,79788.32%70.59%
                      $46 $47,423,346.55$22,092,33989.04%79.93%
                      $36 $36,394,572.77$16,954,54589.77%89.77%
                         
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