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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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Posted: December 11, 2006, 9:47 pm - IP Logged

The Powerball jackpot has rolled over.  The cash jackpot is now $16M.  The advertised annuity is $3M.  The average sales for a third drawing are $15.4M.

If this is the average number of tickets that sell, the randomized distribution of probability of various numbers of winners is:

 

090.01%
19.47%
20.50%
30.02%

 

The linear/exponential model function predicts the following long term evolution of the jackpot.

 

Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
$561,837,804.78$272,406,20827.11%0.28%
$353 $442,700,373.57$214,642,60537.86%1.03%
$300 $354,039,940.23$171,655,72948.54%2.73%
$245 $288,060,068.39$139,665,48858.39%5.63%
$208 $238,958,757.67$115,858,79267.01%9.64%
$193 $202,418,239.35$98,142,17774.24%14.39%
$180 $175,225,289.53$84,957,71680.11%19.38%
$159 $154,988,671.28$75,146,02283.88%24.19%
$132 $138,944,158.71$67,366,86584.51%28.84%
$119 $123,586,697.32$59,920,82385.15%34.13%
$105 $108,916,287.11$52,807,89785.80%40.08%
$92 $94,932,928.08$46,028,08686.44%46.71%
$79 $81,636,620.24$39,581,39287.10%54.04%
$68 $69,027,363.57$33,467,81387.76%62.04%
$57 $57,105,158.09$27,687,34988.42%70.70%
$47 $45,870,003.79$22,240,00289.09%79.96%
$36 $35,321,900.67$17,125,77089.76%89.76%
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    New Jersey
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    Posted: December 14, 2006, 7:28 am - IP Logged

    The Powerball jackpot has rolled over.  The cash jackpot is now $21.2M.  The advertised annuity is $43M.  The average sales for a fourth drawing are $15.2M.

    If this is the average number of tickets that sell, the randomized distribution of probability of various numbers of winners is:

     

    090.06%
    19.42%
    20.49%
    30.02%

     

     

    Long term evolution of the jackpot, as modelled mathematically looks like this:

     

    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
    $552,468,651.63$272,379,89327.11%0.31%
    $353 $435,306,626.65$214,616,29037.86%1.15%
    $300 $348,116,263.39$171,629,41448.54%3.04%
    $245 $283,230,397.43$139,639,17358.39%6.27%
    $208 $234,943,230.79$115,832,47767.01%10.74%
    $193 $199,008,587.28$98,115,86274.24%16.03%
    $180 $172,266,521.13$84,931,40180.11%21.60%
    $159 $152,365,444.29$75,119,70783.88%26.96%
    $132 $136,585,296.27$67,339,72784.51%32.14%
    $119 $121,481,769.79$59,893,33885.15%38.03%
    $105 $107,054,864.85$52,780,53885.80%44.66%
    $92 $93,304,581.44$46,001,32986.45%52.05%
    $79 $80,230,919.57$39,555,70987.10%60.22%
    $68 $67,833,879.24$33,443,68087.76%69.13%
    $57 $56,113,460.45$27,665,24188.42%78.78%
    $47 $45,069,663.20$22,220,39289.09%89.09%
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      New Jersey
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      Posted: December 17, 2006, 8:08 am - IP Logged

      The Powerball jackpot has rolled over.  The cash jackpot is now $25.9M.  The advertised annuity is $53M.  The average sales for a fifth drawing are $15.9M.

      If ticket sales are averarge, the randomized distribution of probability of various numbers of winners is:

       

      089.68%
      19.76%
      20.53%
      30.02%

       

      The long term mixed linear exponential mathematical model I use - the actual jackpot is only 94% of what the model suggests - predicts the following:

       

      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
      $557,379,704.56$272,379,89327.11%0.35%
      $353 $439,176,192.61$214,616,29037.86%1.29%
      $300 $351,210,769.09$171,629,41448.54%3.42%
      $245 $285,748,113.99$139,639,17358.39%7.04%
      $208 $237,031,708.83$115,832,47767.01%12.06%
      $193 $200,777,631.92$98,115,86274.24%18.00%
      $180 $173,797,847.85$84,931,40180.11%24.24%
      $159 $153,719,864.60$75,119,70783.88%30.26%
      $132 $137,799,442.30$67,339,72784.51%36.08%
      $119 $122,561,656.22$59,893,33885.15%42.69%
      $105 $108,006,506.37$52,780,53885.80%50.13%
      $92 $94,133,992.73$46,001,32986.45%58.43%
      $79 $80,944,115.32$39,555,70987.10%67.59%
      $68 $68,436,874.13$33,443,68087.76%77.60%
      $57 $56,612,269.16$27,665,24188.42%88.42%
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        New Jersey
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        Posted: December 21, 2006, 6:36 am - IP Logged

        The Powerball jackpot has rolled over.  The cash jackpot is now $31.6  The advertised annuity is $65M.  The average sales for a seventh drawing are $17.1M.

        If ticket sales are averarge, the randomized distribution of probability of various numbers of winners is:

         

        088.93%
        110.43%
        20.61%
        30.02%

         

        The projection models suggests this:

         

        Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
        $560,224,471.96$272,355,28227.11%0.40%
        $353 $441,406,934.12$214,591,67937.86%1.46%
        $300 $352,984,561.01$171,604,80248.54%3.87%
        $245 $287,181,850.32$139,614,56158.39%7.97%
        $208 $238,212,380.47$115,807,86567.01%13.64%
        $193 $201,769,976.32$98,091,25074.24%20.36%
        $180 $174,650,041.71$84,906,79080.11%27.42%
        $159 $154,467,760.37$75,095,09683.88%34.23%
        $132 $138,467,529.91$67,316,52284.52%40.81%
        $119 $123,153,648.63$59,871,62085.16%48.28%
        $105 $108,526,116.52$52,760,38985.80%56.70%
        $92 $94,584,933.58$45,982,82986.45%66.09%
        $79 $81,330,099.82$39,538,94187.10%76.44%
        $68 $68,761,615.23$33,428,72487.76%87.76%

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          Posted: December 24, 2006, 12:21 am - IP Logged

          Prob988, PB Jackpot for 12/27 has rolled to 75 million. Lets see how the long term jackpot figures out.

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            New Jersey
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            Posted: December 24, 2006, 12:41 am - IP Logged

            The Powerball jackpot has rolled over.  The cash jackpot is now $36.3M  The advertised annuity is $75M.  The average sales for a seventh drawing are $18.5M.

            If ticket sales are averarge, the randomized distribution of probability of various numbers of winners is:

             

            088.11%
            111.15%
            20.71%
            30.03%

             

            Here's the long term:

             

            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
            $562,717,524.28$272,355,28227.11%0.45%
            $353 $443,371,237.07$214,591,67937.86%1.67%
            $300 $354,555,375.97$171,604,80248.54%4.41%
            $245 $288,459,836.94$139,614,56158.39%9.08%
            $208 $239,272,448.28$115,807,86567.01%15.54%
            $193 $202,667,871.96$98,091,25074.24%23.20%
            $180 $175,427,251.05$84,906,79080.11%31.25%
            $159 $155,155,156.63$75,095,09683.88%39.00%
            $132 $139,083,723.62$67,316,52284.52%46.50%
            $119 $123,701,694.11$59,871,62085.16%55.02%
            $105 $109,009,068.09$52,760,38985.80%64.61%
            $92 $95,005,845.56$45,982,82986.45%75.30%
            $79 $81,692,026.52$39,538,94187.10%87.10%

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              Posted: December 28, 2006, 12:17 am - IP Logged

              Prob988, PB Jackpot for 12/30 has rolled to 88 million.

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                New Jersey
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                Posted: December 28, 2006, 12:39 am - IP Logged

                The Powerball jackpot has rolled over.  The cash jackpot is now $42.8M  The advertised annuity is $88M.  The average sales for an ninth drawing are $21.1M.

                If ticket sales are averarge, the randomized distribution of probability of various numbers of winners is:

                 

                086.57%
                112.49%
                20.90%
                30.04%

                 

                The long term jackpot evolution suggests the following:

                 

                Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                $559,872,365.64$272,301,56027.11%0.52%
                $353 $441,106,079.08$214,537,95737.86%1.92%
                $300 $352,721,846.46$171,551,08048.54%5.06%
                $245 $286,947,519.40$139,560,83958.39%10.43%
                $208 $237,999,172.26$115,754,14367.01%17.86%
                $193 $201,572,487.33$98,037,52874.24%26.65%
                $180 $174,464,250.75$84,853,06780.11%35.90%
                $159 $154,290,674.92$75,041,37483.89%44.81%
                $132 $138,311,879.84$67,269,86984.53%53.41%
                $119 $123,018,131.70$59,831,54685.17%63.19%
                $105 $108,409,430.50$52,726,40585.81%74.19%
                $92 $94,485,776.23$45,954,44686.46%86.46%

                 

                The model is off by 5% right now.


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                  Posted: January 4, 2007, 1:12 am - IP Logged

                  Prob988, PB Jackpot for 1/6/07 has rolled to 115 million this time.

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                    Posted: January 4, 2007, 9:10 am - IP Logged

                    The Powerball jackpot has rolled over.  The cash jackpot is now $52.8M  The advertised annuity is $115M.  The average sales for an 11th drawing are $24.3M.

                    If ticket sales are averarge, the randomized distribution of probability of various numbers of winners is:

                     

                     

                    084.66%
                    114.10%
                    21.17%
                    30.07%

                     

                     

                    The long term probability function is running ahead of the actual outcome but here it is anyway:

                     

                     

                    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                    $567,295,716.24$272,301,94427.11%0.70%
                    $353 $446,954,876.64$214,538,34137.86%2.58%
                    $300 $357,398,883.36$171,551,46448.54%6.82%
                    $245 $290,752,548.17$139,561,22358.39%14.06%
                    $208 $241,155,264.61$115,754,52767.01%24.07%
                    $193 $204,245,650.15$98,037,91274.24%35.92%
                    $180 $176,778,024.07$84,853,45280.11%48.39%
                    $159 $156,336,995.53$75,041,75883.89%60.40%
                    $132 $140,146,125.89$67,270,14084.53%71.99%
                    $119 $124,649,414.07$59,831,71985.17%85.17%

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                      Posted: January 7, 2007, 1:24 am - IP Logged

                      Prob988, PB Jackpot for 1/10 has rolled to 131 million. Lets see how the long term jackpot evolution figures now.

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                        New Jersey
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                        Posted: January 7, 2007, 11:21 pm - IP Logged

                        The Powerball jackpot has rolled over.  The cash value is $63.5M; the advertised annuity value is $131M.  Twelfth round drawings sell on average 27.3M tickets.  If this is the number that sell, the randomized probability for various numbers of winners will be as follows:

                         

                        082.93%
                        115.52%
                        21.45%
                        30.09%

                         

                        The modeling program suggests the following jackpot evolution:

                         

                        Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                        $562,030,372.13$272,434,57027.11%0.82%
                        $353 $442,864,513.95$214,670,96737.86%3.03%
                        $300 $354,182,925.65$171,684,09048.54%8.00%
                        $245 $288,187,310.58$139,693,84958.39%16.48%
                        $208 $239,074,283.96$115,887,15367.01%28.23%
                        $193 $202,525,046.84$98,170,53874.24%42.12%
                        $180 $175,325,608.61$84,986,07780.11%56.74%
                        $159 $155,084,161.76$75,174,38483.84%70.82%
                        $132 $138,990,217.17$67,373,12184.48%84.48%

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                          Posted: January 11, 2007, 12:13 am - IP Logged

                          Prob988, PB Jackpot for 1/13 has rolled to 155 million.

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                            Posted: January 11, 2007, 12:26 am - IP Logged

                            The Powerball jackpot has rolled over.  The cash value is $74.7; the advertised annuity value is $155M.  Thirteenth round drawings sell on average 31.0M tickets.  If this is the number that sell, the randomized probability for various numbers of winners will be as follows:

                             

                             

                            080.89%
                            117.16%
                            21.82%
                            30.13%
                            40.01%

                             

                            The long term jackpot evolution is suggested as follows with the modeling program:

                             

                             

                            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                            $565,342,150.38$272,458,44327.11%0.97%
                            $353 $445,484,607.32$214,694,84037.86%3.58%
                            $300 $356,288,276.66$171,707,96348.54%9.47%
                            $245 $289,909,597.44$139,717,72258.39%19.51%
                            $208 $240,511,499.76$115,911,02667.01%33.41%
                            $193 $203,750,116.68$98,194,41174.24%49.85%
                            $180 $176,392,802.35$85,009,95180.11%67.16%
                            $159 $156,033,866.30$75,198,25783.83%83.83%

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                              Posted: January 14, 2007, 1:48 am - IP Logged

                              Prob988, PB Jackpot for 1/17 has rolled to 180 million. Lets see how the long term jackpot evolution figures now.

                                 
                                Page 19 of 21