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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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Posted: August 27, 2006, 12:33 am - IP Logged

Prob988, PB Jackpot has rolled to 75 million for 8/30.

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    Posted: August 27, 2006, 11:12 am - IP Logged

    The Powerball jackpot has rolled.  The cash value jackpot is estimated at $34.9M, and the advertised annuity value is $75M.    Note that the difference between the MM jackpot and the Powerball jackpot is 5 million in both annuity and in cash, but the cash value of powerball is lower by 5 million while the advertised annuity is higher than MM.

    Thus you win more money with MM, but need to beat longer odds.

    The number of  tickets sold on 7th draws averages 16.9M.  If this is the number of tickets sold, the randomized probability for various numbers of winners is as follows:

     

    089.07%
    110.31%
    20.60%
    30.02%

     

    Lottoreport has not posted the sales figures for the most recent drawing as of yet, and I will therefore not post long term jackpot evolution model figures.

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      Posted: August 29, 2006, 8:29 pm - IP Logged

      The data on sales of the most recent drawing is now available.

      Here is what the mixed linear exponential model predicts for jackpot evolution:

       

      Average Historical AnnuityDrawing NumberCalculated AnnuityCash Value AveragesSingle Draw Rollover ProbabilityOverall Probability from baseline
      $353 19$451,408,146.95$210,186,918.4232.69%1.81%
      $300 18$345,126,992.33$160,699,755.8052.87%5.55%
      $245 17$284,550,079.35$132,493,630.7064.38%10.49%
      $208 16$242,702,870.95$113,008,524.2971.52%16.30%
      $193 15$210,845,510.99$98,174,941.0676.58%22.79%
      $173 14$185,487,103.22$86,367,432.4477.64%29.76%
      $152 13$161,431,339.82$75,166,467.6081.23%38.33%
      $126 12$141,676,256.98$65,968,007.1683.40%47.19%
      $112 11$124,422,943.85$57,934,433.2385.04%56.58%
      $102 10$109,018,671.89$50,761,819.1086.61%66.54%
      $90 9$95,360,836.70$44,402,389.5986.82%76.82%
      $78 8$81,928,386.58$38,147,905.0088.48%88.48%

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        Posted: August 31, 2006, 12:25 am - IP Logged

        Prob988, PB Jackpot for 9/2 is 89 million. Everyone, I think the annunity jackpot is running higher than expected for each run because it keeps rolling to at least 100+ Million.

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          Posted: August 31, 2006, 1:20 am - IP Logged

          PB has rolled.  The cash value is $41.3M.  The advertised annuity is $89M.  The average 8th draw produces sales of $17.9M.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

           

          088.48%
          110.83%
          20.66%
          30.03%

           

          A modelling program that I have written, not very accurate right now, suggests the following jackpot evolution:

           

           

          $583,391,611.73$270,719,92826.78%0.47%
          $457,746,939.00$212,415,15337.71%1.74%
          $364,730,056.92$169,251,13948.57%4.61%
          $295,868,081.62$137,296,08758.59%9.48%
          $244,888,393.45$113,639,22167.32%16.18%
          $207,147,265.71$96,125,64174.60%24.04%
          $179,206,868.79$83,160,04180.50%32.23%
          $158,522,119.09$73,561,38884.35%40.03%
          $142,286,471.12$66,027,31784.94%47.46%
          $126,724,429.62$58,805,83185.55%55.87%
          $111,835,994.59$51,896,92886.15%65.31%
          $97,621,166.03$45,300,60986.76%75.81%
          $84,079,943.93$39,016,87387.38%87.38%
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            Posted: September 3, 2006, 9:51 pm - IP Logged

            PB has rolled.  The cash value is $47.9M.  The advertised annuity is $102M.  The average 9th draw produces sales of $17.9M.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

             

            086.82%
            112.27%
            20.87%
            30.04%

             

            The model function developed for this game shows the following jackpot evolution, for what it's worth:

             

            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
            Average Jackpots$583,796,182.73$270,907,66726.78%0.46%
            $353 $458,151,510.00$212,602,89237.71%1.73%
            $300 $365,134,627.93$169,438,87848.57%4.59%
            $245 $296,272,652.62$137,483,82658.59%9.46%
            $208 $245,292,964.45$113,826,96067.32%16.14%
            $193 $207,551,836.72$96,313,38074.60%23.97%
            $173 $179,611,439.79$83,347,78080.50%32.14%
            $152 $158,926,690.10$73,749,12784.30%39.92%
            $126 $142,637,809.10$66,190,35484.90%47.36%
            $112 $127,026,219.94$58,945,87585.50%55.78%
            $102 $112,091,922.61$52,015,69086.11%65.23%
            $92 $97,834,917.10$45,399,79986.73%75.75%
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              Posted: September 7, 2006, 6:04 am - IP Logged

              PB has rolled.  The cash value is $55.8.  The advertised annuity is $119M.  The average 10th draw produces sales of $23.7.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

               

              083.93%
              114.70%
              21.29%
              30.08%

               

              The long term mixed linear modeling function, ignoring caps, reserves and minimums and is running about 6% behind the actual run.  Nevertheless this is what it predicts for long term jackpot evolution:

               

              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
              $578,117,065.63$271,083,46426.78%0.61%
              $353 $453,775,340.95$212,778,68937.71%2.28%
              $300 $361,723,053.42$169,614,67548.57%6.05%
              $245 $293,575,183.82$137,659,62458.59%12.45%
              $208 $243,124,160.21$114,002,75767.32%21.26%
              $193 $205,774,411.82$96,489,17874.60%31.58%
              $173 $178,123,759.65$83,523,57880.50%42.33%
              $152 $157,653,512.92$73,924,92584.24%52.58%
              $126 $141,471,855.43$66,337,22384.85%62.41%
              $112 $125,965,941.97$59,066,38385.46%73.56%
              $102 $111,135,772.54$52,112,40486.07%86.07%
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                Posted: September 10, 2006, 9:32 am - IP Logged

                PB has rolled.  The cash value is $64.5.  The advertised annuity is $137M.  The average 11th draw produces sales of $26.5M.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

                 

                083.40%
                115.14%
                21.37%
                30.08%

                 

                The long term probability modelling function is lagging on this draw, because sales are running ahead of the average values.  Nonetheless here is what the model predicts for long term jackpot evolution:

                 

                Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                $576,517,226.03$271,425,99326.78%0.71%
                $353 $452,676,075.82$213,121,21837.71%2.64%
                $300 $360,994,372.05$169,957,20448.57%7.00%
                $245 $293,120,851.90$138,002,15358.59%14.41%
                $208 $242,872,933.83$114,345,28667.32%24.60%
                $193 $205,673,547.92$96,831,70774.60%36.54%
                $173 $178,134,211.65$83,866,10780.50%48.97%
                $152 $157,746,373.96$74,267,45384.12%60.84%
                $126 $141,487,901.12$66,612,91784.73%72.33%
                $112 $125,916,784.34$59,281,99085.36%85.36%
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                  Posted: September 14, 2006, 1:57 am - IP Logged

                  PB has rolled.  The cash value is $73.9.  The advertised annuity is $157M.  These figures are more consistent with a 13th draw in an average run, rather than a 12th.  I will therefore treat it as a 13th draw.  The average 13th draw produces sales of $30.4M.  If this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

                   

                  081.23%
                  116.88%
                  21.75%
                  30.12%
                  40.01%

                   

                   

                  The modeling function predicts the following for jackpot evolution, ignoring caps, reserves and minimums:

                   

                  Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                  $576,963,808.21$271,577,23226.78%0.98%
                  $353 $453,095,747.45$213,272,45737.71%3.65%
                  $300 $361,394,121.34$170,108,44348.57%9.67%
                  $245 $293,505,852.34$138,153,39258.59%19.91%
                  $208 $243,247,015.46$114,496,52567.32%33.98%
                  $193 $206,039,546.15$96,982,94674.60%50.48%
                  $173 $178,494,225.62$84,017,34680.50%67.66%
                  $152 $158,101,957.67$74,418,69284.05%84.05%

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                    Posted: September 14, 2006, 11:09 am - IP Logged

                    Prob988, I'm happy that PB rolled. However, MM's annunity jackpot is higher than PB in the next draw. I hope PB continues to roll and follow MM.

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                      Posted: September 17, 2006, 1:53 am - IP Logged

                      The Powerball jackpot has rolled.  The cash value is now $83.5M.  The advertised annuity value is represented as being $179M.    The lottery has been selling above average sales on this run.  Although in a temporal sense, the upcoming draw is the 13th in this series, the jackpots are better reflected by an average 14th draw.  I will therefore treat the system as if it were a 14th draw.  The average number of sales on a 14th draw is about $40.0M tickets.  If this is the number of sales realized on the next draw the randomized probability distribution of winners will be as follows:

                       

                      077.64%
                      119.65%
                      22.49%
                      30.21%
                      40.01%

                       

                       

                      The long term jackpot evolution as predicted by my mixed linear/exponential modeling function predicts the following jackpot evolution:

                       

                      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                      $582,891,434.82$271,907,45726.78%1.16%
                      $353 $457,902,755.27$213,602,68237.71%4.34%
                      $300 $365,371,516.07$170,438,66848.57%11.51%
                      $245 $296,869,070.43$138,483,61758.59%23.69%
                      $208 $246,155,548.16$114,826,75067.32%40.43%
                      $193 $208,611,467.55$97,313,17174.60%60.06%
                      $173 $180,816,947.96$84,347,57180.50%80.50%

                       

                       

                      These numbers ignore minimums, reserves and caps.


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                        Posted: September 17, 2006, 12:50 pm - IP Logged

                        I hope PB continues to roll and set records Prob988. If it does, it reaches at least 200+ million for Saturday 9/26.

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                          Posted: September 21, 2006, 10:05 am - IP Logged

                          The Powerball jackpot has rolled.  The cash value is now $94.5M.  The advertised annuity value is represented as being $203M.    The lottery has been selling above average sales on this run.  Although in a temporal sense, the upcoming draw is the 14th in this series, the jackpots are better reflected by an average 15th draw.  I will therefore treat the system as if it were a 15th draw.  The average number of sales on a 14th draw is about $39.0M tickets.  If this is the number of sales realized on the next draw the randomized probability distribution of winners will be as follows:

                           

                          076.58%
                          120.43%
                          22.73%
                          30.24%
                          40.02%

                           

                          The long term jackpot evolution modeling program suggests the following, ignoring caps, reserves, and minimums:

                           

                          Calculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                          $584,024,547.01$271,873,49626.91%1.45%
                          $459,231,657.10$213,780,25437.77%5.38%
                          $366,675,265.59$170,693,65848.57%14.23%
                          $298,028,040.46$138,737,19158.53%29.30%
                          $247,113,766.01$115,035,71967.22%50.07%
                          $209,351,666.56$97,456,81074.48%74.48%

                           

                          Note that the cash value estimated beforehand by the Powerball lottery in the last run, $83.5M, was exceeded in the actual event.  The last cash jackpot reached $85.6M.


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                            Posted: September 21, 2006, 10:19 pm - IP Logged

                            Prob988, I'm happy that PB's annunity jackpot rolled to over 200+ million. I hope it continues to roll.

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                              Posted: September 24, 2006, 8:01 am - IP Logged

                              Powerball has been one and the the jackpot has been reset at $7.2M cash and $15 million as an advertised annuity.

                              A first round draw produces on average, 14.5M in sales.  If this is the number of tickets that sell, the randomized distribution of winners will be as follows:

                               

                              090.55%
                              18.99%
                              20.45%
                              30.01%

                               

                               

                              The long term model equation for the evolution of Powerball jackpots suggests this:

                               

                              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                              $551,094,924.37$271,873,49626.91%0.21%
                              $353 $433,338,353.05$213,780,25437.77%0.80%
                              $300 $346,000,658.35$170,693,65848.57%2.11%
                              $245 $281,224,036.31$138,737,19158.53%4.35%
                              $208 $233,180,510.80$115,035,71967.22%7.43%
                              $193 $197,547,588.44$97,456,81074.48%11.06%
                              $180 $171,119,362.32$84,418,88580.37%14.84%
                              $159 $151,518,075.38$74,748,91783.90%18.47%
                              $132 $135,766,252.99$66,978,01884.54%22.01%
                              $119 $120,697,194.91$59,543,94985.18%26.04%
                              $105 $106,310,901.12$52,446,71185.83%30.57%
                              $92 $92,607,371.65$45,686,30386.49%35.62%
                              $79 $79,586,606.47$39,262,72687.15%41.18%
                              $68 $67,248,605.60$33,175,97987.82%47.25%
                              $57 $55,593,369.03$27,426,06288.49%53.81%
                              $47 $44,620,896.77$22,012,97689.16%60.81%
                              $36 $34,331,188.81$16,936,72089.84%68.20%
                              $27 $24,724,245.15$12,197,29490.53%75.91%
                              $20 $15,800,065.80$7,794,69991.22%83.85%
                              $15 $7,558,650.75$3,728,93491.92%91.92%
                                 
                                Page 16 of 21