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Probability of a MegaMillions rollover.

Topic closed. 352 replies. Last post 10 years ago by Prob988.

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Posted: December 9, 2006, 1:35 am - IP Logged

Prob988, MM Jackpot for 12/12 has rolled to 22 million according to usamega.com

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    Posted: December 9, 2006, 2:59 am - IP Logged

    MM has rolled over.  The cash jackpot is $13.1M.  The advertised annuity value is $22M.  Third round draws sell on average $15.9M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

     

    091.33%
    18.28%
    20.38%
    30.01%

     

    The modeling fuction suggests the following for the long term evolution of the jackpot:

     

    Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
    $585,787,522.81$348,809,84344.79%0.22%
    $510,410,748.43$303,926,40049.31%0.50%
    $444,068,993.46$264,422,90153.67%1.01%
    $385,679,277.41$229,654,47957.83%1.88%
    $315 $334,288,431.00$199,053,56661.75%3.24%
    $262 $289,057,536.36$172,120,62465.43%5.25%
    $247 $249,248,232.32$148,415,99368.84%8.02%
    $217 $214,210,661.18$127,552,71271.99%11.66%
    $180 $183,372,860.30$109,190,20374.88%16.19%
    $153 $156,231,425.20$93,028,71277.53%21.62%
    $131 $132,343,291.86$78,804,41579.93%27.89%
    $111 $111,318,504.03$66,285,10982.10%34.90%
    $94 $92,813,847.47$55,266,42784.07%42.50%
    $82 $76,527,247.24$45,568,49785.83%50.56%
    $68 $62,192,836.53$37,033,00787.42%58.90%
    $56 $49,576,616.60$29,520,62288.84%67.38%
    $46 $38,472,636.92$22,908,70790.11%75.84%
    $34 $28,699,633.16$17,089,32791.24%84.17%
    $25 $20,098,068.21$11,967,48692.25%92.25%
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      Posted: December 13, 2006, 10:13 pm - IP Logged

      MM has rolled over.  The cash jackpot is $17.9M.  The advertised annuity value is $30M.  Fourth round draws sell on average $16.7M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

       

      090.94%
      18.64%
      20.41%
      30.01%

       

       

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

       

       

      Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
      $584,646,703.58$348,839,20044.77%0.24%
      $509,395,892.72$303,939,54949.30%0.54%
      $443,168,165.18$264,423,67253.67%1.09%
      $384,881,592.00$229,646,01757.82%2.03%
      $315 $333,583,974.84$199,038,43861.75%3.52%
      $262 $288,437,290.39$172,100,91765.42%5.69%
      $247 $248,704,000.04$148,393,38768.84%8.70%
      $217 $213,735,001.08$127,528,55171.99%12.64%
      $180 $182,959,022.61$109,165,55074.88%17.56%
      $153 $155,873,292.99$93,004,39877.53%23.45%
      $131 $132,035,326.32$78,781,07879.93%30.24%
      $111 $111,055,693.76$66,263,23182.11%37.84%
      $94 $92,591,661.64$55,246,35884.07%46.09%
      $82 $76,341,592.38$45,550,48385.84%54.82%
      $68 $62,040,016.80$37,017,21087.42%63.86%
      $56 $49,453,297.27$29,507,13488.84%73.05%
      $46 $38,375,810.90$22,897,56790.11%82.22%
      $34 $28,626,590.38$17,080,53291.24%91.24%
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        Posted: December 16, 2006, 10:31 am - IP Logged

        MM has rolled over.  The cash jackpot is $23.9M.  The advertised annuity value is $40M.  Fifth round draws sell on average $18.6M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

         

        089.97%
        19.51%
        20.50%
        30.02%

         

        The long term model for jackpot evolution suggests the following:

         

        Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
        $583,841,857.41$348,845,51044.77%0.26%
        $508,689,112.96$303,941,74549.30%0.59%
        $442,548,532.00$264,422,74853.66%1.20%
        $384,339,394.29$229,642,78857.82%2.23%
        $315 $333,110,577.39$199,033,57061.75%3.85%
        $262 $288,025,015.49$172,094,94765.42%6.24%
        $247 $248,346,022.01$148,386,74868.84%9.54%
        $217 $213,425,252.31$127,521,58871.99%13.85%
        $180 $182,692,109.93$109,158,53674.88%19.24%
        $153 $155,644,423.16$92,997,54377.53%25.70%
        $131 $131,840,239.70$78,774,54379.93%33.15%
        $111 $110,890,605.26$66,257,13782.11%41.47%
        $94 $92,453,208.15$55,240,79284.07%50.51%
        $82 $76,226,786.01$45,545,50585.84%60.08%
        $68 $61,946,203.25$37,012,85687.42%69.99%
        $56 $49,378,118.78$29,503,42688.84%80.06%
        $46 $38,317,173.30$22,894,51190.11%90.11%
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          Posted: December 20, 2006, 2:17 am - IP Logged

          MM has rolled over.  The cash jackpot is $29/7M.  The advertised annuity value is $60M.  Sixth round draws sell on average $19.4M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

           

          089.60%
          19.84%
          20.54%
          30.02%

           

           

          The long term model suggests the following:

           

          Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
          $587,332,915.83$348,875,75244.75%0.29%
          $511,691,978.02$303,945,03549.28%0.65%
          $445,127,642.47$264,405,82053.65%1.33%
          $386,550,754.13$229,611,14857.81%2.47%
          $315 $335,002,852.11$198,991,69461.74%4.28%
          $262 $289,640,486.88$172,046,44965.42%6.93%
          $247 $249,721,419.39$148,334,52368.84%10.59%
          $217 $214,592,476.26$127,467,93171.99%15.38%
          $180 $183,678,862.20$109,105,24474.89%21.37%
          $153 $156,474,755.02$92,946,00477.53%28.53%
          $131 $132,535,029.11$78,725,80779.94%36.80%
          $111 $111,467,972.11$66,211,97582.11%46.04%
          $94 $92,928,875.53$55,199,75284.08%56.07%
          $82 $76,614,394.49$45,508,95085.85%66.69%
          $68 $62,257,584.26$36,981,00587.43%77.69%
          $56 $49,623,532.36$29,476,37888.85%88.85%
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            Posted: December 23, 2006, 2:00 am - IP Logged

            MM has rolled over.  The cash jackpot is $35.6M.  The advertised annuity value is $60M.  Seventh round draws sell on average $21.6M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

             

            088.45%
            110.86%
            20.67%
            30.03%

             

            The long term model suggests the following:

             

            Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
            $587,988,586.03$348,873,22844.75%0.33%
            $512,272,166.29$303,948,15249.29%0.74%
            $445,640,045.85$264,413,09453.65%1.49%
            $387,002,309.29$229,621,37057.81%2.78%
            $315 $335,399,806.99$199,003,88561.74%4.81%
            $262 $289,988,466.09$172,059,82365.42%7.80%
            $247 $250,025,483.87$148,348,45468.84%11.92%
            $217 $214,857,177.54$127,481,92571.99%17.31%
            $180 $183,908,291.80$109,118,92074.89%24.05%
            $153 $156,672,589.30$92,959,07077.53%32.11%
            $131 $132,704,570.02$78,738,04579.93%41.42%
            $111 $111,612,184.07$66,223,22982.11%51.81%
            $94 $93,050,418.93$55,209,91584.08%63.10%
            $82 $76,715,655.95$45,517,95685.84%75.05%
            $68 $62,340,704.01$36,988,81887.43%87.43%
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              Posted: December 27, 2006, 11:10 am - IP Logged

              MM has rolled over.  The cash jackpot is $35.6M.  The advertised annuity value is $60M.  Seventh round draws sell on average $21.6M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

               

              087.68%
              111.53%
              20.76%
              30.03%

               

              Note that the MM has been running below average in sales on this run.

              The long term projections, based on a mathematical model generated from average sales gives the following probability for long term jackpot evolution:

               

              Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
              $588,210,922.15$348,841,75544.72%0.38%
              $512,397,270.74$303,880,04849.26%0.84%
              $445,690,008.43$264,318,93653.63%1.71%
              $386,995,317.42$229,509,72357.80%3.19%
              $315 $335,350,764.28$198,881,63461.74%5.51%
              $262 $289,909,518.69$171,932,45165.42%8.93%
              $247 $249,926,467.72$148,220,28068.84%13.64%
              $217 $214,745,997.98$127,356,30772.00%19.82%
              $180 $183,791,245.39$108,998,41974.90%27.53%
              $153 $156,554,636.12$92,845,59777.54%36.76%
              $131 $132,589,563.81$78,632,97779.95%47.40%
              $111 $111,503,066.38$66,127,51382.13%59.29%
              $94 $92,949,382.60$55,124,14884.09%72.20%
              $82 $76,624,282.47$45,442,45685.86%85.86%
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                Posted: December 28, 2006, 9:39 am - IP Logged

                I didn't change all of the numbers in the opening paragraph of my last post.  Here is the corrected post: 

                 

                MM has rolled over.  The cash jackpot is $42.7M.  The advertised annuity value is $72M.  Seventh round draws sell on average $23.1 tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

                 

                087.68%
                111.53%
                20.76%
                30.03%

                 

                The long term projections, based on a mathematical model generated from average sales gives the following probability for long term jackpot evolution:

                 

                Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                $588,210,922.15$348,841,75544.72%0.38%
                $512,397,270.74$303,880,04849.26%0.84%
                $445,690,008.43$264,318,93653.63%1.71%
                $386,995,317.42$229,509,72357.80%3.19%
                $315 $335,350,764.28$198,881,63461.74%5.51%
                $262 $289,909,518.69$171,932,45165.42%8.93%
                $247 $249,926,467.72$148,220,28068.84%13.64%
                $217 $214,745,997.98$127,356,30772.00%19.82%
                $180 $183,791,245.39$108,998,41974.90%27.53%
                $153 $156,554,636.12$92,845,59777.54%36.76%
                $131 $132,589,563.81$78,632,97779.95%47.40%
                $111 $111,503,066.38$66,127,51382.13%59.29%
                $94 $92,949,382.60$55,124,14884.09%72.20%
                $82 $76,624,282.47$45,442,45685.86%85.86%

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                  Posted: January 4, 2007, 1:18 am - IP Logged

                  Prob988, MM Jackpot for 1/5/07 has rolled to 102 million, up from 84 million in last draw (roll) on 1/2/07.

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                    Posted: January 4, 2007, 8:22 am - IP Logged

                    MM has rolled over.  The cash jackpot is $59.7M.  The advertised annuity value is $102M.  Seventh round draws sell on average $30.8M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

                     

                    083.93%
                    114.70%
                    21.29%
                    30.08%

                     

                    This run has lower than average sales overall, although the pace for the last several draws has been near average.  The mathematical projection model shows a jackpot that is about 10% larger.  For what it's worth here it is:

                     

                    Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                    $595,754,266.49$348,691,46844.72%0.52%
                    $518,932,641.79$303,728,22349.26%1.17%
                    $451,343,908.60$264,168,93553.64%2.37%
                    $391,878,401.69$229,364,12357.81%4.42%
                    $315 $339,559,822.17$198,742,36761.74%7.64%
                    $262 $293,529,208.70$171,800,91965.43%12.38%
                    $247 $253,030,835.17$148,097,45968.85%18.92%
                    $217 $217,399,803.24$127,242,82672.01%27.48%
                    $180 $186,051,126.09$108,894,63074.91%38.16%
                    $153 $158,470,124.20$92,751,63277.55%50.94%
                    $131 $134,203,975.38$78,548,79779.96%65.68%
                    $111 $112,854,280.36$66,052,94682.14%82.14%
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                      Posted: January 6, 2007, 9:31 am - IP Logged

                      MM has rolled over.  The cash jackpot is $71.6M.  The advertised annuity value is $122M.  Eleventh round draws sell on average $34.9M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

                       

                      083.57%
                      115.00%
                      21.35%
                      30.08%

                       

                      For the last draw, sales were above average.  However for the entire run, sales a running just above historical lows for an 11 draw run.  The modeling function I use, which is based on average values is running ahead of the actual performance.  However, because of the return to higher sales, the model may still give an idea of the number of rollovers that are probable.  For what it's worth, here's what it says:

                       

                      Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                      $594,715,461.60$349,029,73044.70%0.63%
                      $518,058,814.49$304,041,07549.24%1.42%
                      $450,610,517.51$264,456,66453.62%2.88%
                      $391,264,421.14$229,627,31657.78%5.36%
                      $315 $339,047,251.67$198,981,83061.72%9.28%
                      $262 $293,102,649.51$172,017,62165.40%15.04%
                      $247 $252,677,124.94$148,292,47768.83%22.99%
                      $217 $217,107,700.89$127,417,30671.98%33.41%
                      $180 $185,811,040.16$109,049,75874.88%46.41%
                      $153 $158,273,878.71$92,888,60477.53%61.98%
                      $131 $134,044,608.14$78,668,80379.94%79.94%
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                        Posted: January 10, 2007, 1:16 pm - IP Logged

                        The MM jackpot has been won.  The value of the prize is reset to $7.0M cash, $12.0M annuity.    First draws average $15.1, although the drawing beginning the last run was the lowest recorded since the matrix change.

                        If an average number of tickets sell on this round, the distribution probability for various numbers of winners is as follows:

                         

                        091.76%
                        17.89%
                        20.34%
                        30.01%

                         

                        The long term jackpot evolution model, which ignores minimums predicts the following:

                         

                        Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                        $599,077,904.49$349,462,11144.66%0.19%
                        $521,860,821.00$304,418,81249.20%0.43%
                        $453,919,126.24$264,786,15753.57%0.87%
                        $394,138,651.80$229,914,21457.75%1.63%
                        $315 $341,539,064.22$199,231,12161.68%2.83%
                        $262 $295,257,788.60$172,233,71065.37%4.58%
                        $247 $254,535,863.36$148,479,25468.79%7.01%
                        $217 $218,705,494.11$127,578,20571.96%10.20%
                        $180 $187,179,102.53$109,187,81074.86%14.17%
                        $153 $159,439,690.79$93,006,48677.51%18.93%
                        $131 $135,032,363.28$78,768,87979.92%24.42%
                        $111 $113,556,866.93$66,241,50682.10%30.56%
                        $94 $94,661,027.42$55,218,93384.07%37.22%
                        $82 $78,034,973.92$45,520,40185.84%44.28%
                        $68 $63,406,057.63$36,986,86787.43%51.58%
                        $56 $50,534,380.52$29,478,38988.85%59.00%
                        $46 $39,208,861.38$22,871,83690.12%66.41%
                        $34 $29,243,774.27$17,058,86891.25%73.69%
                        $25 $20,475,702.79$11,944,16092.26%80.75%
                        $16 $12,760,860.31$7,443,83593.16%87.53%
                        $12 $5,972,731.97$3,484,09493.96%93.96%

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                          Posted: January 12, 2007, 11:05 pm - IP Logged

                          Prob988, if MM jackpot will roll on this run, it'll be 16 million.

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                            Posted: January 13, 2007, 10:17 am - IP Logged

                            MM has rolled over.  The cash jackpot is $9.3M.  The advertised annuity value is $16M.  Second round draws sell on average $14.9M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

                             

                            091.89%
                            17.77%
                            20.33%
                            30.01%

                             

                            The long term projection program, which ignores minimums and does not accurately predict prizes (although it does predict sales in making the calculations) suggests the following:

                             

                            Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                            $601,155,066.38$349,421,38244.67%0.20%
                            $523,693,576.26$304,396,89149.21%0.46%
                            $455,533,290.25$264,778,72553.59%0.93%
                            $395,557,364.39$229,917,71857.75%1.74%
                            $315 $342,783,059.97$199,242,65461.69%3.01%
                            $262 $296,345,640.85$172,250,90465.37%4.88%
                            $247 $255,484,204.23$148,500,19468.80%7.46%
                            $217 $219,529,212.89$127,601,35571.96%10.85%
                            $180 $187,891,524.42$109,211,94974.86%15.07%
                            $153 $160,052,737.80$93,030,65477.51%20.14%
                            $131 $135,556,699.12$78,792,33179.91%25.98%
                            $111 $114,002,027.25$66,263,67882.09%32.51%
                            $94 $95,035,536.97$55,239,40684.06%39.61%
                            $82 $78,346,451.85$45,538,87585.83%47.11%
                            $68 $63,661,312.00$37,003,13887.42%54.89%
                            $56 $50,739,493.30$29,492,33088.84%62.79%
                            $46 $39,369,264.60$22,883,38590.12%70.67%
                            $34 $29,364,318.41$17,068,01091.25%78.42%
                            $25 $20,560,718.16$11,950,91792.26%85.94%
                            $16 $12,814,211.99$7,448,26193.15%93.15%
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                              Posted: January 17, 2007, 8:12 am - IP Logged

                              MM has rolled over.  The cash jackpot is $14.5M; the advertised annuity value is $25M.  Third round draws sell on average 15.9M tickets.

                              If this is how many tickets sell, the randomized probability for numbers of winners is as follows:

                               

                              091.36%
                              18.26%
                              20.37%
                              30.01%

                               

                              The long term modelling function, which does not account for early minimums predicts the following behavior for jackpot evolution:

                               

                              Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                              $602,519,082.85$349,461,06844.66%0.22%
                              $524,856,700.44$304,416,88649.20%0.49%
                              $456,523,463.03$264,783,60953.57%1.00%
                              $396,398,712.94$229,911,25457.75%1.87%
                              $315 $343,496,410.77$199,227,91861.68%3.23%
                              $262 $296,948,964.49$172,230,39965.37%5.24%
                              $247 $255,993,001.02$148,475,94168.79%8.01%
                              $217 $219,956,846.98$127,574,97171.96%11.65%
                              $180 $188,249,513.37$109,184,71874.86%16.19%
                              $153 $160,351,003.33$93,003,58277.51%21.63%
                              $130 $135,803,784.32$78,766,19579.92%27.90%
                              $109 $114,205,284.61$66,239,06582.10%34.92%
                              $92 $95,201,291.13$55,216,74984.07%42.53%
                              $81 $78,480,140.47$45,518,48185.84%50.59%
                              $67 $63,767,607.54$36,985,21287.43%58.94%
                              $55 $50,822,408.41$29,476,99788.85%67.41%
                              $45 $39,432,243.22$22,870,70190.12%75.87%
                              $34 $29,410,314.47$17,057,98291.25%84.19%
                              $25 $20,592,263.64$11,943,51392.26%92.26%
                                 
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