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Probability of a MegaMillions rollover.

Topic closed. 352 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: March 14, 2007, 9:20 am - IP Logged

The MM jackpot has rolled over.  The cash prize is $16.7M; the advertised annuity is $28M.  The average sales on a third drawing is 15.89M.  Sales as this level would approximately produce the following randomized probability for numbers of winners:

 

091.35%
18.26%
20.37%
30.01%

 

As is often the case after a big jackpot has been run, the first drawing of the next run sold unusually high amounts of tickets.    For this reason, I will be treating the system as if one extra rollover had taken place and this is the fourth drawing.  Thus for the long term program - and I'm not sure that the recent behavior corresponds all that well to my exponential model - suggests the following for long term rollovers:

 

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
$736,586,531.75$440,531,35930.87%0.05%
$626,762,787.99$374,848,91636.53%0.15%
$532,677,501.39$318,579,19442.20%0.40%
$452,075,248.62$270,373,29047.75%0.96%
$315 $383,023,823.20$229,075,60553.09%2.00%
$262 $323,867,916.40$193,696,14758.13%3.77%
$247 $273,189,436.00$163,386,79662.83%6.48%
$217 $229,773,511.64$137,420,97267.16%10.32%
$180 $192,579,371.76$115,176,22071.10%15.36%
$153 $160,715,394.18$96,119,28574.66%21.61%
$130 $133,417,731.94$79,793,33477.86%28.94%
$109 $110,032,002.33$65,806,99780.70%37.17%
$92 $89,997,599.97$53,824,99383.22%46.06%
$81 $72,834,257.84$43,560,08985.44%55.35%
$67 $58,130,534.32$34,766,21287.39%64.79%
$55 $45,533,950.07$27,232,55589.09%74.14%
$45 $34,742,538.32$20,778,52090.58%83.22%
$34 $25,497,606.10$15,249,39091.87%91.87%

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    March 19, 2007
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    Posted: March 19, 2007, 9:47 pm - IP Logged

    One of those key questions is:

     What are the odds the Jackpot reached $390 million?

    The closest data is:

    1- The odds of 1.63% for a similar estimated jackpot ($394, see post from January 10 2007) as Overall Calculated Model Rollover Probability of the long term jackpot evolution model, which is significantly outphased with the observed (more precisely: official) evolution.

    2- the distribution probability for zero winners for each round, IF an average number of tickets sells on that round, which normally Prob988 gives before each round. Multiplying all of them would give the information I asked for IF an average number of tickets would have been sold on each round.

    This simple math will shed more light on the underlying question.

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      New Jersey
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      Posted: March 20, 2007, 11:43 am - IP Logged

      One of those key questions is:

       What are the odds the Jackpot reached $390 million?

      The closest data is:

      1- The odds of 1.63% for a similar estimated jackpot ($394, see post from January 10 2007) as Overall Calculated Model Rollover Probability of the long term jackpot evolution model, which is significantly outphased with the observed (more precisely: official) evolution.

      2- the distribution probability for zero winners for each round, IF an average number of tickets sells on that round, which normally Prob988 gives before each round. Multiplying all of them would give the information I asked for IF an average number of tickets would have been sold on each round.

      This simple math will shed more light on the underlying question.

      Based on actual sales during the run, the probability of a $390 jackpot was about 4.5%.   

      This figure includes all of the rollovers, but not the final drawing, since the final draw was won.

      When one says "reach $390M," of course, one assumes that the final drawing will have sales similar to those actually obtained, about $212M. 

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        New Jersey
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        Posted: March 21, 2007, 5:49 am - IP Logged

        The MM Jackpot has been won.  The cash value is $28.6M.    The advertised annuity is 48M.    The average 6th round jackpot sells 19.3M tickets.  If sales are average, the probability of various numbers of winners will be:

         

        089.61%
        19.83%
        20.54%
        30.02%

         

        The long term modelling program suggests the following:

         

        Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
        $739,158,032.14$440,414,99430.90%0.05%
        $629,028,264.35$374,796,00836.56%0.18%
        $534,667,892.37$318,572,95342.23%0.48%
        $453,818,908.68$270,400,43347.77%1.15%
        $315 $384,546,628.10$229,125,69953.10%2.40%
        $262 $325,193,391.52$193,761,06258.14%4.53%
        $247 $274,338,898.72$163,460,26062.84%7.78%
        $217 $230,766,221.21$137,498,20767.16%12.39%
        $180 $193,432,681.51$115,253,63971.10%18.45%
        $153 $161,444,902.33$96,194,25474.66%25.95%
        $130 $134,037,428.37$79,863,96877.85%34.75%
        $109 $110,554,409.30$65,872,00280.69%44.64%
        $92 $90,433,905.48$53,883,53583.21%55.33%
        $81 $73,194,440.94$43,611,68885.43%66.49%
        $67 $58,423,481.93$34,810,65887.38%77.83%
        $55 $45,767,565.06$27,269,84189.08%89.08%
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          Posted: March 24, 2007, 2:09 pm - IP Logged

          The MM has rolled over.    The cash prize is now $35.6M.  The advertised annuity is $60M.  Average sales for 6th round draws are 19.2M.  If this draw produces average sales, the probability of various numbers of winners will be as follows:

           

          089.61%
          19.83%
          20.54%
          30.02%

           

          The long term jackpot model program I use for long term evolution of jackpots suggests the following:

           

          Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
          $742,173,213.03$440,356,10630.92%0.06%
          $631,648,127.35$374,777,88936.58%0.20%
          $536,940,044.38$318,584,42642.24%0.54%
          $455,785,427.55$270,432,68747.79%1.29%
          $315 $386,244,670.03$229,171,83853.11%2.70%
          $316 $326,655,737.87$193,815,73858.15%5.08%
          $254 $275,594,447.16$163,519,37262.84%8.73%
          $217 $231,840,425.83$137,558,65367.16%13.90%
          $179 $194,347,946.58$115,313,11571.10%20.70%
          $131 $162,220,933.84$96,251,08774.65%29.11%
          $113 $134,691,547.46$79,916,98577.84%39.00%
          $109 $111,101,831.22$65,920,42080.68%50.10%
          $92 $90,887,987.56$53,926,87383.20%62.09%
          $81 $73,566,902.75$43,649,69685.42%74.63%
          $67 $58,724,600.42$34,843,26387.37%87.37%
          $51 $46,006,347.44$27,297,09989.07%100.00%
          $44 $35,108,175.76$20,830,85190.56%100.00%
          $34 $25,769,617.54$15,289,97391.85%100.00%
          $25 $17,767,479.91$10,542,03892.98%100.00%
          $16 $10,910,510.66$6,473,57093.95%100.00%
          $12 $5,034,827.24$2,987,33194.79%100.00%
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            New Jersey
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            Posted: March 29, 2007, 8:09 am - IP Logged

            The MM has rolled over.    The cash prize is now $43.4M.  The advertised annuity is $74M.  Average sales for 6th round draws are 21.2M.  If this draw produces average sales, the probability of various numbers of winners will be as follows:

             

            088.64%
            110.69%
            20.64%
            30.03%

             

            The long term probability model suggests the following:

             

            Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
            $750,791,285.67$440,328,94330.94%0.07%
            $639,023,541.25$374,778,67136.59%0.23%
            $543,243,835.00$318,605,16842.25%0.62%
            $461,165,126.35$270,467,11547.79%1.48%
            $315 $390,827,528.99$229,215,06453.12%3.09%
            $262 $330,551,512.43$193,863,99558.15%5.81%
            $247 $278,897,797.93$163,569,79062.84%9.99%
            $217 $234,632,991.23$137,609,07967.16%15.90%
            $180 $196,700,131.39$115,361,96971.09%23.68%
            $153 $164,193,452.55$96,297,24174.65%33.31%
            $130 $136,336,755.90$79,959,66577.84%44.62%
            $109 $112,464,875.55$65,959,13080.68%57.33%
            $92 $92,007,795.56$53,961,32983.19%71.06%
            $81 $74,477,039.05$43,679,77785.41%85.41%
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              Posted: March 31, 2007, 12:07 pm - IP Logged

              The MM jackpot has rolled.  The estimated cash jackpot is $51.5M.  The advertised annuity is $88M.

              The average 8th draw in a run produces $23.M  in sales.    (The Standard Deviation is 2.3M).

              If an average number of tickets are sold, the randomized probability of various numbers of winners will be as follows:

               

              087.75%
              111.47%
              20.75%
              30.03%

               

              Here is the long term program model:

               

              Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
              $752,400,386.12$440,325,22630.96%0.08%
              $640,445,859.49$374,806,38436.61%0.27%
              $544,497,290.79$318,654,66442.26%0.73%
              $462,266,334.06$270,530,86647.80%1.73%
              $315 $391,791,804.46$229,287,24953.12%3.61%
              $316 $331,392,904.58$193,940,16658.15%6.80%
              $186 $279,629,137.91$163,646,59862.84%11.69%
              $217 $235,265,953.39$137,684,05267.15%18.61%
              $179 $197,245,301.75$115,433,33071.09%27.71%
              $153 $164,660,401.29$96,363,75874.64%38.98%
              $130 $136,734,111.44$80,020,53177.83%52.22%
              $109 $112,800,398.17$66,013,86980.67%67.10%
              $92 $92,288,449.24$54,009,71783.18%83.18%
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                Posted: April 4, 2007, 2:47 am - IP Logged

                MM has rolled over.  The cash jackpot is $61.3M; the advertised annuity is $105M.  The average sales for a ninth draw is $25.6M.

                Every drawing on this run has produced above average sales though.

                Even so, average sales would produce a probability distribution of number of winners as follows:

                 

                086.43%
                112.61%
                20.92%
                30.04%

                 

                 

                The exponential model function, for what it's worth, predicts the following long range evolution of the jackpot:

                 

                Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                $754,269,673.18$440,349,81930.96%0.10%
                $642,065,550.66$374,843,98336.61%0.32%
                $545,898,310.09$318,700,63242.27%0.88%
                $463,475,864.71$270,581,62447.80%2.07%
                $315 $392,833,726.48$229,340,07153.12%4.34%
                $316 $332,288,183.67$193,993,00658.15%8.17%
                $186 $280,396,170.70$163,697,95562.83%14.05%
                $217 $235,920,873.51$137,732,85367.15%22.36%
                $179 $197,802,250.87$115,478,83871.08%33.30%
                $153 $165,131,768.97$96,405,49974.63%46.85%
                $130 $137,130,747.07$80,058,23677.82%62.77%
                $109 $113,131,798.10$66,047,42180.66%80.66%
                   
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