Welcome Guest
Log In | Register )
You last visited December 4, 2016, 9:25 pm
All times shown are
Eastern Time (GMT-5:00)

Probability of a MegaMillions rollover.

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

Page 16 of 24
52
PrintE-mailLink
Avatar
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
Offline
Posted: June 28, 2006, 5:37 am - IP Logged

MM has been won.  The jackpot is reset at $6.8M cash, 12M annuity.

The average 1st draw sells 15.9M tickets.

The winner probability distribution is, if the draw sells an average number of tickets, as follows:

091.35%
18.27%
20.37%
30.01%

Here is the long term probability:

 

 $470,784,121.87$265,469,93554.34%0.86%
(Average Annuity, M)$410,344,090.99$231,388,47458.32%1.59%
$315 $356,919,038.34$201,262,68062.09%2.73%
$262 $309,694,769.77$174,633,44065.62%4.39%
$247 $267,951,590.65$151,094,92568.91%6.69%
$217 $231,053,337.79$130,288,41071.95%9.71%
$186 $198,437,684.33$111,896,80574.76%13.50%
$158 $169,607,569.95$95,639,82477.32%18.06%
$135 $144,123,625.68$81,269,71179.67%23.35%
$115 $121,597,477.95$68,567,46781.80%29.31%
$96 $101,685,829.81$57,339,51083.73%35.84%
$84 $84,085,229.10$47,414,72685.47%42.80%
$71 $68,527,443.87$38,641,86487.04%50.08%
$59 $54,775,374.54$30,887,22588.46%57.53%
$48 $42,619,440.51$24,032,62989.72%65.04%
$36 $31,874,386.17$17,973,61290.86%72.49%
$26 $22,376,457.65$12,617,83691.88%79.79%
$17 $13,980,907.14$7,883,67892.78%86.84%
$12 $6,559,787.05$3,698,99193.59%93.59%


    United States
    Member #16612
    June 2, 2005
    3493 Posts
    Offline
    Posted: June 30, 2006, 10:28 pm - IP Logged

    Congratulations to Ohio on winning MM in the last draw. Prob988, I think MM sales are slow this round because of CA SLP currently at 98 million. I'm happy that NY Lotto jackpot won.

      Avatar
      New Jersey
      United States
      Member #21206
      September 4, 2005
      949 Posts
      Offline
      Posted: July 1, 2006, 8:07 am - IP Logged

      MM has rolled over.  The cash jackpot is 7.7 million dollars and the advertised annuity jackpot is $14M.  This is the smallest rise in the MM jackpot since the matrix change.

      Second round MM sales average of around 15.8M in sales.  If the MM sells an average number of tickets for a second round draw, the probability of various numbers of winners will be:

       

       

      091.41%
      18.21%
      20.37%
      30.01%

       

      Lottoreport has not posted the sales figures for this last drawing, although clearly they are unusually low.  I will update the long range projection when these figures are available.

      I note that usually the long range predictions do not match the early drawings, underestimating what is occurring because of the minimums.  That hasn't happened this time.  The previous long range jackpot prediction was very close to predicting the jackpot. 


        United States
        Member #16612
        June 2, 2005
        3493 Posts
        Offline
        Posted: July 1, 2006, 10:37 am - IP Logged

        Prob988, I think MM set a new roll 1 low based on the current matrix. I think the cause of MM sales starting to drop is because they're waiting for CA SLP Jackpot to hit. CA SLP had 22 straight rolls without a jackpot winner. Their current jackpot is 98 million.

          Avatar
          New Jersey
          United States
          Member #21206
          September 4, 2005
          949 Posts
          Offline
          Posted: July 1, 2006, 6:09 pm - IP Logged

          The sales figures at lottoreport are now available.  Surprisingly the sales for the last jackpot are not the lowest seen since the institution of the new matrix, although they are lower than average.  In fact the last first draw sold almost 700,000 fewer tickets than the first draw from yesterday.  The small growth in the jackpot may be a function of the MM consideration of the possible effect of the California jackpot.  Remember that even the MM's prediction of a jackpot amount is just that, a prediction.

          Surprisingly enough, in this recent drawing, California sales for MM were still the second highest of all states, behind New York.  It may be that people drawn to the "big one" play a few MM tickets "just for the hell of it."

          Here is the long term prediction data from my modeling program which models the growth of jackpots and the probability of rollovers as an exponential function:

           

           $470,877,352.58$265,522,50754.25%0.92%
          Average Annuity, M$410,284,257.51$231,354,73458.26%1.70%
          $315 $356,746,219.42$201,165,22962.04%2.92%
          $262 $309,441,794.38$174,490,79065.59%4.70%
          $247 $267,645,181.97$150,922,14468.89%7.17%
          $217 $230,715,089.10$130,097,67571.94%10.41%
          $186 $198,084,890.62$111,697,86974.75%14.47%
          $158 $169,253,935.42$95,440,41477.33%19.36%
          $135 $143,779,864.88$81,075,86879.68%25.03%
          $115 $121,271,825.69$68,383,83581.82%31.41%
          $96 $101,384,472.87$57,169,57883.75%38.39%
          $84 $83,812,671.14$47,261,03485.50%45.84%
          $71 $68,286,813.12$38,506,17587.07%53.62%
          $59 $54,568,682.75$30,770,67488.49%61.58%
          $48 $42,447,800.24$23,935,84389.76%69.59%
          $36 $31,738,192.67$17,896,81490.89%77.54%
          $26 $22,275,540.57$12,560,93091.91%85.31%
          $17 $13,914,656.74$7,846,32092.82%92.82%

           

           

            Avatar
            Morrison, IL
            United States
            Member #4657
            May 13, 2004
            1884 Posts
            Offline
            Posted: July 1, 2006, 6:50 pm - IP Logged

            I think, like Powerball, Mega Millions sees more ticket sales for a weekend drawing than for a weekday drawing for any given jackpot level. That may explain why sales were higher for this reset jackpot than the last.


              United States
              Member #16612
              June 2, 2005
              3493 Posts
              Offline
              Posted: July 2, 2006, 1:51 am - IP Logged

              Prob988, if CA SLP jackpot gets hit tonight, we'll see how MM sales will fare after the win.


                United States
                Member #16612
                June 2, 2005
                3493 Posts
                Offline
                Posted: July 5, 2006, 11:09 am - IP Logged

                Prob988, do me a favor and quote my message when you're online. MM Jackpot set a new roll 2 low under the current matrix. The MM Jackpot for 7/7 has rolled to 22 million.


                  United States
                  Member #16612
                  June 2, 2005
                  3493 Posts
                  Offline
                  Posted: July 8, 2006, 11:56 am - IP Logged

                  MM set a new roll 3 low of 29 million since it rolled.

                    Avatar
                    New Jersey
                    United States
                    Member #21206
                    September 4, 2005
                    949 Posts
                    Offline
                    Posted: July 27, 2006, 8:55 am - IP Logged

                    Powerball has rolled over.  The cash value is 70.7M, the annuity jackpot is $155M.    Although the upcoming roll is a 12th draw, the jackpot size is now equivalent to an average 13th draw.  The average sales for a thirteen draw are $28.9M.

                    If this is the number of tickets that sell, the randomized probability for various numbers of winner is:

                    082.04%
                    116.24%
                    21.61%
                    30.11%
                    40.01%

                    A long term mixed linear/exponential model suggests that the jackpot may evolve in this way with the last column representing the probability of all the jackpots including that one rolling over:

                     

                    $353 $460,754,854.66$210,163,66637.37%3.22%
                    $300 $365,255,799.82$166,603,77448.65%8.62%
                    $245 $295,359,042.69$134,721,83459.02%17.72%
                    $208 $244,200,875.05$111,387,10967.98%30.03%
                    $193 $206,757,677.05$94,308,17975.39%44.17%
                    $173 $179,352,608.79$81,807,93281.32%58.58%
                    $152 $159,294,552.69$72,658,87084.58%72.04%
                      Avatar
                      New Jersey
                      United States
                      Member #21206
                      September 4, 2005
                      949 Posts
                      Offline
                      Posted: July 28, 2006, 10:41 am - IP Logged

                      The most recent MM drawing rolled.  The cash value is $13.0M; the advertised annuity is $23M.

                      If the current drawing sells an average amount for third drawings, the sales will be 16.0M and the randomized probability of various numbers of winners will be:

                       

                       

                      091.03%
                      18.55%
                      20.40%
                      30.01%

                       

                      The long term jackpot evolution model based on average data and curve fitting suggests the following:

                       

                      $540,013,762.28$304,507,76049.70%0.49%
                      $470,741,031.42$265,445,63753.97%0.99%
                      (Average Annuity, M)$409,630,477.18$230,986,07558.04%1.84%
                      $315 $355,720,377.31$200,586,76861.88%3.17%
                      $262 $308,162,326.10$173,769,31265.48%5.12%
                      $247 $266,207,882.68$150,111,66768.83%7.82%
                      $217 $229,196,792.49$129,241,52571.93%11.36%
                      $186 $196,546,596.57$110,830,44274.78%15.79%
                      $158 $167,743,465.18$94,588,67677.38%21.12%
                      $135 $142,334,111.44$80,260,62479.75%27.29%
                      $115 $119,918,657.77$67,620,79981.91%34.22%
                      $96 $100,144,342.82$56,470,28283.86%41.78%
                      $84 $82,699,969.96$46,633,59485.62%49.82%
                      $71 $67,311,009.82$37,955,93187.20%58.19%
                      $57 $53,735,279.93$30,300,72788.62%66.73%
                      $45 $41,759,133.37$23,547,51189.89%75.30%
                      $35 $31,194,096.52$17,590,00491.02%83.78%
                      $26 $21,873,903.00$12,334,45192.04%92.04%
                        Avatar
                        New Jersey
                        United States
                        Member #21206
                        September 4, 2005
                        949 Posts
                        Offline
                        Posted: July 29, 2006, 6:51 pm - IP Logged

                        The MM has rolled.  The cash jackpot is now $17.6M.  The advertised annuity is $31M.  On average, fourth drawings in MM since the matrix change average $17.6 in sales.  If this is how many tickets sell, the randomized probability of various numbers of winners is as follows:

                         

                        090.61%
                        18.93%
                        20.44%
                        30.01%

                         

                        The long term exponential function for modelled jackpot evolution looks like this:

                         

                         

                        $540,056,535.81$304,531,88049.68%0.54%
                        $470,742,277.20$265,446,34053.95%1.08%
                        (Average Annuity, M)$409,600,656.06$230,969,25958.03%2.00%
                        $315 $355,668,061.09$200,557,26861.87%3.44%
                        $262 $308,094,497.52$173,731,06465.48%5.56%
                        $247 $266,130,190.92$150,067,85868.83%8.50%
                        $217 $229,113,770.55$129,194,71071.93%12.35%
                        $186 $196,461,845.88$110,782,65274.78%17.17%
                        $158 $167,659,812.25$94,541,50577.38%22.96%
                        $135 $142,253,740.50$80,215,30479.76%29.67%
                        $115 $119,843,222.88$67,578,26281.91%37.20%
                        $96 $100,075,062.55$56,431,21683.86%45.41%
                        $84 $82,637,707.03$46,598,48585.62%54.15%
                        $71 $67,256,338.09$37,925,10287.20%63.24%
                        $57 $53,688,540.49$30,274,37188.62%72.52%
                        $45 $41,720,481.42$23,525,71689.89%81.83%
                        $35 $31,163,540.50$17,572,77491.03%91.03%
                          Avatar
                          New Jersey
                          United States
                          Member #21206
                          September 4, 2005
                          949 Posts
                          Offline
                          Posted: August 3, 2006, 7:43 am - IP Logged

                          The MM jackpot has been won and reset to the $6.8M cash value and $12M annuity value.  First round drawings in MM typically sell 15.5M tickets.  If this is how many tickets are sold, then the distribution of winners will be as follows:

                           

                          091.58%
                          18.06%
                          20.35%
                          30.01%

                           

                          The long term probability looks like this:

                           

                          (Average Annuity, M)$409,469,345.57$230,895,21457.99%1.60%
                          $315 $355,472,288.41$200,446,87461.85%2.77%
                          $262 $307,855,282.82$173,596,17365.46%4.47%
                          $247 $265,864,490.35$149,918,03268.82%6.84%
                          $217 $228,835,142.73$129,037,59471.93%9.93%
                          $186 $196,181,017.76$110,624,29674.78%13.81%
                          $158 $167,385,158.64$94,386,63177.39%18.47%
                          $135 $141,991,689.86$80,067,53679.77%23.86%
                          $115 $119,598,600.16$67,440,32281.93%29.91%
                          $96 $99,851,378.12$56,305,08383.88%36.51%
                          $84 $82,437,399.80$46,485,53485.64%43.52%
                          $71 $67,080,979.53$37,826,21987.23%50.82%
                          $57 $53,539,005.43$30,190,05088.65%58.26%
                          $45 $41,597,090.63$23,456,13789.92%65.72%
                          $35 $31,066,179.24$17,517,87391.05%73.09%
                          $26 $21,779,553.40$12,281,24892.07%80.27%
                          $17 $13,590,193.87$7,663,35992.97%87.18%
                          $12 $6,368,452.55$3,591,10093.78%93.78%

                            United States
                            Member #16612
                            June 2, 2005
                            3493 Posts
                            Offline
                            Posted: August 5, 2006, 1:12 pm - IP Logged

                            MM has rolled to 15 million Prob988. Lately, we've seen a run of 6 straight jackpot winners of 50 million or less in a row and 9 jackpot winners of 100 million or less this year. So what's the probability update?

                              Avatar
                              Morrison, IL
                              United States
                              Member #4657
                              May 13, 2004
                              1884 Posts
                              Offline
                              Posted: August 5, 2006, 4:16 pm - IP Logged

                              Actually, the run is five consecutive jackpot winners under $50 million and seven jackpot winners under $100 million this year. Nine is the total number of MM jackpots awarded (and jackpot winners, since they were all won by one ticket each time) this year.

                                 
                                Page 16 of 24