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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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Posted: March 15, 2006, 7:07 am - IP Logged

The Megamillions has rolled over.  The cash value is $32.8M, the annuity value is $56.

For whatever reason, the jackpot is rising faster than it does on average, and at this point it is probably wiser to treat the jackpot as if it were a sixth draw coming up rather than a fifth.  I will do this as a temporary measure and see what develops.

Sixth draws have average sales of $19.4M.  If this is the amount of tickets sold, the distribution probability of winners is given here:

 

089.55%
19.89%
20.55%
30.02%

The long term probability given by the modeling formula is as follows:

 $500,744,766.92$298,170,74850.75%0.73%
$437,104,838.17$260,276,06354.92%1.44%
Average Annuity$380,872,127.19$226,792,03958.89%2.63%
$315 $331,184,488.54$197,205,30962.63%4.46%
$262 $287,280,124.13$171,062,25666.14%7.13%
$247 $248,485,903.53$147,962,06169.40%10.78%
$201 $214,207,043.74$127,550,55872.41%15.53%
$169 $183,917,990.12$109,514,80375.19%21.44%
$147 $157,154,358.67$93,578,27777.72%28.52%
$135 $133,505,816.30$79,496,64580.04%36.69%
$113 $112,609,789.63$67,054,01182.14%45.84%
$92 $94,145,906.17$56,059,60884.04%55.81%
$79 $77,831,082.40$46,344,87285.76%66.41%
$67 $63,415,183.64$37,760,85987.31%77.44%
$56 $50,677,189.05$30,175,96388.70%88.70%

Again, this is treating the matter as if it were a sixth, and not a fifth draw.

 

 

 

 


    United States
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    Posted: March 17, 2006, 1:51 pm - IP Logged

    Interest rates were the reason why MM jackpots are hitting new records at this point. In addition, people are buying more MM tickets than expected. I wish it continues to roll and set records. The lower the interest rates and more jackpot winners it produced, the fewer the interest in the game as well as lower jackpots in the future.

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      New Jersey
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      Posted: March 18, 2006, 4:20 am - IP Logged

      The Megamillions has rolled over.  The cash value is $40.0M, the annuity value is $68.

      As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a sixth drawing than a fifth drawing.  I will therefore treat this upcoming drawing as a 7th drawing statistically rather than as if it were a 6th - an ad hoc approach.

      Seventh draws have average sales of $21.1M  If this is the amount of tickets sold, the distribution probability of winners is given here:

      088.68%
      110.65%
      20.64%
      30.03%

      The long term probability looks like this, again treating this as a 7th draw:

       

       $572,451,665.43$340,868,94646.58%0.39%
      $500,749,762.21$298,173,72250.88%0.83%
      $437,351,475.35$260,422,92455.03%1.63%
      (Average Annuity, M)$381,295,184.00$227,043,95058.97%2.96%
      $315 $331,730,630.21$197,530,51262.69%5.02%
      $262 $287,906,022.23$171,434,95066.17%8.01%
      $247 $249,156,631.45$148,361,44969.41%12.11%
      $201 $214,894,709.76$127,960,03272.41%17.44%
      $169 $184,600,574.72$109,921,25175.17%24.09%
      $147 $157,814,726.95$93,971,49777.69%32.05%
      $135 $134,130,880.58$79,868,84380.00%41.25%
      $113 $113,189,800.65$67,399,38182.09%51.56%
      $92 $94,673,854.31$56,373,97783.99%62.81%
      $79 $78,302,192.96$46,625,39785.70%74.78%
      $67 $63,826,492.38$38,005,77587.25%87.25%

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        Canada
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        Posted: March 19, 2006, 8:50 pm - IP Logged

        Prob988,

        I have a probability question for you. What is the probability that the Mega Millions jackpot reaches at least $200 million in this run. I have wagered with a friend that it will reach $200 million. I thought I had made the better bet but now that I look at your charts, I am not so sure.

        Thanks.

        Lotto Groups - the best way to win

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          New Jersey
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          Posted: March 19, 2006, 9:04 pm - IP Logged

          Prob988,

          I have a probability question for you. What is the probability that the Mega Millions jackpot reaches at least $200 million in this run. I have wagered with a friend that it will reach $200 million. I thought I had made the better bet but now that I look at your charts, I am not so sure.

          Thanks.

          My model indicates that the probability of reaching that jackpot is about 24%.

          The model is not perfect however.  To my mind it represents an approximation, a good approximation, but an approximation nonetheless.

          It would seem however that the odds are with your friend and not with you. 

           

           

            LottoGroups's avatar - peace

            Canada
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            Posted: March 19, 2006, 9:09 pm - IP Logged

            Prob988,

            Thanks for the quick response. I made the bet last Friday, before the draw. It was even a worse bet then.

            Lotto Groups - the best way to win

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              New Jersey
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              Posted: March 20, 2006, 8:50 pm - IP Logged

              Prob988,

              Thanks for the quick response. I made the bet last Friday, before the draw. It was even a worse bet then.

              Well then, you're still in the game.

              The odds are against you, but you still may not lose. 

               

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                New Jersey
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                Posted: March 22, 2006, 6:29 am - IP Logged

                The Megamillions has rolled over.  The cash value is $48.2M, the annuity value is $84.  The cash value is now higher than Powerball's

                As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 7th drawing than a sixth drawing.  I will therefore treat this upcoming drawing as a 8th drawing statistically rather than as if it were a 6th - an ad hoc approach.

                Seventh draws have average sales of $22.3M  If this is the amount of tickets sold, the distribution probability of winners is given here:

                 

                088.08%
                111.18%
                20.71%
                30.03%

                Longterm looks like this:

                 

                 $572,430,495.32$340,856,34046.62%0.44%
                $500,827,940.55$298,220,27450.92%0.95%20
                $437,503,075.04$260,513,19555.06%1.87%19
                (Average Annuity, M)$381,498,947.73$227,165,28358.99%3.39%18
                $315 $331,969,236.93$197,672,59162.70%5.75%17
                $262 $288,165,460.85$171,589,43466.18%9.17%16
                $247 $249,425,666.74$148,521,64769.41%13.86%15
                $201 $215,164,427.59$128,120,63672.40%19.97%14
                $169 $184,863,995.32$110,078,10675.16%27.58%13
                $147 $158,066,476.64$94,121,40277.68%36.69%12
                $135 $134,366,913.51$80,009,38979.98%47.23%11
                $113 $113,407,163.50$67,528,81182.07%59.05%10
                $92 $94,870,487.61$56,491,06383.97%71.95%9
                $79 $78,476,763.79$46,729,34685.68%85.68%8

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                  New Jersey
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                  Posted: March 22, 2006, 8:39 pm - IP Logged

                  The long term probability function does not match the results of the current drawing very well, although it does mimic the average results very well indeed, if you look at it graphically.  (I can't post the graph here.)

                  Just for reference, if I substitute the sales figure of this drawing into the function generating program, I get another long term probability table that looks like this:

                   

                   $496,790,802.36$295,816,34154.52%1.11%20
                  $439,863,737.14$261,918,86257.96%2.03%19
                  (Average Annuity, M)$388,683,407.44$231,443,30261.24%3.51%18
                  $315 $342,669,685.54$204,044,22264.35%5.72%17
                  $262 $301,301,007.08$179,411,05467.28%8.90%16
                  $247 $264,108,459.13$157,264,58270.02%13.22%15
                  $201 $230,670,465.12$137,353,77772.59%18.88%14
                  $169 $200,608,006.24$119,452,94974.97%26.02%13
                  $147 $173,580,325.27$103,359,19477.19%34.70%12
                  $135 $149,281,064.15$88,890,08879.23%44.96%11
                  $113 $127,434,791.37$75,881,62681.11%56.74%10
                  $92 $107,793,879.99$64,186,35682.85%69.95%9
                  $79 $90,135,700.77$53,671,71384.44%84.44%8

                  I will continue to post generally, the long term average data, which, while it isn't doing well on this set of drawings, may give better results over all sets of drawings.  (In any case, the new data will effect the averages themselves, especially if sales remain high for many sets of drawings.)  This new data is rather noisy, but the point is just to give an idea, not an exact outcome.

                   

                   

                   

                   

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                    New Jersey
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                    Posted: March 25, 2006, 4:37 am - IP Logged

                    The Megamillions has rolled over.  The cash value is $56.3M, the annuity value is $96.  The cash value is now higher than Powerball's.    The previous jackpot reached a cash value of $48.3M

                    As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 8th drawing than a 7th drawing.  I will therefore treat this upcoming drawing as a 9th drawing statistically rather than as if it were a 8th - an ad hoc approach.

                    Seventh draws have average sales of $28.6M  If this is the amount of tickets sold, the distribution probability of winners is given here:

                    086.10%
                    112.89%
                    20.96%
                    30.05%

                    The average data long term function is now approximating the actual behavior of the MM if we assume a drawing is skipped.  Under these conditions it looks like this:

                     $572,490,464.37$340,892,04946.65%0.52%
                    $500,933,623.26$298,283,20350.94%1.11%
                    $437,641,252.49$260,595,47355.07%2.18%
                    (Average Annuity, M)$381,658,845.56$227,260,49459.00%3.96%
                    $315 $332,142,136.87$197,775,54562.70%6.71%
                    $262 $288,344,369.43$171,695,96566.18%10.70%
                    $247 $249,605,033.08$148,628,45269.41%16.16%
                    $201 $215,339,903.41$128,225,12472.40%23.28%
                    $169 $185,032,231.10$110,178,28375.15%32.16%
                    $147 $158,224,948.90$94,215,76577.67%42.80%
                    $135 $134,513,778.62$80,096,84179.97%55.10%
                    $113 $113,541,134.26$67,608,58482.06%68.90%
                    $92 $94,990,729.25$56,562,66283.96%83.96%

                     

                    Note that the averaged function was close on the last draw (two posts ago) and it looks fairly accurate for this draw. 

                     

                     

                     


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                      Posted: March 27, 2006, 2:02 pm - IP Logged

                      I hope it continues to roll until someone hits a MM Jackpot around 300+ million. These probabilities are great in terms of the formula Prob988.

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                        Posted: March 27, 2006, 8:55 pm - IP Logged

                        The annuity value in my projection program needed updating.

                        Here is the corrected form:

                         

                         

                         $581,272,410.78$340,892,04946.65%0.52%
                        $508,617,894.90$298,283,20350.94%1.11%
                        $444,354,625.49$260,595,47355.07%2.18%
                        (Average Annuity, M)$387,513,454.05$227,260,49459.00%3.96%
                        $315 $337,237,164.00$197,775,54562.70%6.71%
                        $262 $292,767,543.19$171,695,96566.18%10.70%
                        $247 $253,433,949.30$148,628,45269.41%16.16%
                        $201 $218,643,195.97$128,225,12472.40%23.28%
                        $169 $187,870,607.00$110,178,28375.15%32.16%
                        $147 $160,652,103.78$94,215,76577.67%42.80%
                        $135 $136,577,206.52$80,096,84179.97%55.10%
                        $113 $115,282,843.89$67,608,58482.06%68.90%
                        $92 $96,447,877.53$56,562,66283.96%83.96%

                         

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                          Posted: March 29, 2006, 6:38 am - IP Logged

                          The Megamillions has rolled over.  The cash value is $67.7M, the annuity value is $117.  The cash value is now higher than Powerball's.    The previous jackpot reached a cash value of $57.1

                          As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 9th drawing than a 8th drawing.  I will therefore treat this upcoming drawing as a 10th drawing statistically rather than as if it were a 9th - an ad hoc approach.

                          10th drawing sales average $33.5M.  If this many tickets were sold the probability of various numbers of winners would be as follows:

                           

                          082.64%
                          115.76%
                          21.50%
                          30.10%

                          Long term looks like this:

                           $589,474,960.73$341,089,35846.68%0.62%
                          $515,896,124.33$298,514,25350.96%1.32%
                          $450,800,254.35$260,847,66955.08%2.59%
                          (Average Annuity, M)$393,209,342.40$227,523,69659.00%4.70%
                          $315 $342,258,135.51$198,041,67362.70%7.97%
                          $262 $297,181,136.46$171,958,65866.17%12.71%
                          $247 $257,301,102.83$148,882,77569.39%19.22%
                          $201 $222,018,872.10$128,467,33072.38%27.69%
                          $169 $190,804,359.65$110,405,60075.13%38.26%
                          $147 $163,188,594.80$94,426,22177.65%50.92%
                          $135 $138,756,674.89$80,289,11979.94%65.58%
                          $113 $117,141,531.75$67,781,89582.03%82.03%

                          The skipped draw long term probability function is fitting quite well in this region.

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                            Posted: April 1, 2006, 7:30 am - IP Logged

                            The Megamillions has rolled over.  The cash value is $78.9, the annuity value is $138.  The cash value is now higher than Powerball's.    The previous jackpot reached a cash value of $68.1M

                            As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 10th drawing than a 9th drawing.  I will therefore treat this upcoming drawing as a 11th drawing statistically rather than as if it were a 10th - an ad hoc approach, that is nonetheless giving reasonable predictions of jackpot evolution.

                            11th drawing sales average $37.5M.  If this many tickets were sold the probability of various numbers of winners would be as follows:

                            080.78%
                            117.24%
                            21.84%
                            30.13%
                            40.01%

                             The long term probabilities are given by my modelling program are here: 

                             $596,365,232.72$340,965,34046.68%0.75%
                            $521,898,992.62$298,390,07650.96%1.61%20
                            $456,022,105.18$260,725,68255.08%3.16%19
                            (Average Annuity, M)$397,743,826.43$227,405,70959.01%5.74%18
                            $315 $346,187,690.32$197,929,04962.71%9.73%17
                            $262 $300,578,327.33$171,852,39166.18%15.51%16
                            $247 $260,229,803.38$148,783,56169.40%23.44%15
                            $201 $224,535,303.87$128,375,61972.39%33.77%14
                            $169 $192,958,007.60$110,321,64375.14%46.65%13
                            $147 $165,023,013.30$94,350,11477.66%62.09%12
                            $135 $140,310,197.50$80,220,83079.96%79.96%11

                            The model is in a region of jackpot behavior where agreement is reasonable with actual events.

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                              Canada
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                              Posted: April 1, 2006, 11:30 am - IP Logged

                              Prob988,

                              I have a probability question for you. What is the probability that the Mega Millions jackpot reaches at least $200 million in this run. I have wagered with a friend that it will reach $200 million. I thought I had made the better bet but now that I look at your charts, I am not so sure.

                              Thanks.

                              My model indicates that the probability of reaching that jackpot is about 24%.

                              The model is not perfect however.  To my mind it represents an approximation, a good approximation, but an approximation nonetheless.

                              It would seem however that the odds are with your friend and not with you. 

                               

                               

                              Prob988,

                              I think I now have a better than 50% chance of winning the bet. I decided not to wait until the $200 million level. One of my groups bought tickets for yesterday's draw and we will buy again for the next draw.

                              Lotto Groups - the best way to win

                                 
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