Welcome Guest
Log In | Register )
You last visited January 20, 2017, 8:51 am
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 18 of 24
52
PrintE-mailLink
Avatar
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
Offline
Posted: September 14, 2006, 2:07 am - IP Logged

MM has rolled over.    The cash value prize is estimated at $94.7; the advertised annuity value is $163M.

Because of slow sales early in the drawing, I will treat the up coming drawing as an 12th round drawing rather than as a 13th round drawing.

An eleventh round drawing sells on average sells 34.8M tickets.  If this is the number of tickets that sell, the randomized distribution of the probability of various numbers of winner is as follows:

 

078.90%
118.70%
22.22%
30.17%
40.01%

 

Here's the long term model jackpot evolution figures:

 

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
$603,956,395.39$350,887,55043.86%0.75%
$524,686,711.42$304,833,32348.53%1.70%
$455,158,487.38$264,438,70453.04%3.50%
$394,174,594.21$229,008,18457.34%6.60%
$315 $340,685,018.19$197,931,72561.40%11.51%
$262 $293,768,781.87$170,674,25565.19%18.74%
$247 $252,618,086.85$146,766,45968.71%28.75%
$217 $216,524,405.13$125,796,69471.95%41.85%
$186 $184,866,279.82$107,403,90674.92%58.16%
$158 $157,098,624.90$91,271,41077.63%77.63%

    United States
    Member #16612
    June 2, 2005
    3493 Posts
    Offline
    Posted: September 14, 2006, 11:08 am - IP Logged

    Prob988, PB also rolled. However, MM jackpot (annunity) is now higher than PB. I hope MM continues to roll.

      Avatar
      New Jersey
      United States
      Member #21206
      September 4, 2005
      949 Posts
      Offline
      Posted: September 16, 2006, 8:46 am - IP Logged

      The MM jackpot has been won and the jackpot has been reset to $7.0M cash and $12M as an advertised annuity.

      The average number of sales for a first round drawing is $14.3M.  If this is how many tickets sell this draw, the probability distribution for numbers of winners is as follows:

       

      092.18%
      17.51%
      20.31%
      30.01%

       

      The long term proability model function, which ignores minimums and reserves suggests the following behavior:

       

      Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
      $602,303,598.36$351,343,76643.79%0.19%
      $523,209,412.78$305,205,49148.47%0.42%
      $453,841,488.71$264,740,86852.99%0.88%
      $393,003,781.68$229,252,20657.29%1.65%
      $315 $339,647,325.57$198,127,60761.35%2.88%
      $262 $292,852,146.27$170,830,41965.15%4.70%
      $247 $251,811,399.46$146,889,98368.68%7.22%
      $217 $215,817,458.97$125,893,51871.92%10.51%
      $186 $184,249,715.87$107,479,00174.90%14.61%
      $158 $156,563,877.91$91,328,92977.61%19.51%
      $131 $132,282,584.77$77,164,84180.07%25.13%
      $111 $110,987,177.44$64,742,52082.29%31.39%
      $94 $92,310,479.69$53,847,78084.28%38.15%
      $82 $75,930,467.14$44,292,77386.07%45.26%
      $69 $61,564,715.00$35,912,75087.68%52.59%
      $56 $48,965,528.39$28,563,22589.10%59.98%
      $46 $37,915,671.64$22,117,47590.38%67.31%
      $35 $28,224,622.69$16,464,36391.51%74.48%
      $26 $19,725,288.10$11,506,41892.51%81.39%
      $17 $12,271,122.00$7,158,15593.40%87.98%
      $12 $5,733,599.38$3,344,60094.19%94.19%
        Avatar
        New Jersey
        United States
        Member #21206
        September 4, 2005
        949 Posts
        Offline
        Posted: September 20, 2006, 6:04 am - IP Logged

        The MM jackpot has been won and the jackpot has been reset to $7.0M cash and $12M as an advertised annuity.

        The average number of sales for a first round drawing is $14.3M.  If this is how many tickets sell this draw, the probability distribution for numbers of winners is as follows:

         

        092.18%
        17.51%
        20.31%
        30.01%

         

        The long term proability model function, which ignores minimums and reserves suggests the following behavior:

         

        Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
        $602,303,598.36$351,343,76643.79%0.19%
        $523,209,412.78$305,205,49148.47%0.42%
        $453,841,488.71$264,740,86852.99%0.88%
        $393,003,781.68$229,252,20657.29%1.65%
        $315 $339,647,325.57$198,127,60761.35%2.88%
        $262 $292,852,146.27$170,830,41965.15%4.70%
        $247 $251,811,399.46$146,889,98368.68%7.22%
        $217 $215,817,458.97$125,893,51871.92%10.51%
        $186 $184,249,715.87$107,479,00174.90%14.61%
        $158 $156,563,877.91$91,328,92977.61%19.51%
        $131 $132,282,584.77$77,164,84180.07%25.13%
        $111 $110,987,177.44$64,742,52082.29%31.39%
        $94 $92,310,479.69$53,847,78084.28%38.15%
        $82 $75,930,467.14$44,292,77386.07%45.26%
        $69 $61,564,715.00$35,912,75087.68%52.59%
        $56 $48,965,528.39$28,563,22589.10%59.98%
        $46 $37,915,671.64$22,117,47590.38%67.31%
        $35 $28,224,622.69$16,464,36391.51%74.48%
        $26 $19,725,288.10$11,506,41892.51%81.39%
        $17 $12,271,122.00$7,158,15593.40%87.98%
        $12 $5,733,599.38$3,344,60094.19%94.19%

        MM has been won on the first draw. 

        Since the last draw was also a first draw, the probabilities remain the same.

          Avatar
          Morrison, IL
          United States
          Member #4657
          May 13, 2004
          1884 Posts
          Offline
          Posted: September 20, 2006, 8:02 am - IP Logged

          All right; it's nice to see a PB or MM opening jackpot won. It conveys the message that the odds aren't insurmountable.

            dvdiva's avatar - 8ball

            United States
            Member #2338
            September 17, 2003
            2063 Posts
            Offline
            Posted: September 20, 2006, 9:40 am - IP Logged

            For MM it means another long string of pathetic low jackpots IMO. No wonder I don't play it.

              Avatar
              New Jersey
              United States
              Member #21206
              September 4, 2005
              949 Posts
              Offline
              Posted: September 20, 2006, 10:33 pm - IP Logged

              There have been 15 "first draws" since the matrix change.  Only one first drawing has been won, meaning that 93% of the time, the first jackpot has rolled over.

              This is consistent with the figures I routinely give here when first jackpots crop up, close to what I predict for the likelyhood that the next first jackpot will roll over.

              If no could ever win a first jackpot, no one would ever play it of course.  A single ticket playing in a $300 million jackpot has the same probability of winning as a single ticket in a $12 million dollar jackpot, although the expectation values are very different.

              I would expect that out of every hundred sequences beginning with a first draw, two would give give jackpots over $400 million annuity.

              The average run gives about 8 drawings.  The run that ended recently went beyond average. 


                United States
                Member #16612
                June 2, 2005
                3493 Posts
                Offline
                Posted: September 23, 2006, 3:24 am - IP Logged

                After two straight MM jackpot winners Prob988, MM jackpot for 9/26 has rolled to 15 million.

                  Avatar
                  New Jersey
                  United States
                  Member #21206
                  September 4, 2005
                  949 Posts
                  Offline
                  Posted: September 23, 2006, 12:25 pm - IP Logged

                  The MM jackpot has rolled.  The cash value is $8.8M.  The advertised annuity is $15.0M.  The average number of tickets sold for a second draw in a series is $14.0M.  If this is the number of tickets that sell, the probability of various numbers of winners is given as follows:

                   

                  092.33%
                  17.37%
                  20.29%
                  30.01%

                   

                  The long term jackpot evolution model, an exponential function generating model sales, predicts the following probabilities for this run:

                   

                  Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                  $598,727,859.65$351,253,67843.82%0.20%
                  $520,152,864.82$305,156,34748.50%0.45%
                  $451,232,662.79$264,723,16253.01%0.93%
                  $390,780,934.38$229,258,14857.31%1.75%
                  $315 $337,757,127.71$198,150,84861.37%3.06%
                  $262 $291,248,547.26$170,865,81465.16%4.99%
                  $247 $250,454,643.72$146,933,39168.68%7.66%
                  $217 $214,673,234.13$125,941,63171.93%11.15%
                  $186 $183,288,415.30$107,529,20474.90%15.50%
                  $158 $155,759,962.26$91,379,17877.61%20.69%
                  $131 $131,614,029.47$77,213,56480.06%26.66%
                  $111 $110,434,994.46$64,788,53082.28%33.30%
                  $94 $91,858,303.82$53,890,20584.28%40.47%
                  $82 $75,564,198.10$44,330,99686.07%48.03%
                  $69 $61,272,207.88$35,946,36287.67%55.80%
                  $56 $48,736,326.01$28,591,97889.10%63.65%
                  $46 $37,740,773.13$22,141,25490.37%71.44%
                  $35 $28,096,283.45$16,483,15391.50%79.05%
                  $26 $19,636,846.98$11,520,28492.51%86.40%
                  $17 $12,216,851.96$7,167,22093.39%93.39%
                    Avatar
                    New Jersey
                    United States
                    Member #21206
                    September 4, 2005
                    949 Posts
                    Offline
                    Posted: September 27, 2006, 7:51 am - IP Logged

                    The MM jackpot has been won.  The jackpot has been reset to $7.1M cash, $12M for the advertised annuity.

                    It happens that to have been won on a second draw, after a previous sequence in which the jackpot was won on the first draw was a 7 in 1000 shot.

                    The average sales for opening runs is 15.3M.  If this is how many tickets that sell, the randomized distribution probability for various numbers of winners is as follows:

                     

                    091.67%
                    17.98%
                    20.35%
                    30.01%

                     

                    The long term exponential program 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
                    $590,821,944.39$349,569,65044.45%0.19%
                    $514,252,435.83$304,266,02549.03%0.43%
                    $446,944,096.61$264,441,92453.45%0.88%
                    $387,776,777.75$229,434,59457.65%1.65%
                    $315 $335,765,813.56$198,661,44061.62%2.86%
                    $262 $290,045,634.78$171,610,33465.34%4.64%
                    $247 $249,855,363.74$147,831,09068.79%7.10%
                    $217 $214,526,151.79$126,927,97371.98%10.31%
                    $186 $183,470,048.31$108,553,11274.90%14.33%
                    $158 $156,170,215.95$92,400,71177.56%19.13%
                    $131 $132,172,329.43$78,201,96279.98%24.67%
                    $111 $111,077,014.64$65,720,56782.17%30.85%
                    $94 $92,533,202.23$54,748,81184.15%37.54%
                    $82 $76,232,285.06$45,104,10285.92%44.61%
                    $69 $61,902,982.41$36,625,93187.51%51.92%
                    $56 $49,306,825.25$29,173,20588.94%59.33%
                    $46 $38,234,187.66$22,621,89490.21%66.71%
                    $35 $28,500,798.21$16,862,97291.34%73.95%
                    $26 $19,944,673.31$11,800,59892.34%80.96%
                    $17 $12,423,421.46$7,350,52493.24%87.67%
                    $12 $5,811,873.61$3,438,69294.03%94.03%
                      Avatar
                      New Member

                      United States
                      Member #18769
                      July 19, 2005
                      6 Posts
                      Offline
                      Posted: September 27, 2006, 8:57 pm - IP Logged

                      "It happens that to have been won on a second draw, after a previous sequence in which the jackpot was won on the first draw was a 7 in 1000 shot."

                      But if you look at it as 2 out of 3, the odds aren't so long.

                      I figure the odds of the MM being won in 2 of 3 draws after a reset is about 18 in 1000 or 1 in 56.

                      hit hit miss ~ 0.34%

                      hit miss hit ~ 0.72%

                      miss hit hit ~ 0.72%

                      Total ~ 1.78%


                        United States
                        Member #16612
                        June 2, 2005
                        3493 Posts
                        Offline
                        Posted: September 28, 2006, 1:47 am - IP Logged

                        Prob988, I'll be surprised if MM jackpot hits again in next draw.

                          Avatar
                          New Jersey
                          United States
                          Member #21206
                          September 4, 2005
                          949 Posts
                          Offline
                          Posted: September 30, 2006, 8:31 am - IP Logged

                          The MM jackpot has rolled.  The cash value is $8.8M, the advertised annuity is $15M.

                          Second round jackpots on average sell 15.0 M tickets.  If this is the number of tickets that sell, the distribution of probability of various numbers of winners will be:

                           

                          091.83%
                          17.82%
                          20.33%
                          30.01%

                           

                           

                          The mathematical model for jackpot evolution, which tends to be more accurate in later drawings suggests the following:

                           

                          Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                          $595,883,754.74$349,585,13644.45%0.20%
                          $518,649,521.98$304,274,38649.03%0.46%
                          $450,758,187.47$264,444,80353.44%0.94%
                          $391,079,556.18$229,433,34057.65%1.75%
                          $315 $338,620,150.87$198,657,15561.62%3.04%
                          $262 $292,506,673.64$171,603,91565.34%4.93%
                          $247 $251,971,468.00$147,823,26168.79%7.55%
                          $217 $216,339,739.60$126,919,31471.97%10.97%
                          $186 $185,018,322.84$108,544,08374.90%15.24%
                          $158 $157,485,806.42$92,391,67377.56%20.35%
                          $131 $133,283,853.28$78,193,19479.98%26.24%
                          $111 $112,009,570.66$65,712,28182.17%32.81%
                          $94 $93,308,803.05$54,741,16484.15%39.93%
                          $82 $76,870,236.58$45,097,20585.92%47.45%
                          $69 $62,420,216.49$36,619,86087.51%55.22%
                          $56 $49,718,191.59$29,168,00688.94%63.10%
                          $46 $38,552,709.78$22,617,59090.21%70.95%
                          $35 $28,737,897.96$16,859,56791.34%78.65%
                          $26 $20,110,367.81$11,798,08292.35%86.10%
                          $17 $12,526,495.80$7,348,87893.24%93.24%

                            United States
                            Member #16612
                            June 2, 2005
                            3493 Posts
                            Offline
                            Posted: October 4, 2006, 2:34 pm - IP Logged

                            Prob988, MM Jackpot for 10/6 is 25 million (rolled).

                              Avatar
                              New Jersey
                              United States
                              Member #21206
                              September 4, 2005
                              949 Posts
                              Offline
                              Posted: October 4, 2006, 8:53 pm - IP Logged

                              The MM jackpot has rolled.  The cash value is $14.7M.  The advertised annuity value is $25M.

                              The average third draw sells $14.7M.

                              If this draw sells this much, the randomized probability of various numbers of winners is as follows:

                               

                              091.95%
                              17.72%
                              20.32%
                              30.01%

                               

                              The model for Jackpot growth predicts the following:

                               

                               

                              Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability
                              $594,544,263.46$349,592,02744.44%0.22%
                              $517,479,381.76$304,277,87649.02%0.49%
                              $449,737,562.34$264,445,68753.44%1.00%
                              $390,190,931.01$229,432,26757.65%1.88%
                              $315 $337,848,060.19$198,654,65961.62%3.26%
                              $262 $291,837,462.05$171,600,42865.34%5.29%
                              $247 $251,393,078.53$147,819,13068.79%8.09%
                              $217 $215,841,526.85$126,914,81871.97%11.77%
                              $186 $184,590,887.89$108,539,44274.90%16.35%
                              $158 $157,120,851.02$92,387,06077.56%21.83%
                              $131 $132,974,051.13$78,188,74279.98%28.14%
                              $111 $111,748,453.66$65,708,09182.17%35.19%
                              $94 $93,090,660.91$54,737,30984.15%42.82%
                              $82 $76,690,028.10$45,093,73785.92%50.89%
                              $69 $62,273,491.25$36,616,81387.52%59.23%
                              $56 $49,601,020.81$29,165,40088.94%67.67%
                              $46 $38,461,625.21$22,615,43690.21%76.09%
                              $35 $28,669,837.96$16,857,86591.34%84.35%
                              $26 $20,062,629.74$11,796,82692.35%92.35%
                                 
                                Page 18 of 24