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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: April 1, 2006, 7:02 pm - IP Logged

If the model is accurate you have a fair shot of winning the bet.

Within the limits of the accuracy of the model, I think it's now about even, which is better than where you were when you first asked. 

 

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    New Jersey
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    Posted: April 5, 2006, 8:26 am - IP Logged

    The Megamillions has rolled over.  The cash value is $92.8, the annuity value is $162.  The cash value is now higher than Powerball's.    The previous jackpot reached a cash value of $79.6M

    As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 11th drawing than a 10th drawing.  I will therefore treat this upcoming drawing as a 12th drawing statistically rather than as if it were a 11th - an ad hoc approach, that is nonetheless giving reasonable predictions of jackpot evolution.

    11th drawing sales average $40.9M.  If this many tickets were sold the probability of various numbers of winners would be as follows:

    079.23%
    118.44%
    22.15%
    30.17%
    40.01%

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

     $681,230,943.86$389,486,38742.24%0.40%
     $597,003,812.64$341,330,44146.65%0.94%
     $522,486,998.82$298,726,26250.94%2.01%
     $456,561,026.25$261,033,80455.06%3.94%
    (Average Annuity, M)$398,235,480.15$227,686,80758.98%7.16%
    $315 $346,634,127.99$198,184,29562.68%12.14%
    $262 $300,981,755.69$172,083,04766.15%19.36%
    $247 $260,592,521.51$148,990,94269.38%29.27%
    $201 $224,859,652.53$128,561,06272.36%42.20%
    $169 $193,246,329.05$110,486,48875.11%58.31%
    $147 $165,277,619.85$94,495,68377.63%77.63%

     

     Note that in the last drawing, the cash value was better predicted by my formula than by Megamillions.  My formula was closer.


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      Posted: April 7, 2006, 12:55 pm - IP Logged

      Prob988, that's a great probability you've got. I hope MM continues to roll until it breaks the North American Record Jackpot set by PB.

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        New Jersey
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        Posted: April 8, 2006, 8:23 am - IP Logged

        The Megamillions has rolled over.  The cash value is $107.3M  the annuity value is $189M.  The cash value is higher than Powerball's and I doubt that Powerball will catch up again in this run.    The previous jackpot reached a cash value of $92.9M

        As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 12th drawing than a 11th drawing.  I will therefore treat this upcoming drawing as a 13th drawing statistically rather than as if it were a 12th - an ad hoc approach, that is nonetheless giving reasonable predictions of jackpot evolution.

        13th drawing sales average $41.2M.  If this many tickets were sold the probability of various numbers of winners would be as follows:

        079.10%
        118.55%
        22.17%
        30.17%
        40.01%

         

        The exponential modeling function I have developed is performing within 1.7% of the actual behavior in this region, slightly better than the MM's own predictions.  Here is the long term model probability chart:

         $778,176,461.94$441,790,12937.93%0.20% 
         $682,765,520.28$387,622,96542.42%0.52% 
         $598,353,457.32$339,700,13746.82%1.23% 
         $523,672,333.23$297,301,80651.10%2.63%20
         $457,600,375.03$259,791,11255.22%5.15%19
        (Average Annuity, M)$399,145,126.62$226,604,61459.13%9.33%18
        $315 $347,428,541.25$197,243,82362.82%15.77%17
        $262 $301,673,792.53$171,267,71466.28%25.11%16
        $247 $261,193,605.85$148,286,10569.50%37.88%15
        $201 $225,379,934.93$127,953,79472.47%54.51%14
        $169 $193,694,828.46$109,965,37175.21%75.21%13


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          Posted: April 11, 2006, 10:12 am - IP Logged

          I hope MM continues to roll and set new roll records Prob988. MM Sales are way ahead of PB. In addition, PB has backload annunity and less cash.

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            New Jersey
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            Posted: April 12, 2006, 6:03 am - IP Logged

            The Megamillions has rolled over.  The cash value is $125M the annuity value is $220M.  The cash value is higher than Powerball's and I doubt that Powerball will catch up again in this run.    The previous jackpot reached a cash value of $107.7M, which is close to what MM predicted and less than I predicted

            As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 13th drawing than a 12th drawing.  I will therefore treat this upcoming drawing as a 14th drawing statistically rather than as if it were a 13th - an ad hoc approach, that is nonetheless giving reasonable predictions of jackpot evolution.

            13th drawing sales average $57.4M.  If this many tickets were sold the probability of various numbers of winners would be as follows:

             

            072.13%
            123.56%
            23.85%
            30.42%
            40.03%

            Treated as a 14th drawing, the long term probability model is lagging slightly behind actual events, but it is still close, within 2%.

            Here is what it suggests for jackpot evolution, should the MM continue to roll:

             $684,862,181.24$388,813,29142.28%0.68%
            $600,124,807.05$340,705,77746.69%1.62%
            $525,165,496.53$298,149,51250.98%3.46%
            $458,855,933.74$260,503,92455.10%6.79%
            (Average Annuity, M)$400,198,002.04$227,202,35859.02%12.32%
            $315 $348,308,760.02$197,743,54562.73%20.87%
            $262 $302,407,151.17$171,684,06066.20%33.28%
            $247 $261,802,247.08$148,631,64669.42%50.27%
            $201 $225,882,847.37$128,239,31072.41%72.41%

            If the model predicts things accurately, we see we now have a 50% chance of an annuity jackpot around $300M.

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              Morrison, IL
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              Posted: April 12, 2006, 11:52 am - IP Logged

              Since Mega Millions sales are back to normal for the jackpot level it is currently at, it's very possible it may break $400 million this run.

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                New Jersey
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                Posted: April 12, 2006, 1:11 pm - IP Logged

                Since Mega Millions sales are back to normal for the jackpot level it is currently at, it's very possible it may break $400 million this run.

                Possible, but not probable.

                 I expect, by the way, that the accuracy of my model will break down soon.  It generally does so when the jackpot gets in the $200M range, underestimating the real situation.  (Right now it is overestimating the real situation slightly.)  Still I think it a useful approximation even within its limits.  I would estimate a 20-30% chance of a $400M jackpot.

                The last time the MM was in this area, the jackpot rose from 212M to 267M. 

                 

                 

                  LottoGroups's avatar - peace

                  Canada
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                  Posted: April 14, 2006, 3:42 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. 

                   

                   

                  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.

                  Good news. I won my bet with my friend.

                  And better news, the jackpot is big enough for group play.

                  Lotto Groups - the best way to win

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                    New Jersey
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                    Posted: April 14, 2006, 8:48 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. 

                     

                     

                    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.

                    Good news. I won my bet with my friend.

                    And better news, the jackpot is big enough for group play.

                    Well, you beat the odds.  Congratulations to you.

                    You should have had a handicap, but since you won, it doesn't matter.

                    If you repeat the bet in the future, I'd suggest looking at my charts.  They're not perfect, but they are instructive and give a decent rule of thumb. 

                     

                     

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                      New Jersey
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                      Posted: April 15, 2006, 6:59 am - IP Logged

                      The Megamillions has rolled over.  The cash value is $a48.9M the annuity value is $265M.  The cash value is higher than Powerball's and I doubt that Powerball will catch up again in this run.    The previous jackpot reached a cash value of $126.7M, and I did slightly better at my prediction than MM did for cash value size.

                      As before, the lottery continues to rise as if it had skipped a drawing.  The jackpot/sales were more consistent with a 14th drawing than a 13th drawing.  I will therefore treat this upcoming drawing as a 15th drawing statistically rather than as if it were a 13th - an ad hoc approach, that is nonetheless giving reasonable predictions of jackpot evolution.

                      15th drawing sales average $72.2M.  If this many tickets were sold the probability of various numbers of winners would be as follows:

                      066.31%
                      127.24%
                      25.60%
                      30.77%
                      40.08%
                      50.01%

                      Here is the long term probability:

                       

                      $798,094,787.29$448,438,92037.18%0.33%
                      $699,701,270.07$393,152,90241.70%0.89%
                      $612,727,771.93$344,283,64246.16%2.12%
                      $535,848,831.18$301,086,38150.49%4.60%
                      $467,892,825.56$262,902,79954.66%9.11%
                      $407,824,116.80$229,150,98558.63%16.67%
                      $354,727,267.76$199,316,56762.38%28.42%
                      $307,793,091.29$172,944,87365.89%45.57%
                      $266,306,318.32$149,634,00369.16%69.16%

                       

                      I expect that my program will break down in a few drawings, should the lottery continue to roll, but we'll see.  Right now it's pretty accurate.

                        dvdiva's avatar - 8ball

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                        Posted: April 15, 2006, 9:42 am - IP Logged

                        So far sales are in line with the run that went to 315. It's only if it can roll past that point where it would break down but since there isn't any data for Mega doing that it would be difficult to model.

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                          New Jersey
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                          Posted: April 16, 2006, 1:13 pm - IP Logged

                          So far sales are in line with the run that went to 315. It's only if it can roll past that point where it would break down but since there isn't any data for Mega doing that it would be difficult to model.

                          A model is designed to predict the experimental behavior, and is not, in and of itself, the experimental behavior.

                          I construct my models to see if they conform to experiment, and discard or keep them based on how well they do.

                          They are rules of thumb however, and will never be perfectly accurate.  Neither it is always accurate to say that history will repeat itself.  Sometimes it does, and sometimes it doesn't. 

                           

                           


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                            Posted: April 16, 2006, 1:25 pm - IP Logged

                            Prob988, I'm happy that MM is continuing to roll and set new roll records despite higher interest rates and gas prices going up across the country. I hope it rolls two more times then a winner occurs.

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                              New Jersey
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                              Posted: April 19, 2006, 8:15 am - IP Logged

                              The MM has been won.  The annuity value is $12M.  The cash value is $6.7M.  First draw ticket average sales are 15.7M.  If this many tickets are sold, the following numbers of winners are probable: 

                              091.45%
                              18.17%
                              20.37%
                              30.01%

                               

                              My model gives the following long term probabilities:

                               

                               $471,912,420.87$265,161,35654.20%0.87%
                              (Average Annuity, M)$411,000,727.93$230,935,88158.22%1.60%
                              $315 $357,210,562.93$200,711,89762.02%2.75%
                              $262 $309,709,308.07$174,021,57065.59%4.44%
                              $247 $267,761,691.55$150,451,75868.90%6.77%
                              $201 $230,718,406.36$129,637,62571.97%9.83%
                              $169 $198,006,059.57$111,256,99074.79%13.65%
                              $147 $169,118,296.87$95,025,33777.37%18.26%
                              $135 $143,607,964.67$80,691,41979.73%23.60%
                              $115 $121,080,188.60$68,033,35981.87%29.59%
                              $96 $101,186,261.30$56,855,22483.81%36.15%
                              $81 $83,618,244.70$46,983,98785.56%43.13%
                              $69 $68,104,203.55$38,266,85287.13%50.42%
                              $57 $54,403,996.03$30,568,88788.54%57.86%
                              $46 $42,305,556.67$23,770,93489.81%65.35%
                              $36 $31,621,613.78$17,767,76790.95%72.76%
                              $27 $22,186,790.62$12,466,46591.96%80.00%
                              $17 $13,855,045.60$7,784,96792.87%86.99%
                              $12 $6,497,411.66$3,650,81093.68%93.68%

                                 
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