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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: December 21, 2005, 4:03 am - IP Logged

The Megamillions jackpot has rolled over and the annuity value is now $64M.  It is probably valid to assume, from recent history that this drawing will sell around $20.0M in tickets.  If sales are similar for this jackpot, the following table gives the probability for various numbers of winners:

088.74%
110.61%
20.63%
30.03%

There is a 53% chance that the jackpot will rise to $128M annuity.  There is a 10%  chance that the lottery will reproduce a jackpot near the $315 jackpot produced in the recent large run.  There is a 6% chance of exceeding this run and a 1% chance of exceeding $500M.  All the jackpots given here are annuity, and the calculation is based on the formula I generated from previous modeling of jackpot growth I developed earlier in this thread.  They do not reflect the experimental growth.
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    New Jersey
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    Posted: December 21, 2005, 9:42 pm - IP Logged

    Here is the spreadsheet giving the longterm probabilities.  I have updated the data generating the exponential function so as the average data for each drawing number since the change of the matrix.  The predictive changes have been small.  The first column gives the historical annuity prizes posted on the last large run.  The second prize give a calculated annuity prize for putative drawings.    You can see that the equation fits better in some areas than in others.  The third column gives cash value of the prize.  Predicted sales are not shown in this table, but the probabilities given are generated from an exponential equation generated from curve fitting the historical sales in the last 4 runs since the matrix changed.  From these unshown sales figures, the probability of a rollover for that single drawing is calculated and shown in column 5.  The last column is that all drawing including that one and those before it will roll.  The starting point is the current $64 annuity jackpot.

     

     $675,296,590.27$393,172,68143.49%0.15%
    $595,381,201.87$346,644,16647.67%0.34%
    $524,279,697.12$305,247,29051.73%0.71%
    $461,019,991.10$268,416,08455.63%1.38%
    $404,737,210.31$235,646,99859.35%2.48%
    $354,661,868.31$206,492,02162.86%4.19%
    $315 $310,109,345.47$180,552,55266.16%6.66%
    $262 $270,470,529.01$157,473,95269.25%10.06%
    $225 $235,203,485.28$136,940,69672.11%14.53%
    $192 $203,826,050.64$118,672,05674.76%20.15%
    $165 $175,909,239.34$102,418,26877.20%26.95%
    $147 $151,071,378.56$87,957,11479.43%34.92%
    $128 $128,972,890.26$75,090,88381.48%43.96%
    $108 $109,311,648.51$63,643,67183.34%53.95%
    $90 $91,818,848.92$53,458,97485.03%64.74%
    $77 $76,255,333.58$44,397,55086.56%76.14%
    $65 $62,408,321.37$36,335,51287.95%87.95%
     

    Note that this is just mathematical modeling.  It gives reasonable matches in the region in which we now find ourselves, but it may break down for very large drawings.

     Anyway, here it is for what it's worth. 

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      BILOXI, MISSISSIPPI
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      Posted: December 21, 2005, 9:53 pm - IP Logged

      thanks

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        New Jersey
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        Posted: December 24, 2005, 10:09 am - IP Logged

        The Megamillions jackpot has rolled over and the cash value is now $44.9M.  The cash value reached on the last drawing was $38.8M.  The annuity value is now $75M.  The lottery is apparently predicting 19.7M in sales.  If this proves to be correct, the probability of various numbers of winners is given in the following table:

         

        089.39%
        110.02%
        20.56%
        30.02%

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          New Jersey
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          Posted: December 24, 2005, 11:14 am - IP Logged

          I estimate that there is a 12% (mathematic model) to 13% (based on sales of last run) of the MM jackpot approximately matching the $315 annuity jackpot.    I estimate that there is 7% chance (both models) of exceeding it.  There is a 52%-54% chance that the jackpot will grow to be near $130M annuity.

          Happy Holidays. 

           

           

           

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            New Jersey
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            Posted: December 26, 2005, 8:17 am - IP Logged

            The last sentence (before Happy Holidays) in my last post is wrong.  There is a 52-54% chance that the MM jackpot will grow to the $145-150M area.

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              New Jersey
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              Posted: December 28, 2005, 11:06 am - IP Logged

              The Megamillions jackpot has rolled over and the cash value is now $52.4M.  The cash value reached on the last drawing was $45.2M.  The annuity value is now $88M, just shy of the $90M annuity record for this number of drawings in a prize building pool.  The lottery is apparently predicting 22.6M in sales.  If this proves to be correct, the probability of various numbers of winners is given in the following table:

              087.93%
              111.31%
              20.73%
              30.03%

              I have updated the data fitted into my exponential modeling equation to reflect new average sales data since the change in the matrix in MM, including the sales on the current winless run.  I have also adjusted for slight changes in the annuity/cash ratio reported by the Massachusetts lottery web site.  (The annuity values are probably the least reliable pieces of data - since the annuity varies with financial markets and their volatility.)  The model now seems to be operating within a few percent of the actual behavior of the lottery - something that I expect to prevail almost until we get into record breaking areas - if, in fact, we do so.

              The following table gives the modeled probability for rollovers over the long term.

               

               $512,485,514.18$305,161,82951.75%0.94%
              $450,676,550.44$268,357,40055.65%1.82%
              $395,680,472.35$235,609,73659.36%3.27%
              $346,746,330.39$206,471,67962.88%5.50%
              $315 $303,205,948.38$180,545,36066.18%8.75%
              $262 $264,464,799.78$157,476,76769.26%13.22%
              $225 $229,993,889.65$136,950,90772.12%19.09%
              $192 $199,322,531.47$118,687,50774.76%26.47%
              $165 $172,031,920.08$102,437,18977.20%35.40%
              $147 $147,749,413.07$87,978,06079.43%45.86%
              $128 $126,143,442.50$75,112,68681.48%57.73%
              $108 $106,918,987.45$63,665,39783.34%70.86%
              $90 $89,813,545.66$53,479,88485.03%85.03%

               

              The first column gives the historical annuity prizes posted on the last large run.  The second prize give a calculated annuity prize for putative drawings.   The third column gives cash value of the prize.  Predicted sales are not shown in this table, but the probabilities are generated from these unshown modeled sales figures.  The probability of a rollover for that single drawing is calculated and shown in column 5.  The last column is that all drawing including that one and those before it will roll.  The starting point is the current $88M annuity jackpot.  Note that the model gives a rollover probability that is 2% lower than the figure obtained by using the MM's prediction of the cash prize.

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                New Jersey
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                Posted: December 28, 2005, 7:23 pm - IP Logged

                The sales based long term rollover probability (based on the last large $315M annuity run) is similar to the modelled long term probability, 14.4% for approximately matching the $315M jackpot, 8.0% for exceeding it.

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                  BILOXI, MISSISSIPPI
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                  Posted: December 28, 2005, 10:32 pm - IP Logged

                  if lotto south rolls could you please do the math

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                    New Jersey
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                    Posted: January 2, 2006, 1:07 pm - IP Logged

                    The MM jackpot has been one and reset.  It is reasonable to assume that the number of tickets sold for the new jackpot will be around $15M.  Thus the probability of various numbers of winners is given in the following table:

                    091.82%
                    17.84%
                    20.33%
                    30.01%

                    There is, according to my model equation for jackpot growth, about a 48% of the jackpot reaching the neighborhood of 90M annuity value.  There is a 6-7% chance of matching the last large ($315M annuity) jackpot and a less than 4% chance of exceeding it.

                     

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                      New Jersey
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                      Posted: January 4, 2006, 10:57 am - IP Logged
                      The MM has rolled over.  The cash value is now $8.9M and the annuity value is $15M.  The recent jackpot sold enough tickets to fund a $4.4M cash jackpot.  The lottery is therefore predicting $14.2M in sales, which is reasonable based on past history. If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

                      092.24%
                      17.45%
                      20.30%
                      30.01%

                      There is, according to my model equation for jackpot growth, about a 51% of the jackpot reaching the neighborhood of 90M annuity value.  There is a 6-7% chance of matching the last large ($315M annuity) jackpot and a less than 5% chance of exceeding it.

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                        New Jersey
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                        Posted: January 8, 2006, 9:28 am - IP Logged

                        The MM jackpot has been won and reset.  It is reasonable to assume that the number of tickets sold for the new jackpot will be around $15M.  (Note though that all of the biggest MM states, California, New York, Illinois, and Texas, all have jackpots in their home state lotterires bigger than MM.  California has a $65M jackpot - this may cut MM sales.) 

                         

                        If however MM reaches $15M in sales anyway, the probability of various numbers of winners is given in the following table:

                        091.82%
                        17.84%
                        20.33%
                        30.01%

                        There is, according to my model equation for jackpot growth, about a 48% of the jackpot reaching the neighborhood of 90M annuity value.  There is a 6-7% chance of matching the last large ($315M annuity) jackpot and a less than 4% chance of exceeding it.  As we have just seen though, a high probability is not the same as a certainty.

                         


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                          Posted: January 9, 2006, 4:02 pm - IP Logged

                          Prob988, as long as more MM jackpot winners happen in 2006, their sales will fall. I hope the lawsuit allows CA to continue playing MM or sales will suffer big time.

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                            New Jersey
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                            Posted: January 9, 2006, 10:35 pm - IP Logged

                            Prob988, as long as more MM jackpot winners happen in 2006, their sales will fall. I hope the lawsuit allows CA to continue playing MM or sales will suffer big time.

                            I expect there will be many large jackpots in the future.  Even when the lottery resets, there is roughly a 50-50 chance of it reaching about $90M and a 15% chance of reaching $200M.

                            California is a large contributor to lottery sales, of course, although often New York has larger sales.  The loss of California would mean slower jackpot growth.

                            I lived in California for many years and I expect that the state will find a way to remain in Megamillions.  The game is rather popular.  Sales for the abbreviated year were $223M from the end of June.

                            This means the state can expect a revenue stream of close to half a billion dollars, hundreds of millions in profit from this game. 

                             

                             

                             

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                              Morrison, IL
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                              Posted: January 9, 2006, 11:42 pm - IP Logged

                              Prob988, as long as more MM jackpot winners happen in 2006, their sales will fall. I hope the lawsuit allows CA to continue playing MM or sales will suffer big time.

                              Yeah, I remember how pathetic Powerball sales were last year until it hit a record $340 million jackpot. The first time Powerball made it over the $100 million mark in 2005, it took 12 rolls for that to happen as a result of its previous lucky string of 8 jackpot winners < $50 million.

                                 
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