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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: September 7, 2005, 8:07 am - IP Logged

9/07/05:  The cash value for the MM jackpot is estimated at $.  Up to now the cash value accumulated, based on sales, was 92.1M.  This means that the lottery anticipates sales of $45.2M for this jackpot.  In the table below the first column refers to the number of winners, and the second column offers, based on the odds, the probability - stated as a percentage - that that number of winners will be obtained.

077.32%
119.89%
22.56%
30.22%
40.01%


 

Thus there is a 77% that the lottery will roll over again.

    dvdiva's avatar - 8ball

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    Posted: September 7, 2005, 2:41 pm - IP Logged

    You might have to do two charts with a higher and lower sales estimates.  I would love to see a chart giving an estimate how high the jackpot can get with a higher/lower sales estimate. You look like you have the math skills to do it.

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      New Jersey
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      Posted: September 10, 2005, 2:40 am - IP Logged
      9/07/05:  The MM has rolled again.  The cash value for the MM jackpot is estimated at $122.9.  Up to now the cash value accumulated, based on sales, was $107.4M.  This means that the lottery anticipates sales of $48.7M for this jackpot.  In the table below the first column refers to the number of winners, and the second column offers, based on the odds, the probability that that number will result
      075.78%
      121.01%
      22.91%
      30.27%
      40.02%
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        New Jersey
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        Posted: September 14, 2005, 8:35 am - IP Logged

        9/14/05:  The MM has rolled again.  The cash value for the MM jackpot is estimated at $153.3.  Up to now the cash value accumulated, based on sales (including the estimated sales figure for yesterday's jackpot of $62.57M , was $115.6M.  This means that the lottery anticipates sales of $118.4M for this jackpot.  In the table below the first column refers to the number of winners, and the second column offers, based on the odds, the probability that that number will result.

         

         

        050.96%
        134.35%
        211.58%
        32.60%
        40.44%
        50.06%
        60.01%


         

        The odds are slightly better than even that it will rollover again.

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          New Jersey
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          Posted: September 18, 2005, 2:25 pm - IP Logged

          It appears that the MM sold somewhat less well than anticipated for the $250 million jackpot, actual sales coming in at an estimated $90M.

          The actual outcome, 1 winner, was actually not the most probable outcome, which would have been another rollover.  The probability distribution for the number of winners looked like this:

           

          059.92%
          130.69%
          27.86%
          31.34%
          40.17%
          50.02%


          If the MM sells what it did at the last $12M starter jackpot, roughly 14.5M, the winner probability distribution will now look like this:

           

          092.08%
          17.60%
          20.31%
          30.01%


          Using the sales figures of the last run as a guide, one can estimate the probability that jackpot will get as high as it was again on this run (or probably any reset run).  This figure is about 12%.  Using the figure for the last drawing we see that the overall probability of a run that exceeds $250M annuity value is roughly between 7 and 8%.

           

           

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            New Jersey
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            Posted: September 21, 2005, 8:51 am - IP Logged

            The MM pot as rolled, and the annuity value is $15,000,000.  If the sales are similar to what they the were last run, which also had a first rolloever annuity jackpot of 15M and produced sales $15,358,719, the the probability of the numbers of winners occurring is given in the table below:

             

            091.63%
            18.01%
            20.35%
            30.01%



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              New Jersey
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              Posted: September 24, 2005, 9:10 am - IP Logged

              The MM pot as rolled, and the annuity value is $23,000,000.  If the sales are similar to what they the were last run, which also had a first rolloever annuity jackpot of 15M and produced sales $15,000,000, the the probability of the numbers of winners occurring is given in the table below:

               

              091.63%
              18.01%
              20.35%
              30.01%

              If sales continue to track the last run closely, the overall probability of reaching a $250M jackpot again are roughly 16%.  The probability of exceeding that run is roughly 10%.
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                Morrison, IL
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                Posted: September 24, 2005, 12:21 pm - IP Logged

                  I think MM will break $300 million within a year from now, but before then, we'll see one or two winners of jackpots under $100 million.

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                  New Jersey
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                  Posted: September 28, 2005, 9:26 am - IP Logged

                  The MM pot has rolled, and the annuity value is $32,000,000.  If the sales are similar to what they the were last run, which also had a first rolloever annuity jackpot of 32M and produced sales $15,000,000, the the probability of the numbers of winners occurring is given in the table below:

                  090.89%
                  18.68%
                  20.41%
                  30.01%


                  In my last post on the probability of a larger jackpot, I made an entry error on the spreadsheet where I do my calculations.  I have corrected this error on this recent run:

                  The overall probability of the jackpot reaching the level of the last run, around $250 M annuity, is around 13%.  The overall probability of it exceeding that jackpot is around 8%.  These figures assume sales are the same for this run as they were for the last one.

                   

                   


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                    Posted: September 28, 2005, 3:57 pm - IP Logged

                    I like these calculations. It must be harder though to calculate the probability of the jackpot reaching X million dollars.

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                      New Jersey
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                      Posted: September 28, 2005, 5:15 pm - IP Logged

                      I like these calculations. It must be harder though to calculate the probability of the jackpot reaching X million dollars.

                      The long range calculations are certainly less certain than the short ranged ones.  I am relying mostly on historical sales data - most dependent of course on the recent run which is tracking this run closely thus far - to derive these numbers.  The calculations themselves are pretty straightforward since I have a spreadsheet that does all of it.  Setting up the spreadsheet took some time - and it evolved since I started - but now it doesn't take all that long to generate the numbers.  They more or less are spit out.

                      Some caveats on these calculations:  Sales figures can and do change with events, and these numbers assume that tickets are chosen randomly.  Since some tickets are in fact chosen with deliberation, lots of people still play their birthdates for instance, the probabilities of rollovers are probably generally, if only slightly, higher than my numbers indicate.  Still I think these numbers are a good first approximation and I think they do help one decide on how to play the lottery.  If for instance, one has budgeted a certain amount to play, one needs to decide on how likely one is to deplete one's funds before the jackpot has reached a likely peak.  One may, for example, desire to hold some playing funds in reserve for a potentially bigger jackpot.  Knowing how likely this larger jackpot is is I think useful.

                       

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                        Posted: October 1, 2005, 6:42 pm - IP Logged

                        The MM pot has rolled, and the annuity value is $42,000,000.  If the sales are similar to what they the were last run, which also had a first rolloever annuity jackpot of 32M and produced sales $17,000,000, the the probability of the numbers of winners occurring is given in the table below:

                         

                        090.78%
                        18.78%
                        20.42%
                        30.01%


                         

                        The overall probability of the jackpot reaching the level of the last run, around $250 M annuity, is around 14%.  The overall probability of it exceeding that jackpot is around 9%.  These figures assume sales are the same for this run as they were for the last one.

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                          Posted: October 5, 2005, 8:17 am - IP Logged

                          The MM pot has rolled, and the annuity value is $53,000,000.  The cash value is $31.6 million.   If the sales continue to be similar to what they the were last run, but running about 1 million higher per run, the number sold should be around 19 million. The probabilities of the numbers of winners occurring is given in the table below:

                          089.75%
                          19.70%
                          20.52%
                          30.02%

                           

                          The overall probability of the jackpot reaching the level of the last run, around $250 M annuity, is around 16%.  The overall probability of it exceeding that jackpot is around 10%.  These figures assume sales remain close to the last run.

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                            Posted: October 8, 2005, 11:32 am - IP Logged

                            The Megamillions has rolled over again, and the cash value has risen from $31.6M to 38.6M, the annuity value from $53M to $65M.  The MM lottery is therefore predicting $24.4M in sales.  The probabilities of the number of winners is given in the table below:

                             

                            087.04%
                            112.08%
                            20.84%
                            30.04%


                            The sales performance on this run is actually somewhat better than on the last run and long range probabilities have thus become a little more difficult to determine based on history.  Still a decent estimate is possible.  I would estimate that the probability of matching the $250M annuity jackpot that ended the last run would be between 18-20% and the long range probability of exceeding it would now be 12-13%.

                             


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                              Posted: October 8, 2005, 4:13 pm - IP Logged

                              prob:

                              Are you also calculating Powerball? That would be interesting especially if the jackpot cap is utilized.

                                 
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