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Probability of a MegaMillions rollover.

Topic closed. 352 replies. Last post 10 years ago by Prob988.

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Posted: January 11, 2006, 7:35 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.  A running average of 2nd draw sales since the matrix change suggests that the sales will be around 15.5M . If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

091.56%
18.08%
20.36%
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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    Posted: January 14, 2006, 9:59 pm - IP Logged
    The MM has rolled over.  The cash value is now $13.4M and the annuity value is $23M.  The recent jackpot sold enough tickets to fund a $4.4M cash jackpot.  A running average of 3nd draw sales since the matrix change suggests that the sales will be around 15.5M, similar to what the second drawing has produced.  (The last running average proved to be nearly spot on in predicting the last draw.) If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

    091.56%
    18.08%
    20.36%
    30.01%


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      Posted: January 18, 2006, 3:48 pm - IP Logged

      Prob988, the MM jackpot has rolled to 31 million for annunity. The cash value is $19 million.

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        Posted: January 18, 2006, 9:51 pm - IP Logged

        The MM has rolled over.  The cash value is now $18.5M and the annuity value is $31M.  A running average of 4th draw sales since the matrix change suggests that the sales will be around 17.3M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

        090.62%
        18.92%
        20.44%
        30.01%

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          Posted: January 21, 2006, 8:07 am - IP Logged

          The MM has rolled over.  The cash value is now $24.0M and the annuity value is $40M.  A running average of 5th draw sales since the matrix change suggests that the sales will be around 17.6M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

          090.47%
          19.06%
          20.45%
          30.02%

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            Posted: January 25, 2006, 9:24 am - IP Logged

            The MM has rolled over.  The cash value is now $29.9M and the annuity value is $50M.  A running average of 5th draw sales since the matrix change suggests that the sales will be around 19.5M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

            089.50%
            19.93%
            20.55%
            30.02%


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              Posted: January 25, 2006, 5:44 pm - IP Logged

              Prob988, California just started a promotion in the previous draw in Mega Millions regardless if jackpot is rolled or not. If CA matches 5 numbers, but not the Mega Ball, some more money is added to that prize pool. I'm guessing 60 million the jackpot rolls again.

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                Posted: January 25, 2006, 10:49 pm - IP Logged

                Here are the long range predictions of rollovers based on my exponential curve fitting program that generates long range probabilities.  For what it's worth, the first column is the historical values form the last great run, the first is the number the model predicts for the annuity value.  The second is the cash value.  The fourth column is the probability that that jackpot will itself if the run gets there.  The last column is the probability we will get past that jackpot from where we are now.

                 

                 $513,815,143.80$305,953,56351.39%0.63%
                $451,353,225.38$268,760,33055.35%1.22%
                $395,848,533.84$235,709,80959.12%2.20%
                $346,526,148.93$206,340,57062.68%3.73%
                $315 $302,697,463.71$180,242,58166.03%5.94%
                $262 $263,750,570.70$157,051,47669.16%9.00%
                $225 $229,141,718.82$136,443,47872.06%13.01%
                $192 $198,387,721.88$118,130,87174.73%18.06%
                $165 $171,059,212.65$101,857,98677.20%24.17%
                $147 $146,774,648.34$87,397,63279.46%31.31%
                $128 $125,194,983.72$74,547,92281.52%39.40%
                $108 $106,018,937.59$63,129,45883.39%48.34%
                $90 $88,978,786.54$52,982,82385.10%57.96%
                $77 $73,836,627.09$43,966,35586.64%68.11%
                $65 $60,381,054.31$35,954,17388.04%78.61%
                $53 $48,424,210.28$28,834,41689.29%89.29%

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                  Posted: January 28, 2006, 7:04 am - IP Logged

                  The MM has rolled over.  The cash value is now $36.1M and the annuity value is $61M.  A running average of 6th draw sales since the matrix change suggests that the sales will be around 20.3M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

                  089.09%
                  110.29%
                  20.59%
                  30.02%

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                    Posted: January 28, 2006, 10:18 am - IP Logged

                    Here are the long term modelling results for probabilities of jackpots of various sizes derived from my curve fitting scheme.    As I have discussed, I think, before, modeling gives better results in some areas than it does in others.  It deviates widely in the first several drawing and it also deviates when the jackpots approach records.  It is now operating in a region where it is very accurate though.  This is satisfying to me.

                    (I keep the model updated by inserting new sales figures for each run that give sales averages for particular numbers of drawings.)

                    Here is the table of long term probabilities:

                     

                     

                     $513,814,525.83$305,953,19551.39%0.70%
                    $451,347,787.20$268,757,09155.35%1.37%
                    $395,839,530.41$235,704,44859.12%2.47%
                    $346,514,615.43$206,333,70362.68%4.17%
                    $315 $302,684,248.96$180,234,71266.03%6.66%
                    $262 $263,736,365.80$157,043,01869.16%10.08%
                    $225 $229,127,081.77$136,434,76272.06%14.58%
                    $192 $198,373,098.65$118,122,16374.73%20.23%
                    $165 $171,044,955.23$101,849,49677.20%27.07%
                    $147 $146,761,030.13$87,389,52279.46%35.06%
                    $128 $125,182,212.66$74,540,31881.52%44.13%
                    $108 $106,007,167.39$63,122,45083.40%54.13%
                    $90 $88,968,126.13$52,976,47585.10%64.91%
                    $77 $73,827,148.74$43,960,71186.64%76.28%
                    $65 $60,372,800.39$35,949,25888.04%88.04%

                    As before, the first column is the actual jackpots from the last very large MM run.  The second column is the annuity value predicted by the model.  The third column is the cash value predicted.  The fourth column is the probabilty that each individual drawing will rollover.  The last column is the probability that a particular drawing and all of the drawings before it will roll over.  The current jackpot is annuity $61M and cash $36.1M.  (The annuity is a bit of a fudge, and the model actually calculates cash values without the extra possible error associated with extra data of annuity yield.

                     

                    For anyone who may be interested in such a thing, the form of the equation is this C = $9,793,867*exp(0.118*N) where N is the drawing number with the reset jackpot being N = 1.

                     

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                      Posted: January 29, 2006, 11:12 am - IP Logged

                      Here are the long term modelling results for probabilities of jackpots of various sizes derived from my curve fitting scheme.    As I have discussed, I think, before, modeling gives better results in some areas than it does in others.  It deviates widely in the first several drawing and it also deviates when the jackpots approach records.  It is now operating in a region where it is very accurate though.  This is satisfying to me.

                      (I keep the model updated by inserting new sales figures for each run that give sales averages for particular numbers of drawings.)

                      Here is the table of long term probabilities:

                       

                       

                       $513,814,525.83$305,953,19551.39%0.70%
                      $451,347,787.20$268,757,09155.35%1.37%
                      $395,839,530.41$235,704,44859.12%2.47%
                      $346,514,615.43$206,333,70362.68%4.17%
                      $315 $302,684,248.96$180,234,71266.03%6.66%
                      $262 $263,736,365.80$157,043,01869.16%10.08%
                      $225 $229,127,081.77$136,434,76272.06%14.58%
                      $192 $198,373,098.65$118,122,16374.73%20.23%
                      $165 $171,044,955.23$101,849,49677.20%27.07%
                      $147 $146,761,030.13$87,389,52279.46%35.06%
                      $128 $125,182,212.66$74,540,31881.52%44.13%
                      $108 $106,007,167.39$63,122,45083.40%54.13%
                      $90 $88,968,126.13$52,976,47585.10%64.91%
                      $77 $73,827,148.74$43,960,71186.64%76.28%
                      $65 $60,372,800.39$35,949,25888.04%88.04%

                      As before, the first column is the actual jackpots from the last very large MM run.  The second column is the annuity value predicted by the model.  The third column is the cash value predicted.  The fourth column is the probabilty that each individual drawing will rollover.  The last column is the probability that a particular drawing and all of the drawings before it will roll over.  The current jackpot is annuity $61M and cash $36.1M.  (The annuity is a bit of a fudge, and the model actually calculates cash values without the extra possible error associated with extra data of annuity yield.

                       

                      For anyone who may be interested in such a thing, the form of the equation is this C = $9,793,867*exp(0.118*N) where N is the drawing number with the reset jackpot being N = 1.

                       

                      I wrote:

                      "For anyone who may be interested in such a thing, the form of the equation is this C = $9,793,867*exp(0.118*N) where N is the drawing number with the reset jackpot being N = 1."

                       

                      To be explicit, this formula gives the cash value of the lottery, not the annuity value.  The annuity value depends on many financial variables such as interest rates that I do not include in my models.  I merely take a ratio of a recent claimed annuity to cash to make an annuity estimate.

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                        Posted: January 31, 2006, 10:33 pm - IP Logged

                        So whaddaya think?  Am I going to call it?  Will it go to $73.8 annuity and $44.0M cash?

                        I'm hoping this model will hold in this region. 

                         

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                          Posted: February 1, 2006, 7:49 am - IP Logged


                          The MM has rolled over.  The cash value is now $44.3M and the annuity value is $75M.  A running average of 7th draw sales since the matrix change suggests that the sales will be around 21.8M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

                          088.33%
                          110.96%
                          20.68%
                          30.03%

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                            Posted: February 1, 2006, 9:52 pm - IP Logged

                            Here is the long range model probability table updated for the last drawing:

                             $513,808,366.41$305,949,52751.39%0.80%
                             $451,338,491.35$268,751,55655.35%1.55%
                             $395,828,017.45$235,697,59259.12%2.80%
                             $346,501,638.77$206,325,97662.68%4.74%
                            $315 $302,670,421.65$180,226,47866.03%7.56%
                            $262 $263,722,182.48$157,034,57269.16%11.45%
                            $225 $229,112,937.43$136,426,34072.06%16.56%
                            $192 $198,359,304.70$118,113,95074.74%22.98%
                            $165 $171,031,753.21$101,841,63577.20%30.75%
                            $147 $146,748,603.40$87,382,12379.46%39.83%
                            $128 $125,170,696.42$74,533,46081.52%50.13%
                            $108 $105,996,657.06$63,116,19183.40%61.49%
                            $90 $88,958,684.59$52,970,85385.10%73.73%
                            $77 $73,818,812.36$43,955,74786.64%86.64%
                             

                            The current jackpot if 75M annuity and 44.3M cash, so the model has been very close to actual behavior.  It will be interesting to see if it holds.

                              dvdiva's avatar - 8ball

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                              Posted: February 4, 2006, 1:17 am - IP Logged

                              After 315 (Closer to 310) it would probably jump to 390 on the next roll like powerball would have except for the cap rule. How does higher sales impact these predictions? Like if it went from 302 to 375 to 475?

                                 
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