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Probability of a Rollover in Powerball.

Topic closed. 310 replies. Last post 10 years ago by Prob988.

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Morrison, IL
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Posted: April 6, 2006, 3:00 pm - IP Logged

The cash value is not lowered; the annuity value is simply bigger. The cash value is what it is, approximately 30% of sales (although they probably are still taking money out of that to fund the set prize reserve due to the two overwhelming second prize payouts that occurred last year - it must take forever to build up the reserve to support those).

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    New Jersey
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    Posted: April 9, 2006, 1:09 am - IP Logged

    The Powerball has rolled over.  The cash value is now $101.1 million and the annuity value is $220M.  The back loaded annuity means that the cash value is actually lower than the cash value for MM.

    The average sales figures for a Powerball 15th draw since the matrix change is 38.2M.  If the sales figures are close to the average, the probability of various numbers of winners is given in the following table:

    076.99%
    120.13%
    22.63%
    30.23%
    40.01%

    Based on previous sales figure averages, I estimate that the Powerball has a 19% probability of reaching the cap, and a 6% chance of exceeding it.  These estimates are somewhat cruder than the estimates I use for MM.

     

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      New Jersey
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      Posted: April 9, 2006, 1:45 pm - IP Logged

      I have developed a modeling function that fits the experimental behavior of the Powerball pretty well, at least when one looks at it graphically.  This function models the Powerball as a linear growth function to draw 12, and thereafter as an exponential function using the data points of average values from drawings 13 to 19.

      The model does not fit perfectly the behavior of the recent run, which has been above average in performance overall.  Still it is a useful approximation and I offer it for what it's worth:

       

      $471,894,023.98$217,285,74837.36%5.52%
      $372,555,343.88$171,544,80248.68%14.77%
      $299,918,746.49$138,098,95059.08%30.34%
      $246,806,753.52$113,643,29268.05%51.36%
      $207,971,181.66$95,761,27675.47%75.47%

      This model obviously ignores the cap, and says how the drawing would behave in the absense of the cap.  Note that the potential exists for the cap to be pushed ever higher until it is essentially meaningless. 

      The first column is the (inflated) annuity value, the second column, the more meaningful cash value (which is what is directly calculated).  The third column is the probability that a run of that size will rollover, and the fourth colum is the probability that all runs will rollover from this point.  According to this model we have a roughly 30% of reaching the cap, which will easily exceed the cap point which is currently $365M.  Note that the jackpot, according will not reach cap figure of $390, but will fall slightly short of it, if this model proves successful and relevant.

      If my understanding of  the rules is correct, this means that the jackpot might go like this:  It reaches $372M and then (15% chance overall) it goes to $397M. 

       

       

       

        dvdiva's avatar - 8ball

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        Posted: April 10, 2006, 2:17 am - IP Logged

        Considering the declining cash value it could easy hit the cap early. It's the miracle of inflation.

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          New Jersey
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          Posted: April 10, 2006, 10:02 am - IP Logged

          Considering the declining cash value it could easy hit the cap early. It's the miracle of inflation.

          That is true. 

          I note that with the new structure, the cap is set somewhere near the value of Jack Whitaker's jackpot.

           If interest rates rise enough, it may not be possible to reach Jack's Jackpot every easily. 

          They would be more honest if they made the cap dependent on the cash value, but that would draw more attention to their already previous obvious subterfuge. 

           

           

           

           


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            Posted: April 11, 2006, 10:16 am - IP Logged

            Prob988, I hope it continues to roll and then hit the cap once again. I know PB is dropping the cash value because it reached the cap twice already.

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              Morrison, IL
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              Posted: April 11, 2006, 11:56 am - IP Logged

              Considering the declining cash value it could easy hit the cap early. It's the miracle of inflation.

              That is true. 

              I note that with the new structure, the cap is set somewhere near the value of Jack Whitaker's jackpot.

               If interest rates rise enough, it may not be possible to reach Jack's Jackpot every easily. 

              They would be more honest if they made the cap dependent on the cash value, but that would draw more attention to their already previous obvious subterfuge. 

               

               

               

               

              The MUSL said they won't make the cap dependent on cash value because they'd have too difficult a time explaining it to the players, many of whom are stupid enough to believe the cash value is the advertised jackpot after taxes.

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                New Jersey
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                Posted: April 13, 2006, 11:24 am - IP Logged

                The powerball jackpot has been won.  The average sales for 1st draw jackpots is 14.5M.  If this is the number of tickets that are sold, the probability for various numbers of winners occurring will be:

                090.55%
                18.99%
                20.45%
                30.01%
                 

                I have developed a model that is linear through the first 12 drawings, and becomes exponential at the 13th.  This model seems to fit the average sales data very well, when one graphs actual sales vs. model sales.    It will be inaccurate where minimums (such as the $15M opening annuity prize) and caps are applied. 

                Here is what the new model predicts:

                 $755,823,750.77$348,022,48215.92%0.04%
                Average Jackpots$579,226,427.28$266,707,44126.06%0.24%
                $353 $449,972,999.06$207,192,11337.37%0.93%
                $300 $355,371,063.00$163,632,22148.65%2.48%
                $245 $286,130,916.49$131,750,28159.02%5.09%
                $208 $235,453,329.03$108,415,55667.98%8.63%
                $193 $198,361,872.70$91,336,62675.39%12.70%
                $173 $171,214,247.84$78,836,37981.32%16.84%
                $152 $151,344,617.26$69,687,31785.96%20.71%
                $126 $136,801,826.80$62,991,02385.77%24.09%
                $111 $122,044,912.02$56,196,13486.31%28.09%
                $96 $107,898,317.71$49,682,27186.86%32.54%
                $83 $94,362,043.86$43,449,43287.42%37.46%
                $72 $81,436,090.48$37,497,61887.97%42.86%
                $62 $69,120,457.55$31,826,82988.53%48.71%
                $52 $57,415,145.09$26,437,06589.10%55.02%
                $44 $46,320,153.08$21,328,32589.66%61.76%
                $34 $35,835,481.54$16,500,61090.24%68.88%
                $26 $25,961,130.47$11,953,92190.81%76.33%
                $20 $16,697,099.85$7,688,25691.39%84.05%
                $15 $8,043,389.69$3,703,61591.97%91.97%
                 

                 

                 

                 

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                  New Jersey
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                  Posted: April 16, 2006, 1:21 pm - IP Logged

                  Powerball has rolled over.  The cash value is $9.2M, the annuity value is $20M.

                  Second draws in Powerball have averaged 13.8M in sales.  If this is how many tickets are sold, the probability of various numbers of winners will be:

                   

                   

                  090.99%
                  18.59%
                  20.41%
                  30.01%

                  The long term linear/exponential model that I am trying out, predicts the following behavior and probabilities.

                  $353 $450,106,562.42$207,253,61337.37%1.01%
                  $300 $355,504,626.36$163,693,72148.65%2.69%
                  $245 $286,264,479.85$131,811,78159.02%5.53%
                  $208 $235,586,892.39$108,477,05567.98%9.37%
                  $193 $198,495,436.06$91,398,12675.39%13.79%
                  $173 $171,347,811.20$78,897,87981.32%18.29%
                  $152 $151,478,180.61$69,748,81785.96%22.49%
                  $126 $136,935,390.16$63,052,52385.78%26.17%
                  $111 $122,195,598.89$56,265,51986.32%30.50%
                  $96 $108,060,991.04$49,757,17586.87%35.34%
                  $83 $94,531,566.59$43,527,49087.42%40.68%
                  $72 $81,607,325.55$37,576,46487.97%46.53%
                  $62 $69,288,267.92$31,904,09888.53%52.90%
                  $52 $57,574,393.71$26,510,39189.08%59.75%
                  $44 $46,465,702.90$21,395,34489.65%67.07%
                  $34 $35,962,195.50$16,558,95690.21%74.82%
                  $26 $26,063,871.51$12,001,22890.78%82.94%
                  $20 $16,770,730.93$7,722,15991.36%91.36%

                  The probabilities are linked to sales, and do not reflect the various marketing strategies applied at Powerball, including allocations to reserves.

                   

                   

                   

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                    New Jersey
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                    Posted: April 20, 2006, 8:27 am - IP Logged

                    Powerball has rolled.  The cash jackpot is $13M.  The annuity jackpot is $28M.

                    Since the matrix change, 3rd draws in a series have sold 15M tickets on average.  If this is how many tickets are sold, the probability of various numbers of winners is as follows:

                    090.24%
                    19.26%
                    20.48%
                    30.02%

                     

                    The mixed linear/exponential model (switch to exponential at draw 13) suggests the following long term probabilities for jackpot evolution:

                    $353 $450,061,934.86$207,233,06437.37%1.10%
                    $300 $355,459,998.80$163,673,17248.65%2.95%
                    $245 $286,219,852.29$131,791,23259.02%6.06%
                    $208 $235,542,264.83$108,456,50667.98%10.26%
                    $193 $198,450,808.49$91,377,57775.39%15.10%
                    $173 $171,303,183.64$78,877,33081.32%20.03%
                    $152 $151,433,553.05$69,728,26885.96%24.63%
                    $126 $136,890,762.59$63,031,97485.78%28.65%
                    $111 $122,146,966.29$56,243,12686.32%33.40%
                    $96 $108,009,757.76$49,733,58486.87%38.69%
                    $83 $94,479,137.01$43,503,34887.42%44.54%
                    $72 $81,555,104.02$37,552,41887.97%50.95%
                    $62 $69,237,658.81$31,880,79588.53%57.92%
                    $52 $57,526,801.38$26,488,47789.09%65.42%
                    $44 $46,422,531.71$21,375,46689.65%73.44%
                    $34 $35,924,849.82$16,541,76090.22%81.91%
                    $26 $26,033,755.71$11,987,36190.79%90.79%

                     As always, this program ignores the cap.

                     

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                      New Jersey
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                      Posted: April 23, 2006, 6:42 am - IP Logged

                      Powerball has rolled.  The cash jackpot is $16.8M.  The annuity jackpot is $37M.

                      Since the matrix change, 4th draws in a series have sold 14.3M tickets on average.  If this is how many tickets are sold, the probability of various numbers of winners is as follows:

                      090.68%
                      18.87%
                      20.43%
                      30.01%

                      The mixed linear/exponential model (switch to exponential at draw 13) is already relatively close at predicting the cash values - the cash values being what it is designed to predict.  Although I report the average annuity values in these charts, this is for convenience since this about which people tend to think because of the way the media reports jackpots.  The true value is connected with cash value.  In any case the model  suggests the following long term probabilities for jackpot evolution, ignoring caps and reserves:

                      Average Jackpots$579,361,368.23$266,769,57526.06%0.32%
                      $353 $450,107,940.01$207,254,24737.37%1.21%
                      $300 $355,506,003.95$163,694,35548.65%3.25%
                      $245 $286,265,857.44$131,812,41559.02%6.67%
                      $208 $235,588,269.98$108,477,69067.98%11.30%
                      $193 $198,496,813.65$91,398,76075.39%16.63%
                      $173 $171,349,188.79$78,898,51381.32%22.05%
                      $152 $151,479,558.20$69,749,45185.96%27.12%
                      $126 $136,936,767.75$63,053,15785.78%31.55%
                      $111 $122,195,330.68$56,265,39586.32%36.78%
                      $96 $108,059,355.39$49,756,42186.87%42.61%
                      $83 $94,528,841.87$43,526,23587.42%49.05%
                      $72 $81,603,790.13$37,574,83687.97%56.11%
                      $62 $69,284,200.16$31,902,22588.53%63.78%
                      $52 $57,570,071.96$26,508,40189.08%72.05%
                      $44 $46,461,405.53$21,393,36589.65%80.87%
                      $34 $35,958,200.88$16,557,11790.21%90.21%

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                        Posted: April 27, 2006, 5:47 am - IP Logged

                        Powerball has rolled.  The cash jackpot is $22.1.  The annuity jackpot is $49M.

                        Since the matrix change, 5th draws in a series have sold 14.9M tickets on average.  If this is how many tickets are sold, the probability of various numbers of winners is as follows:

                        090.30%
                        19.21%
                        20.47%
                        30.02%

                        The mixed linear/exponential model (switch to exponential at draw 13) suggests the following long term probabilities for jackpot evolution, ignoring caps and reserves:

                        Average Jackpots$579,389,464.04$266,782,51226.06%0.35%
                        $353 $450,136,035.83$207,267,18437.37%1.34%
                        $300 $355,534,099.77$163,707,29248.65%3.60%
                        $245 $286,293,953.26$131,825,35259.02%7.39%
                        $208 $235,616,365.80$108,490,62767.98%12.53%
                        $193 $198,524,909.46$91,411,69775.39%18.43%
                        $173 $171,377,284.61$78,911,45081.32%24.44%
                        $152 $151,507,654.02$69,762,38885.96%30.06%
                        $126 $136,964,863.56$63,066,09485.78%34.97%
                        $111 $122,223,786.70$56,278,49886.32%40.76%
                        $96 $108,087,680.43$49,769,46486.87%47.22%
                        $83 $94,556,544.74$43,538,99187.42%54.36%
                        $72 $81,630,379.64$37,587,07987.97%62.19%
                        $62 $69,309,185.13$31,913,72988.52%70.69%
                        $52 $57,592,961.21$26,518,94189.08%79.86%
                        $45 $46,481,707.87$21,402,71489.64%89.64%


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                          Posted: April 30, 2006, 1:24 am - IP Logged

                          Prob988, there was no PB Jackpot winner. Therefore, the PB Jackpot has rolled to 61 million for 5/3/06.

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                            Posted: April 30, 2006, 1:35 am - IP Logged

                            Powerball has rolled.  The cash jackpot is $27M.  The annuity jackpot is $61M.

                            Since the matrix change, 5th draws in a series have sold 15.3M tickets on average.  If this is how many tickets are sold, the probability of various numbers of winners is as follows:

                            090.06%
                            19.43%
                            20.49%
                            30.02%

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                              Posted: April 30, 2006, 7:54 am - IP Logged

                              The mixed linear/exponential model (switch to exponential at draw 13) suggests the following long term probabilities for jackpot evolution, ignoring caps and reserves, will apply for the current $27M cash, $49M, advertised jackpot:

                              Average Jackpots$602,989,166.88$266,896,84426.06%0.39%
                              $353 $468,528,609.82$207,381,51637.37%1.50%
                              $300 $370,115,521.69$163,821,62448.65%4.01%
                              $245 $298,085,953.11$131,939,68459.02%8.24%
                              $208 $245,366,758.47$108,604,95967.98%13.96%
                              $193 $206,781,028.48$91,526,02975.39%20.54%
                              $173 $178,539,729.11$79,025,78281.32%27.24%
                              $152 $157,869,626.70$69,876,72085.96%33.49%
                              $126 $142,740,962.55$63,180,42685.77%38.97%
                              $111 $127,399,400.56$56,389,89986.31%45.43%
                              $96 $112,684,471.63$49,876,73386.86%52.63%
                              $83 $98,596,175.74$43,640,93087.40%60.59%
                              $72 $85,134,512.90$37,682,48987.95%69.33%
                              $62 $72,299,483.11$32,001,41188.51%78.82%
                              $52 $60,091,086.38$26,597,69489.06%89.06%

                                 
                                Page 11 of 21