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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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New Jersey
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Posted: January 14, 2007, 9:51 pm - IP Logged

The Powerball jackpot has rolled over.  The cash value is $86; the advertised annuity value is $180M.  Fourteenth round drawings sell on average 31.0M tickets.  If this is the number that sell, the randomized probability for various numbers of winners will be as follows:

 

080.66%
117.34%
21.86%
30.13%
40.01%

 

The modeling function, which moves on the 14th draw to an exponential form, being linear for 1 through 13, suggests the following for jackpot evolution, ignoring potential caps:

 

Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
$570,222,427.33$272,439,60427.19%1.16%
$353 $449,603,021.81$214,810,33337.90%4.26%
$300 $359,734,073.99$171,872,94648.53%11.25%
$245 $292,776,126.81$139,881,92758.36%23.19%
$208 $242,888,297.94$116,046,63166.95%39.73%
$193 $205,718,767.29$98,287,85574.16%59.35%
$180 $178,025,158.65$85,056,46580.03%80.03%
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    New Jersey
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    Posted: January 18, 2007, 1:08 am - IP Logged

    The Powerball jackpot has rolled over.  The cash value is $86; the advertised annuity value is $180M.  Fourteenth round drawings sell on average 31.0M tickets.  If this is the number that sell, the randomized probability for various numbers of winners will be as follows:

     

    080.66%
    117.34%
    21.86%
    30.13%
    40.01%

     

    The modeling function, which moves on the 14th draw to an exponential form, being linear for 1 through 13, suggests the following for jackpot evolution, ignoring potential caps:

     

    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
    $570,222,427.33$272,439,60427.19%1.16%
    $353 $449,603,021.81$214,810,33337.90%4.26%
    $300 $359,734,073.99$171,872,94648.53%11.25%
    $245 $292,776,126.81$139,881,92758.36%23.19%
    $208 $242,888,297.94$116,046,63166.95%39.73%
    $193 $205,718,767.29$98,287,85574.16%59.35%
    $180 $178,025,158.65$85,056,46580.03%80.03%

    The long term program did spectactularly well on predicting the new jack pot which is $98.3 cash, $205M advertised.

    Update tomorrow. 

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      Posted: January 18, 2007, 10:23 am - IP Logged

      The long term program did spectactularly well on predicting the new jack pot which is $98.3 cash, $205M advertised.

      Update tomorrow. 

      Prob988...it looks like your predictions were "right on the money." 

      If you could only come up with a way to predict those 6 little numbers, now that would be special!!!!

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        Posted: January 18, 2007, 11:39 pm - IP Logged

        Prob988...it looks like your predictions were "right on the money." 

        If you could only come up with a way to predict those 6 little numbers, now that would be special!!!!

        It would be indeed.  Of course, if I could do that, I wouldn't be posting it here, but using it to win the lottery.

        However it is not possible to predict the numbers since they don't really depend on external factors, but it is reasonable to estimate the probability of jackpot growth since they follow regular patterns.

        My modelling programs are not always accurate particularly  the low range and high range, but they do give a good idea of what one might expect.

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          Posted: January 19, 2007, 8:08 am - IP Logged

          The sales figures at lottoreport for the last drawing are still not available so the long term estimates will not be updated from the last one until they come out.

          The Powerball has, though rolled over.  The cash jackpot for powerball is $98.3M.  The advertised annuity is $205M.  At 15th drawing sells on average $40M tickets.    The randomized probability for various numbers of winners is as follows:

           

          076.58%
          120.43%
          22.73%
          30.24%
          40.02%
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            Posted: January 21, 2007, 8:54 am - IP Logged

            The Powerball jackpot has rolled.  The cash value is $114M.  The advertised annuity is $240M.  The average 16th PB draw sells 49.0M tickets.  If this is the number that sell, the randomized distribution probability for various numbers of winners is as follows:

             

            071.52%
            123.97%
            24.02%
            30.45%
            40.04%

             

            Lottoreport has posted sales figures and the long term projection program, which ignores caps, suggests the following:

             

            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
            $574,443,881.71$272,860,84427.24%1.94%
            $353 $453,295,480.20$215,315,35337.88%7.14%
            $300 $362,862,050.78$172,359,47448.45%18.84%
            $245 $295,356,371.35$140,294,27658.22%38.88%
            $208 $244,965,528.22$116,358,62666.78%66.78%
              dvdiva's avatar - 8ball

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              Posted: January 21, 2007, 2:19 pm - IP Logged

              Judging from the sales its very close to the drawing for 340 million on 10/20/05.

              If it rolls it would be closer to 240, 300, 390 (the cap + 5-10 million in the match 5 bonus). Both the 365 (which had less sales at this point) and the 340 roll would have broken 400+ if it weren't for the cap. 

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                Posted: January 22, 2007, 8:31 am - IP Logged

                Judging from the sales its very close to the drawing for 340 million on 10/20/05.

                If it rolls it would be closer to 240, 300, 390 (the cap + 5-10 million in the match 5 bonus). Both the 365 (which had less sales at this point) and the 340 roll would have broken 400+ if it weren't for the cap. 

                I would not be surprised, in the unlikely case that the jackpot rolls toward the cap, if it rises faster than historical data suggests.  It's been a long time since there's been a jackpot this high, meaning higher excitement.

                The last drawing gave sales 10M above the previous average. 

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                  New Member

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                  Posted: January 22, 2007, 6:53 pm - IP Logged

                  According to the Powerball E-mail the actual jackpot on Saturday, Jan 20 was$212,300,000 Annuity/$100,700,000 cash.

                  A  jackpot of $390,000,000 annuity would have a $185,000,000 cash value at Saturday's ratio.

                  185.0-100.7=84.3

                  30.28855% of Powerball Sales go to the jackpot.

                  84.3/.3028855 ~ 280

                  $280,000,000 in sales for three draws seems likely (assuming no winner).

                  The limited sales history at the current jackpot levels indicates sales should be at least 50, 90, and 140 million tickets.

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                    Posted: January 25, 2007, 4:22 pm - IP Logged

                    The Powerball jackpot has been won and is reset to $7.1M cash, $15M advertised annuity.  The average sales for first drawings is 14.7M.

                    If this is how many tickets sell, the randomized probability of various numbers of winners is as follows:

                     

                    090.41%
                    19.11%
                    20.46%
                    30.02%

                     

                    The long term model for jackpot evolution, ignoring minimums and caps suggests the following:

                     

                    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                    $579,469,194.57$274,282,08527.19%0.20%
                    $353 $457,710,528.63$216,649,65037.72%0.75%
                    $300 $366,552,217.11$173,501,38348.19%1.98%
                    $245 $298,303,787.37$141,197,12657.90%4.11%
                    $250 $208 $247,207,534.22$117,011,56666.42%7.11%
                    $200 $193 $208,952,777.35$98,904,31573.61%10.70%
                    $172 $180 $180,312,195.46$85,347,77379.51%14.54%
                    $150 $159 $158,869,556.73$75,198,25783.83%18.28%
                    $131 $132 $142,375,405.69$67,391,02584.47%21.81%
                    $111 $119 $126,593,490.64$59,920,91985.11%25.82%
                    $97 $105 $111,523,811.57$52,787,93785.76%30.34%
                    $84 $92 $97,166,368.49$45,992,08186.42%35.37%
                    $72 $79 $83,521,161.39$39,533,35087.08%40.93%
                    $61 $68 $70,588,190.27$33,411,74387.75%47.00%
                    $51 $57 $58,367,455.13$27,627,26288.42%53.56%
                    $41 $47 $46,858,955.99$22,179,90689.09%60.58%
                    $32 $36 $36,062,692.82$17,069,67589.78%68.00%
                    $23 $27 $25,978,665.64$12,296,56890.46%75.74%
                    $15 $20 $16,606,874.44$7,860,58791.15%83.73%
                    $12 $15 $7,947,319.23$3,761,73191.85%91.85%
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                      Posted: January 29, 2007, 10:45 am - IP Logged

                      The Powerball jackpot has been won and is reset to $7.1M cash, $15M advertised annuity.  The average sales for first drawings is now 14.8M, having risen slightly in the last jackpot run, because of record sales on the first drawing for this matrix.

                      If an average number of tickets sell this time, the randomized probability of various numbers of winners is as follows:

                       

                      090.34%
                      19.18%
                      20.47%
                      30.02%

                       

                       The long term model for jackpot evolution, ignoring minimums and caps suggests the following:

                       

                       

                      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                      $579,534,429.33$274,312,96327.19%0.20%
                      $353 $457,775,763.38$216,680,52837.72%0.75%
                      $300 $366,617,451.87$173,532,26148.19%1.98%
                      $245 $298,369,022.13$141,228,00457.90%4.11%
                      $208 $247,272,768.97$117,042,44466.42%7.10%
                      $193 $209,018,012.11$98,935,19273.61%10.69%
                      $180 $180,377,430.22$85,378,65079.51%14.53%
                      $159 $158,934,791.49$75,229,13583.84%18.27%
                      $132 $142,453,687.40$67,428,07984.48%21.79%
                      $119 $126,681,808.46$59,962,72385.12%25.80%
                      $105 $111,619,154.68$52,833,06785.77%30.30%
                      $92 $97,265,726.04$46,039,11086.42%35.33%
                      $79 $83,621,522.55$39,580,85487.08%40.89%
                      $68 $70,686,544.21$33,458,29887.74%46.95%
                      $57 $58,460,791.02$27,671,44188.41%53.51%
                      $47 $46,944,262.97$22,220,28489.08%60.53%
                      $36 $36,136,960.08$17,104,82889.76%67.94%
                      $27 $26,038,882.34$12,325,07190.45%75.69%
                      $20 $16,650,029.74$7,881,01491.13%83.69%
                      $15 $7,970,402.30$3,772,65791.83%91.83%
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                        Posted: February 1, 2007, 11:08 pm - IP Logged

                        The Powerball jackpot has rolled.  The cash jackpot is $9.3M.  The advertised annuity is $20M.  An average 2nd PB draw sells $14.2M in tickets.  If this is the amount that sells in the next drawing, the randomized probability of a a rollover we be as follows:

                         

                        090.37%
                        19.15%
                        20.46%
                        30.02%

                         

                        The modeling program I developed suggests the following for jackpot evolution:

                         

                        Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                        $589,892,946.93$274,300,22027.19%0.22%
                        $353 $465,952,226.04$216,667,78537.72%0.81%
                        $300 $373,160,253.03$173,519,51848.19%2.16%
                        $245 $303,688,733.15$141,215,26157.90%4.48%
                        $218 $251,676,776.53$117,029,70166.42%7.74%
                        $196 $212,736,450.55$98,922,45073.61%11.65%
                        $180 $183,582,596.58$85,365,90779.51%15.82%
                        $158 $161,755,681.17$75,216,39283.83%19.90%
                        $132 $144,973,735.98$67,412,78784.47%23.74%
                        $119 $128,914,990.87$59,945,47185.12%28.10%
                        $104 $113,579,445.85$52,814,44285.77%33.01%
                        $92 $98,967,100.90$46,019,70286.42%38.49%
                        $79 $85,077,956.03$39,561,25087.08%44.54%
                        $67 $71,912,011.25$33,439,08587.74%51.15%
                        $57 $59,469,266.54$27,653,20988.41%58.29%
                        $46 $47,749,721.92$22,203,62189.09%65.93%
                        $36 $36,753,377.37$17,090,32089.77%74.00%
                        $27 $26,480,232.91$12,313,30890.45%82.44%
                        $20 $16,930,288.52$7,872,58491.14%91.14%
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                          Posted: February 4, 2007, 8:06 am - IP Logged

                          Powerball has rolled over.  The cash jackpot is $12.9M; the annuity value advertised is $27M.  Third drawings sell 15.0M tickets on average.  The randomized probability of various numbers of winners - if average sales are obtained - is:

                           

                          090.24%
                          19.27%
                          20.48%
                          30.02%

                           

                           

                          The mathematical model I use to predict the long term probabilities of rollovers within a particular run suggests the following:

                           

                          Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                          $587,823,153.61$274,317,47227.19%0.24%
                          $353 $464,325,078.15$216,685,03637.72%0.89%
                          $300 $371,864,505.04$173,536,76948.19%2.37%
                          $245 $302,641,097.73$141,232,51257.90%4.91%
                          $218 $250,814,898.11$117,046,95266.42%8.49%
                          $196 $212,013,644.72$98,939,70173.61%12.78%
                          $180 $182,963,911.65$85,383,15979.51%17.36%
                          $158 $161,214,949.51$75,233,64383.84%21.83%
                          $132 $144,498,038.77$67,432,41884.48%26.04%
                          $119 $128,500,421.49$59,966,86385.12%30.82%
                          $104 $113,222,097.67$52,836,97985.77%36.21%
                          $92 $98,663,067.32$46,042,76586.42%42.22%
                          $79 $84,823,330.43$39,584,22187.08%48.85%
                          $67 $71,702,887.00$33,461,34787.74%56.10%
                          $57 $59,301,737.04$27,674,14488.41%63.94%
                          $46 $47,619,880.54$22,222,61189.08%72.32%
                          $36 $36,657,317.50$17,106,74889.76%81.18%
                          $27 $26,414,047.93$12,326,55690.44%90.44%
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                            Posted: February 9, 2007, 1:22 am - IP Logged

                            The powerball jackpot has rolled over and is now valued at $17.5M cash and is advertised as a $37M annuity.  Fourth drawings average 15.3 M in sales.  If the next drawing is average, the probability of various numbers of winers is as follows:

                             

                            090.06%
                            19.42%
                            20.49%
                            30.02%

                             

                            The long term model suggests this for jackpot evolution:

                             

                            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                            $579,980,981.21$274,315,32927.19%0.27%
                            $353 $458,129,546.75$216,682,89437.72%0.99%
                            $300 $366,901,781.29$173,534,62648.19%2.62%
                            $245 $298,601,352.74$141,230,37057.90%5.43%
                            $218 $247,466,169.11$117,044,81066.42%9.38%
                            $196 $209,182,265.77$98,937,55873.61%14.13%
                            $180 $180,519,862.48$85,381,01679.51%19.19%
                            $158 $159,060,886.50$75,231,50083.84%24.14%
                            $132 $142,566,477.94$67,430,09184.48%28.79%
                            $119 $126,781,895.34$59,964,41085.12%34.08%
                            $104 $111,707,138.70$52,834,45785.77%40.04%
                            $92 $97,342,208.02$46,040,23486.42%46.68%
                            $79 $83,687,103.30$39,581,73887.08%54.01%
                            $67 $70,741,824.53$33,458,97187.74%62.03%
                            $57 $58,506,371.72$27,671,93388.41%70.70%
                            $46 $46,980,744.87$22,220,62389.08%79.96%
                            $36 $36,164,943.98$17,105,04189.76%89.76%
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                              Posted: February 11, 2007, 5:21 pm - IP Logged

                              Powerball rolled over.  The cash jackpot is $22M.  The advertised annuity is $46M.

                              Fifth draws sell on average 15.9M tickets.

                              If the sales are average the randomized probability of various numbers of winners will be as follows:

                               

                              089.68%
                              19.76%
                              20.53%
                              30.02%

                               

                              The long term model suggests the following for jackpot development:

                               

                              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                              $573,662,519.79$274,360,33627.19%0.30%
                              $353 $453,158,337.07$216,727,90037.72%1.10%
                              $300 $362,939,232.40$173,579,63348.19%2.92%
                              $245 $295,393,968.30$141,275,37657.90%6.05%
                              $218 $244,824,161.40$117,089,81666.42%10.45%
                              $196 $206,963,544.45$98,982,56573.61%15.73%
                              $180 $178,618,047.34$85,426,02379.51%21.37%
                              $158 $157,396,332.77$75,276,50783.84%26.88%
                              $132 $141,087,235.59$67,476,50484.48%32.06%
                              $119 $125,478,419.58$60,011,41885.12%37.95%
                              $104 $110,569,884.73$52,881,24985.77%44.58%
                              $92 $96,361,631.03$46,085,99786.42%51.98%
                              $79 $82,853,658.50$39,625,66387.07%60.15%
                              $67 $70,045,967.13$33,500,24587.74%69.08%
                              $57 $57,938,556.91$27,709,74588.40%78.74%
                              $46 $46,531,427.86$22,254,16189.07%89.07%
                                 
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