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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: October 29, 2006, 12:47 am - IP Logged

The Powerball jackpot has rolled over.  The cash value of the jackpot is $44M.  The advertised annuity value is $93.0M.  Ninth draws average 21.134M in sales.  If the number of tickets that sell in the next drawing is average then the randomized probability of various numbers of winners will be as follows:

 

086.53%
112.52%
20.91%
30.04%

 

The accuracy of the long term model is now off 5%, as compared to about 2% on the last draw.  Nevertheless, here is what it predicts for the long term evolution of the jackpot, ignoring minimums, caps and reserves:

 

Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
$575,244,860.08$272,158,85926.91%0.52%
$353 $452,456,871.62$214,065,61737.77%1.94%
$300 $361,387,475.42$170,979,02148.57%5.13%
$245 $293,843,124.98$139,022,55458.53%10.56%
$208 $243,746,830.65$115,321,08167.22%18.04%
$193 $206,591,410.70$97,742,17374.48%26.84%
$180 $179,033,978.56$84,704,24880.37%36.04%
$159 $158,595,182.08$75,034,28083.91%44.84%
$132 $142,186,021.79$67,270,80684.54%53.43%
$119 $126,478,449.98$59,839,26785.18%63.21%
$105 $111,472,466.65$52,739,66285.82%74.20%
$92 $97,168,071.81$45,971,99186.47%86.47%
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    New Jersey
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    Posted: November 2, 2006, 5:00 am - IP Logged

    The Powerball jackpot has had two winners.  The jackpot is reset at $7.1M cash, $15M advertised annuity.

    The average sales for a first drawing is $14.6M.  If this draw sells at the average value the probability of various numbers of winners is as follows:

     

    090.46%
    19.07%
    20.45%
    30.02%

     

    The long term jackpot evolution model program predicts the following evolution exclusive of reserves, minimums and caps:

     

    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
    $575,601,169.17$272,451,22027.11%0.21%
    $353 $453,565,388.16$214,687,61737.86%0.78%
    $300 $362,748,042.86$171,700,74048.54%2.07%
    $245 $295,163,026.90$139,710,49958.39%4.26%
    $208 $244,867,190.05$115,903,80367.01%7.29%
    $193 $207,437,721.87$98,187,18874.24%10.87%
    $180 $179,583,227.81$85,002,72880.11%14.65%
    $159 $158,854,297.46$75,191,03483.86%18.29%
    $132 $142,401,688.11$67,403,46684.50%21.80%
    $119 $126,654,586.76$59,949,83885.14%25.80%
    $105 $111,612,993.41$52,830,15085.78%30.31%
    $92 $97,276,908.06$46,044,40386.43%35.33%
    $79 $83,646,330.71$39,592,59787.09%40.87%
    $68 $70,721,261.37$33,474,73087.75%46.93%
    $57 $58,501,700.02$27,690,80588.41%53.49%
    $47 $46,987,646.68$22,240,81989.08%60.50%
    $36 $36,179,101.34$17,124,77589.76%67.91%
    $27 $26,076,064.00$12,342,67090.44%75.66%
    $20 $16,678,534.67$7,894,50691.12%83.66%
    $15 $7,986,513.33$3,780,28391.81%91.81%
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      Morrison, IL
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      Posted: November 2, 2006, 7:57 am - IP Logged

      Last night was the first time since the matrix change that Powerball had more than one winner for a draw.

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        Posted: November 2, 2006, 11:38 am - IP Logged

        Last night was the first time since the matrix change that Powerball had more than one winner for a draw.

        It was bound to happen eventually.  I don't think it will be all that common, though.

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          Posted: November 5, 2006, 1:45 am - IP Logged

          The Powerball jackpot has rolled.  The cash value is $9.4M.  The advertised annuity value is $20M.  Second round jackpots on average sell 14.3M in tickets.  If this number of tickets is sold for this draw, the randomized probability of various numbers of winners will be as follows:

           

          090.65%
          18.90%
          20.44%
          30.01%

           

          My mixed linear exponential model for long term probability of this run's continuance is as follows:

           

          Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
          $579,729,583.84$272,472,90427.11%0.23%
          $353 $456,828,300.84$214,709,30137.86%0.85%
          $300 $365,366,860.89$171,722,42548.54%2.25%
          $245 $297,302,518.58$139,732,18458.39%4.63%
          $208 $246,649,973.66$115,925,48867.01%7.93%
          $193 $208,955,048.26$98,208,87374.24%11.84%
          $180 $180,903,004.60$85,024,41280.11%15.95%
          $159 $160,027,060.56$75,212,71883.87%19.91%
          $132 $143,466,993.40$67,429,48784.51%23.74%
          $119 $127,615,308.46$59,979,19585.14%28.09%
          $105 $112,472,005.73$52,861,84385.79%32.99%
          $92 $98,037,085.21$46,077,43086.43%38.46%
          $79 $84,310,546.90$39,625,95787.09%44.49%
          $68 $71,292,390.80$33,507,42487.74%51.09%
          $57 $58,982,616.91$27,721,83088.41%58.23%
          $47 $47,381,225.24$22,269,17689.08%65.86%
          $36 $36,488,215.77$17,149,46189.75%73.94%
          $27 $26,303,588.51$12,362,68790.43%82.39%
          $20 $16,827,343.46$7,908,85191.11%91.11%
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            Posted: November 9, 2006, 1:08 am - IP Logged

            The Powerball jackpot has rolled.  The cash value is $9.4M.  The advertised annuity value is $20M.  Second round jackpots on average sell 14.3M in tickets.  If this number of tickets is sold for this draw, the randomized probability of various numbers of winners will be as follows:

             

             

            090.30%
            19.21%
            20.47%
            30.02%

             

             

            The long term modelling function suggests the following:

             

             

            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
            $570,262,480.93$272,458,74127.11%0.25%
            $353 $449,361,916.49$214,695,13837.86%0.93%
            $300 $359,389,383.71$171,708,26148.54%2.47%
            $245 $292,433,065.57$139,718,02058.39%5.09%
            $208 $242,605,096.97$115,911,32467.01%8.71%
            $193 $205,523,809.88$98,194,70974.24%13.00%
            $180 $177,928,427.40$85,010,24980.11%17.51%
            $159 $157,392,324.31$75,198,55583.87%21.86%
            $132 $141,097,750.74$67,413,37084.50%26.06%
            $119 $125,501,089.12$59,961,63185.14%30.84%
            $105 $110,602,339.45$52,843,34085.79%36.22%
            $92 $96,401,501.73$46,058,49586.43%42.22%
            $80 $82,898,575.96$39,607,09787.09%48.85%
            $68 $70,093,562.14$33,489,14687.75%56.09%
            $57 $57,986,460.27$27,704,64288.41%63.92%
            $47 $46,577,270.35$22,253,58589.08%72.30%
            $36 $35,865,992.38$17,135,97489.75%81.17%
            $27 $25,852,626.36$12,351,81090.43%90.43%
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              Posted: November 11, 2006, 8:26 am - IP Logged

              Sometimes, for ease, I cut and paste and change the numbers in the first sentence of my posts in this thread from previous entries.    The last time I forgot to change the relevant numbers.

              The cash jackpot is $12.9M.  The advertised annuity is $27M.  The average sales for a third drawing are $14.9M.

              If this is the average number of tickets that sell, the randomized distribution of probability of various numbers of winners is:

               

              090.30%
              19.21%
              20.47%
              30.02%

               

               

              The mixed linear/exponential model function suggests jackpot evolution as follows:

               

              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
              $570,262,480.93$272,458,74127.11%0.25%
              $353 $449,361,916.49$214,695,13837.86%0.93%
              $300 $359,389,383.71$171,708,26148.54%2.47%
              $245 $292,433,065.57$139,718,02058.39%5.09%
              $208 $242,605,096.97$115,911,32467.01%8.71%
              $193 $205,523,809.88$98,194,70974.24%13.00%
              $180 $177,928,427.40$85,010,24980.11%17.51%
              $159 $157,392,324.31$75,198,55583.87%21.86%
              $132 $141,097,750.74$67,413,37084.50%26.06%
              $119 $125,501,089.12$59,961,63185.14%30.84%
              $105 $110,602,339.45$52,843,34085.79%36.22%
              $92 $96,401,501.73$46,058,49586.43%42.22%
              $80 $82,898,575.96$39,607,09787.09%48.85%
              $68 $70,093,562.14$33,489,14687.75%56.09%
              $57 $57,986,460.27$27,704,64288.41%63.92%
              $47 $46,577,270.35$22,253,58589.08%72.30%
              $36 $35,865,992.38$17,135,97489.75%81.17%
              $27 $25,852,626.36$12,351,81090.43%90.43%

               

              The numerical data from my previous post was correct, but the opening paragraph was incorrect.  I apologize for my error.

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                Posted: November 12, 2006, 7:38 am - IP Logged

                Powerball has rolled.  The cash jackpot is $16.9M.  The advertised annuity is $35M.  The average sales for a fourth drawing are $15.5M.

                If  the average number of tickets sell, the randomized distribution of probability of various numbers of winners is:

                 

                089.96%
                19.52%
                20.50%
                30.02%

                 

                 

                The mixed linear/exponential model function suggests jackpot evolution as follows:

                 

                Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                $564,317,203.43$272,484,59327.11%0.28%
                $353 $444,688,439.80$214,720,99037.86%1.03%
                $300 $355,662,363.64$171,734,11348.54%2.73%
                $245 $289,410,385.47$139,743,87258.39%5.62%
                $208 $240,106,576.96$115,937,17667.01%9.63%
                $193 $203,415,362.58$98,220,56174.24%14.37%
                $180 $176,110,266.83$85,036,10080.11%19.36%
                $159 $155,790,191.13$75,224,40783.87%24.16%
                $132 $139,671,415.05$67,441,34084.51%28.81%
                $119 $124,241,791.51$59,991,03685.14%34.09%
                $105 $109,501,320.50$52,873,49585.79%40.04%
                $92 $95,450,002.03$46,088,71586.43%46.67%
                $80 $82,087,836.10$39,636,69887.09%54.00%
                $68 $69,414,822.71$33,517,44387.74%62.01%
                $57 $57,430,961.85$27,730,95088.41%70.67%
                $47 $46,136,253.54$22,277,22089.07%79.94%
                $36 $35,530,697.75$17,156,25189.74%89.74%
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                  Posted: November 16, 2006, 8:10 am - IP Logged

                  The Powerball Jackpot has rolled.    The cash jackpot is $21.5M, the advertised annuity is $45M.    Fifth round drawing sell 15.8M tickets on average.  If sales of average, he is the randomized probability of various numbers of winners:

                   

                  089.75%
                  19.71%
                  20.52%
                  30.02%

                   

                  The long term model suggests the following for jackpot evolution:

                   

                   

                  Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                  $570,263,911.22$272,459,42427.11%0.31%
                  $353 $449,363,346.79$214,695,82137.86%1.15%
                  $300 $359,390,814.00$171,708,94448.54%3.04%
                  $245 $292,434,495.86$139,718,70458.39%6.27%
                  $208 $242,606,527.26$115,912,00767.01%10.73%
                  $193 $205,525,240.18$98,195,39374.24%16.02%
                  $180 $177,929,857.69$85,010,93280.11%21.57%
                  $159 $157,393,754.60$75,199,23883.87%26.93%
                  $132 $141,101,969.94$67,415,38684.50%32.11%
                  $119 $125,507,614.07$59,964,74985.14%38.00%
                  $105 $110,610,687.00$52,847,32885.79%44.63%
                  $92 $96,411,188.72$46,063,12486.44%52.02%
                  $80 $82,909,119.24$39,612,13587.09%60.18%
                  $68 $70,104,478.55$33,494,36287.75%69.10%
                  $57 $57,997,266.66$27,709,80588.41%78.75%
                  $47 $46,587,483.56$22,258,46489.08%89.08%
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                    Posted: November 19, 2006, 12:53 am - IP Logged

                    The Powerball jackpot has rolled over.  The cash value is $26.1M; the advertised annuity is $54M.

                    On average, sixth drawings in a powerball jackpot run sell $16.89M in tickets. 

                    Were the average number of tickets to sell this time out, the randomized probability of various numbers of winners is as follows:

                     

                    089.08%
                    110.30%
                    20.60%
                    30.02%

                     

                    The model function for the long term evolution of jackpots suggests the following:

                     

                    Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                    $563,775,073.13$272,491,28527.11%0.35%
                    $353 $444,264,170.36$214,727,68237.86%1.29%
                    $300 $355,325,804.62$171,740,80648.54%3.41%
                    $245 $289,139,099.33$139,750,56558.39%7.03%
                    $208 $239,883,866.00$115,943,86967.01%12.04%
                    $193 $203,228,800.60$98,227,25474.24%17.97%
                    $180 $175,950,606.43$85,042,79380.11%24.21%
                    $159 $155,650,550.50$75,231,09983.87%30.22%
                    $132 $139,545,043.85$67,446,77184.50%36.03%
                    $119 $124,128,268.44$59,995,33085.14%42.64%
                    $105 $109,400,224.25$52,876,77585.78%50.08%
                    $92 $95,360,911.30$46,091,10786.43%58.38%
                    $80 $82,010,329.57$39,638,32687.08%67.55%
                    $68 $69,348,479.07$33,518,43287.74%77.57%
                    $57 $57,375,359.80$27,731,42488.40%88.40%
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                      Posted: November 23, 2006, 12:19 am - IP Logged

                      Powerball has rolled over.  The cash value is $31.1M; the advertised annuity is $64M.

                      Seventh draws on average sell $17.2M in tickets.

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

                       

                      088.91%
                      110.45%
                      20.61%
                      30.02%

                       

                      The function that I use to model long term probabilities suggests the following, ignoring minimums and caps:

                       

                      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                      $560,738,452.55$272,483,84227.11%0.40%
                      $353 $441,868,015.49$214,720,23937.86%1.46%
                      $300 $353,406,275.51$171,733,36248.54%3.86%
                      $245 $287,574,268.53$139,743,12158.39%7.96%
                      $208 $238,582,996.80$115,936,42567.01%13.63%
                      $193 $202,124,367.98$98,219,81074.24%20.33%
                      $180 $174,992,359.19$85,035,35080.11%27.39%
                      $159 $154,801,092.42$75,223,65683.87%34.19%
                      $132 $138,782,771.41$67,439,75384.50%40.76%
                      $119 $123,449,541.18$59,988,76185.14%48.24%
                      $105 $108,801,401.73$52,870,68185.79%56.66%
                      $92 $94,838,353.06$46,085,51286.43%66.05%
                      $80 $81,560,395.16$39,633,25587.09%76.41%
                      $68 $68,967,528.04$33,513,90887.74%87.74%
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                        Posted: November 26, 2006, 9:13 am - IP Logged

                        The Powerball jackpot has rolled over.  The cash jackpot is now $36M.  The advertised annuity is now $74M.    Eighth round jackpots sell on average, 18.6M tickets.    If this is the number of tickets that sell on this drawing the randomized probability of a rollover will be as follows:

                         

                        088.02%
                        111.23%
                        20.72%
                        30.03%

                         

                        Note that the last time, in error, I posted the long term probability starting from an eighth draw and not a seventh.  Thus the correct long term model function will look the same, with the numbers slightly adjusted to reflect the sales of the most recent drawing.

                         

                        Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                        $560,086,303.07$272,474,41827.11%0.40%
                        $353 $441,350,008.00$214,710,81537.86%1.46%
                        $300 $352,988,094.63$171,723,93848.54%3.86%
                        $245 $287,230,377.25$139,733,69758.39%7.96%
                        $208 $238,294,390.80$115,927,00167.01%13.63%
                        $193 $201,876,904.53$98,210,38674.24%20.34%
                        $180 $174,775,513.46$85,025,92580.11%27.39%
                        $159 $154,607,031.97$75,214,23283.87%34.19%
                        $132 $138,608,644.76$67,431,23384.51%40.77%
                        $119 $123,294,513.97$59,981,11585.14%48.24%
                        $105 $108,664,639.63$52,863,87985.79%56.66%
                        $92 $94,719,021.71$46,079,52486.43%66.05%
                        $80 $81,457,660.23$39,628,05187.09%76.41%
                        $68 $68,880,555.18$33,509,45987.74%87.74%

                         

                         

                        The model right now is showing itself being off by about 7% lower than the actual event, which is an unusally high inacurracy.  Still it is intended only to give a loose idea of the probability of the jackpot becoming very large.    The model ignores caps, which if I recall correctly is now set somewhere around $390M. 

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                          Posted: November 30, 2006, 8:41 am - IP Logged

                          The Powerball jackpot has been won.  The jackpot is reset at $7.3M cash and $15M in advertised annuity.  First round draws sell on average 14.7M tickets.  If this is the number of tickets that sell, the probability of various numbers of winners is:

                           

                          090.40%
                          19.12%
                          20.46%
                          30.02%

                           

                          The long term model program, which ignores reserves, minimums and caps suggests the following long term probability for jackpot evolution:

                           

                          Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                          $559,774,891.56$272,423,78127.11%0.21%
                          $353 $441,082,556.61$214,660,17837.86%0.78%
                          $300 $352,753,357.76$171,673,30148.54%2.07%
                          $245 $287,019,986.07$139,683,06058.39%4.26%
                          $208 $238,102,117.35$115,876,36467.01%7.29%
                          $193 $201,698,114.05$98,159,74974.24%10.88%
                          $180 $174,606,756.82$84,975,28880.11%14.66%
                          $159 $154,445,742.37$75,163,59583.89%18.30%
                          $132 $138,466,968.94$67,387,25884.52%21.81%
                          $119 $123,171,250.79$59,943,34285.15%25.81%
                          $105 $108,558,587.93$52,831,84685.80%30.31%
                          $92 $94,628,980.36$46,052,77086.44%35.32%
                          $80 $81,382,428.07$39,606,11587.10%40.86%
                          $68 $68,818,931.06$33,491,88087.75%46.92%
                          $57 $56,938,489.34$27,710,06588.41%53.46%
                          $47 $45,741,102.90$22,260,67089.08%60.47%
                          $36 $35,226,771.75$17,143,69689.75%67.88%
                          $27 $25,395,495.89$12,359,14190.43%75.63%
                          $20 $16,247,275.31$7,907,00791.11%83.64%
                          $15 $7,782,110.01$3,787,29491.80%91.80%
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                            Posted: December 3, 2006, 10:20 am - IP Logged

                            The Powerball jackpot has rolled over.  The cash jackpot is now $9.8M.  The advertised annuity is now $20M.    Second round drawings sell on average, 14.2M tickets.    If this is the number of tickets that sell on this drawing the randomized probability of a rollover will be as follows:

                             

                            090.68%
                            18.87%
                            20.43%
                            30.01%

                             

                            The model for long term jackpot evolution suggests the following:

                             

                            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                            $555,959,097.86$272,419,95827.11%0.23%
                            $353 $438,074,193.76$214,656,35537.86%0.85%
                            $300 $350,345,873.81$171,669,47848.54%2.25%
                            $245 $285,059,667.92$139,679,23758.39%4.64%
                            $208 $236,474,573.82$115,872,54167.01%7.94%
                            $193 $200,318,216.79$98,155,92674.24%11.85%
                            $180 $173,411,154.51$84,971,46680.11%15.97%
                            $159 $153,387,289.82$75,159,77283.88%19.93%
                            $132 $137,515,655.28$67,382,67184.52%23.76%
                            $119 $122,322,789.44$59,938,16785.15%28.12%
                            $105 $107,808,692.32$52,826,25985.80%33.02%
                            $92 $93,973,363.90$46,046,94886.44%38.48%
                            $80 $80,816,804.19$39,600,23487.10%44.52%
                            $68 $68,339,013.19$33,486,11687.75%51.11%
                            $57 $56,539,990.90$27,704,59688.42%58.25%
                            $47 $45,419,737.31$22,255,67189.08%65.88%
                            $36 $34,978,252.43$17,139,34489.75%73.95%
                            $27 $25,215,536.26$12,355,61390.43%82.39%
                            $20 $16,131,588.80$7,904,47991.11%91.11%
                              Avatar
                              New Jersey
                              United States
                              Member #21206
                              September 4, 2005
                              949 Posts
                              Offline
                              Posted: December 7, 2006, 8:55 am - IP Logged

                              The Powerball jackpot has rolled over.  The cash jackpot is now $12.9M.  The advertised annuity is $27M.  The average sales for a third drawing are $14.9M.

                              If this is the average number of tickets that sell, the randomized distribution of probability of various numbers of winners is:

                               

                              090.24%
                              19.26%
                              20.48%
                              30.02%

                               

                              The long term model was accurate this time out in predicting the current situation.    The Powerball sales seem to grow in linear for the first 12 draws or so and is somewhat easier to model than MM.

                              Here is the long term model for further jackpot evolution probabilities:

                               

                              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                              $553,665,337.32$272,403,34627.11%0.25%
                              $353 $436,259,640.15$214,639,74337.86%0.94%
                              $300 $348,887,939.39$171,652,86648.54%2.47%
                              $245 $283,867,124.57$139,662,62558.39%5.09%
                              $208 $235,479,530.85$115,855,92967.01%8.72%
                              $193 $199,470,150.89$98,139,31474.24%13.01%
                              $180 $172,672,466.91$84,954,85480.11%17.53%
                              $159 $152,730,000.04$75,143,16083.88%21.88%
                              $132 $136,918,227.21$67,363,76884.51%26.09%
                              $119 $121,783,672.92$59,917,56785.15%30.87%
                              $105 $107,326,337.19$52,804,55885.80%36.25%
                              $92 $93,546,220.00$46,024,74086.44%42.25%
                              $79 $80,443,321.36$39,578,11487.10%48.87%
                              $68 $68,017,641.27$33,464,68087.76%56.11%
                              $57 $56,269,179.73$27,684,43688.42%63.94%
                              $47 $45,197,936.74$22,237,38589.09%72.32%
                              $36 $34,803,912.29$17,123,52589.76%81.18%
                              $27 $25,087,106.40$12,342,85690.44%90.44%
                                 
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