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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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Posted: July 31, 2006, 11:46 pm - IP Logged

Here is the probability table for the jackpot evolution of powerball:

 

$353 $461,830,178.89$210,654,15337.37%4.47%
$300 $366,331,124.05$167,094,26148.65%11.97%
$245 $296,434,366.92$135,212,32159.02%24.60%
$208 $245,276,199.27$111,877,59567.98%41.68%
$193 $207,833,001.28$94,798,66675.39%61.31%
$173 $180,427,933.02$82,298,41881.32%81.32%
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    New Jersey
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    Posted: August 3, 2006, 7:51 am - IP Logged

    The Powerball jackpot has rolled.  The cash value is $92.7M; the advertised annuity jackpot is $204M.  The average number of tickets sold on a 15th draw is 40M.  If this is the number of tickets that sell, the probability distribution for numbers of winners is:

     

    076.58%
    120.43%
    22.73%
    30.24%
    40.02%

     The long term probability looks like this, ignoring caps: 

     

    Average Jackpots$592,077,809.46$270,063,87826.37%1.44%
    $353 $462,750,509.21$211,073,94237.53%5.47%
    $300 $367,667,252.13$167,703,70848.65%14.57%
    $245 $297,760,699.09$135,817,30058.88%29.95%
    $208 $246,364,414.30$112,373,96267.74%50.87%
    $193 $208,577,140.09$95,138,08975.10%75.10%
     

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      Posted: August 4, 2006, 12:40 am - IP Logged

      Prob988, I hope PB continues to roll, set new roll records, and hit the cap annunity value of 390 million.


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        Posted: August 6, 2006, 2:16 am - IP Logged

        Prob988, I hope PB continues to roll, set new roll records, and hit the cap annunity value of 390 million.

        Prob988, PB Jackpot for 8/9 has reseted to 15 million. Someone in Wisconsin won jackpot.

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          Posted: August 7, 2006, 8:57 am - IP Logged

          The Powerball jackpot has been won, and the cash value has been reset at $6.9M, and the advertised set annuity value is now $15M.  First drawing Powerball Sales average 14.5M.  If this is how many tickets sell, the probability for randomized tickets of total numbers of winners is as follows:

           

          090.52%
          19.01%
          20.45%
          30.01%

           

          Long term jackpot evolution, ignoring minimums, caps and reserves, is modelled by a mixed linear/exponential function that suggests the following:

           

          Average Jackpots$592,612,786.04$270,307,89726.78%0.22%
          $353 $464,787,607.25$212,003,12237.71%0.83%
          $300 $370,156,459.57$168,839,10848.57%2.20%
          $245 $300,099,416.05$136,884,05658.59%4.54%
          $208 $248,234,998.62$113,227,19067.32%7.74%
          $193 $209,838,890.81$95,713,61074.60%11.50%
          $173 $181,413,601.02$82,748,01080.50%15.41%
          $152 $160,369,876.92$73,149,35784.35%19.15%
          $126 $143,858,001.05$65,617,81184.96%22.70%
          $112 $128,042,080.44$58,403,71085.57%26.72%
          $102 $112,922,115.07$51,507,05586.19%31.23%
          $90 $98,498,104.95$44,927,84586.81%36.23%
          $78 $84,770,050.07$38,666,08187.43%41.74%
          $67 $71,737,950.45$32,721,76288.06%47.74%
          $56 $59,401,806.07$27,094,88888.69%54.21%
          $46 $47,761,616.94$21,785,46089.33%61.12%
          $36 $36,817,383.06$16,793,47789.98%68.42%
          $27 $26,569,104.42$12,118,94090.62%76.04%
          $20 $17,016,781.03$7,761,84891.28%83.91%
          $15 $8,160,412.89$3,722,20191.93%91.93%
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            Posted: August 8, 2006, 9:48 am - IP Logged

            Here is a slightly different way of looking at the long term probability, by rejecting any modelling function and looking at the actual accumulated sales data since the matrix change.  When one does this this is what the data looks like, ignoring the presence of caps, minimum and reserves:

             

            Drawing NumberCalculated AnnuityCash Value AveragesSingle Draw Rollover ProbabilityOverall Probability from baseline
            19$460,038,075.25$209,836,722.0732.69%0.87%
            18$351,544,295.82$160,349,559.4552.87%2.67%
            17$289,706,256.33$132,143,434.3464.38%5.05%
            16$246,987,847.66$112,658,327.9371.52%7.84%
            15$214,467,262.07$97,824,744.7076.58%10.96%
            14$188,580,927.76$86,017,236.0877.64%14.32%
            13$164,024,357.05$74,816,271.2581.23%18.44%
            12$143,858,001.05$65,617,810.8083.40%22.70%
            11$126,245,498.10$57,584,236.8885.04%27.22%
            10$110,520,530.77$50,411,622.7486.61%32.01%
            9$96,578,358.57$44,052,193.2386.82%36.96%
            8$82,866,263.65$37,797,708.6588.48%42.57%
            7$70,992,010.15$32,381,516.8989.07%48.11%
            6$59,764,774.30$27,260,448.6789.46%54.01%
            5$48,961,535.70$22,332,777.9089.85%60.37%
            4$38,575,439.90$17,595,378.0790.33%67.19%
            3$28,705,422.66$13,093,376.6690.32%74.39%
            2$18,828,544.33$8,588,245.7090.98%82.36%
            1$9,659,027.24$4,405,762.7590.52%90.52%

             

            The annuity calculations are the weakest, since they depend on financial factors not affected by sales.  (An Argentine style collapse of the US currency under a spiral of debt accumulated for arbitrary wars, for instance, would affect interest rates.)

            We see that on averate we have a chance that is slightly lower than half a chance on any reset jackpot of reaching an eigth draw, which on average compares to a $37.78M cash jackpot.

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              Posted: August 10, 2006, 11:09 am - IP Logged

              Powerball has rolled over.  The cash value is $9.2M, the advertised annuity is $20M.  Second drawings have sold at an average of $13.8M.  If this is how many tickets sell, the distribution of winners will have the following probability:

               

              090.98%
              18.60%
              20.41%
              30.01%

               

               

              The long term mixed linear/exponential modeling function gives the following predictions for jackpot evolution:

               

               

              Average Jackpots$592,590,519.86$270,297,74026.78%0.24%
              $353 $464,765,341.07$211,992,96537.71%0.90%
              $300 $370,134,193.39$168,828,95148.57%2.40%
              $245 $300,077,149.87$136,873,90058.59%4.93%
              $208 $248,212,732.44$113,217,03367.32%8.42%
              $193 $209,816,624.63$95,703,45474.60%12.51%
              $173 $181,391,334.84$82,737,85480.50%16.77%
              $152 $160,347,610.74$73,139,20184.35%20.83%
              $126 $143,831,281.64$65,605,62384.95%24.70%
              $112 $128,011,935.45$58,389,96085.57%29.07%
              $102 $112,889,572.19$51,492,21186.18%33.98%
              $90 $98,464,191.84$44,912,37786.81%39.42%
              $78 $84,735,794.41$38,650,45687.43%45.41%
              $67 $71,704,379.90$32,706,44988.06%51.94%
              $56 $59,369,948.30$27,080,35788.70%58.98%
              $46 $47,732,499.63$21,772,17989.34%66.50%
              $36 $36,792,033.87$16,781,91589.98%74.44%
              $27 $26,548,551.02$12,109,56590.63%82.73%
              $20 $17,002,051.10$7,755,12991.28%91.28%

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                Posted: August 13, 2006, 12:27 pm - IP Logged

                Prob988, PB's estimated jackpot for 8/16 has rolled to 29 million.

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                  Posted: August 14, 2006, 10:36 pm - IP Logged

                  The Powerball jackpot has rolled.  The cash value is $13.2M and the advertised annuity value is $29M.

                  The average 3rd draw jackpot has sales of 14.9M.  If this is the number of tickets that sell, the randomized probability distribution for numbers of winners is as follows:

                   

                  090.32%
                  19.19%
                  20.47%
                  30.02%

                   

                  The mixed linear/exponential modeling function suggests the following long term probabilities, ignoring reserves, minimums and caps:

                   

                  Average Jackpots$592,747,107.53$270,369,16526.78%0.26%
                  $353 $464,921,928.74$212,064,38937.71%0.99%
                  $300 $370,290,781.05$168,900,37648.57%2.62%
                  $245 $300,233,737.54$136,945,32458.59%5.40%
                  $208 $248,369,320.11$113,288,45867.32%9.22%
                  $193 $209,973,212.29$95,774,87874.60%13.70%
                  $173 $181,547,922.51$82,809,27880.50%18.36%
                  $152 $160,504,198.40$73,210,62584.37%22.80%
                  $126 $144,009,467.60$65,686,89984.97%27.03%
                  $112 $128,206,112.47$58,478,53085.58%31.81%
                  $102 $113,094,133.00$51,585,51786.19%37.17%
                  $90 $98,673,529.20$45,007,86186.80%43.13%
                  $78 $84,944,301.07$38,745,56287.43%49.69%
                  $67 $71,906,448.60$32,798,61988.05%56.83%
                  $56 $59,559,971.80$27,167,03288.68%64.55%
                  $46 $47,904,870.67$21,850,80289.31%72.79%
                  $36 $36,941,145.20$16,849,92989.95%81.49%
                  $27 $26,668,795.40$12,164,41290.60%90.60%

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                    Posted: August 17, 2006, 12:42 am - IP Logged

                    Prob988, PB Jackpot for 8/19 has rolled to 40 million.

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                      Posted: August 17, 2006, 6:27 am - IP Logged

                      Powerball has rolled.  The new cash jackpot is $18.4M.  The advertised annuity is $40M.  The average sales for 4th round drawing is 14.9M.  If this is how many tickets the randomized distribution of winners is as follows:

                       

                      090.30%
                      19.21%
                      20.47%
                      30.02%

                       

                      The mixed linear/exponential model gives the following results:

                       

                      Average Jackpots$592,764,980.11$270,377,31726.78%0.29%
                      $353 $464,939,801.32$212,072,54237.71%1.09%
                      $300 $370,308,653.63$168,908,52848.57%2.90%
                      $245 $300,251,610.12$136,953,47658.59%5.96%
                      $208 $248,387,192.68$113,296,61067.32%10.18%
                      $193 $209,991,084.87$95,783,03074.60%15.12%
                      $173 $181,565,795.08$82,817,43080.50%20.26%
                      $152 $160,522,070.98$73,218,77784.37%25.17%
                      $126 $144,028,805.15$65,695,72084.97%29.83%
                      $112 $128,226,441.68$58,487,80385.58%35.11%
                      $102 $113,114,980.59$51,595,02786.19%41.03%
                      $90 $98,694,421.86$45,017,39186.80%47.60%
                      $78 $84,964,765.51$38,754,89687.42%54.84%
                      $67 $71,926,011.52$32,807,54288.05%62.73%
                      $56 $59,578,159.91$27,175,32888.68%71.24%
                      $46 $47,921,210.66$21,858,25589.31%80.34%
                      $36 $36,955,163.79$16,856,32389.95%89.95%

                       

                      These projections ignore caps, reserves and minimums.


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                        Posted: August 20, 2006, 12:06 am - IP Logged

                        PB has rolled to 51 million Prob988. I hope it continues to roll and set new records.

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                          Posted: August 22, 2006, 11:42 pm - IP Logged

                          Powerball, as we know, rolled last Saturday night.  The cash jackpot is $23.3M and the advertised annuity jackpot is $51M.

                          Powerball's fifth drawings average 15.6M in sales.  The randomized probability of various numbers of winners will be, if this is the number of tickets sold:

                           

                          089.85%
                          19.62%
                          20.51%
                          30.02%

                           

                          The mixed linear/exponential modeling function suggests the following probabilities of jackpot evolution:

                           

                          Average Jackpots$592,994,190.94$270,481,86626.78%0.32%
                          $353 $465,169,012.15$212,177,09137.71%1.21%
                          $300 $370,537,864.46$169,013,07848.57%3.22%
                          $245 $300,480,820.95$137,058,02658.59%6.62%
                          $208 $248,616,403.51$113,401,16067.32%11.30%
                          $193 $210,220,295.70$95,887,58074.60%16.79%
                          $173 $181,795,005.91$82,921,98080.50%22.51%
                          $152 $160,751,281.81$73,323,32784.37%27.96%
                          $126 $144,265,178.81$65,803,53684.97%33.14%
                          $112 $128,465,845.78$58,597,00285.58%39.00%
                          $102 $113,353,282.71$51,703,72386.18%45.57%
                          $90 $98,927,489.60$45,123,70086.80%52.87%
                          $78 $85,188,466.46$38,856,93387.41%60.92%
                          $67 $72,136,213.28$32,903,42188.03%69.69%
                          $56 $59,770,730.06$27,263,16588.66%79.16%
                          $47 $48,092,016.81$21,936,16589.29%89.29%

                           

                          As usual this ignores caps, reserves and minimums. 


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                            Posted: August 24, 2006, 11:33 am - IP Logged

                            Prob988, PB Jackpot is now 64 million for 8/26. What's your probability stats now?

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                              Posted: August 24, 2006, 4:17 pm - IP Logged

                              The powerball jackpot has rolled.  The cash value is $29.4M, the advertised annuity is $64 million dollars.

                              The average 6th round drawing sells 16.3M tickets.  If this is how many tickets sell on this drawing the distribution of winners will have the following random probability:

                               

                              089.46%
                              19.96%
                              20.55%
                              30.02%

                               

                              My model of jackpot evolution gives the following probability:

                               

                              Average Jackpots$580,995,539.01$270,526,04826.78%0.36%
                              $353 $455,777,230.07$212,221,27337.71%1.36%
                              $300 $363,075,992.34$169,057,25948.57%3.60%
                              $245 $294,447,693.90$137,102,20758.59%7.41%
                              $208 $243,641,000.68$113,445,34167.32%12.65%
                              $193 $206,027,944.04$95,931,76174.60%18.80%
                              $173 $178,182,360.31$82,966,16280.50%25.20%
                              $152 $157,567,802.44$73,367,50884.37%31.30%
                              $126 $141,416,501.22$65,847,05884.97%37.10%
                              $112 $125,936,983.51$58,639,40885.57%43.66%
                              $102 $111,129,249.30$51,744,55786.18%51.02%
                              $90 $96,993,298.59$45,162,50586.79%59.20%
                              $78 $83,529,131.40$38,893,25287.41%68.21%
                              $67 $70,736,747.70$32,936,79888.03%78.04%
                              $56 $58,616,147.52$27,293,14488.65%88.65%
                                 
                                Page 15 of 21