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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: May 25, 2006, 9:09 am - IP Logged

The powerball jackpot has rolled over.  The cash value is 12.4 million.  The advertised annuity value is $28M.

 The average number of tickets sold for a second drawing in this matrix is 15.0M.  If this is the number of tickets sold in this drawing, the probability for various numbers of winners will be as follows:

090.24%
19.26%
20.48%
30.02%

 

The mixed linear/exponential modeling function predicts the following long term probabilities for jackpot evolution, ignoring reserves and caps:

Average Jackpots$603,589,292.64$267,162,47426.06%0.28%
$353 $469,128,735.57$207,647,14537.37%1.09%
$300 $370,715,647.44$164,087,25448.65%2.92%
$245 $298,686,078.87$132,205,31459.02%6.01%
$208 $245,966,884.22$108,870,58867.98%10.17%
$193 $207,381,154.24$91,791,65875.39%14.97%
$173 $179,139,854.87$79,291,41181.32%19.85%
$152 $158,469,752.46$70,142,34985.96%24.41%
$126 $143,341,088.31$63,446,05585.67%28.40%
$111 $127,871,666.39$56,598,93486.22%33.15%
$99 $113,043,031.97$50,035,44086.77%38.45%
$86 $98,855,185.05$43,755,57487.33%44.31%
$75 $85,308,125.62$37,759,33487.89%50.74%
$64 $72,401,853.68$32,046,72288.45%57.74%
$54 $60,136,369.24$26,617,73789.02%65.27%
$45 $48,511,672.30$21,472,38089.60%73.32%
$34 $37,527,762.85$16,610,64990.17%81.83%
$26 $27,184,640.89$12,032,54690.75%90.75%

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    New Jersey
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    Posted: May 28, 2006, 1:38 am - IP Logged

    The powerball jackpot has rolled over.  The cash value is 16.9 million.  The advertised annuity value is $38M.

     The average number of tickets sold for a fourth drawing in this matrix is 14.3M.  If this is the number of tickets sold in this drawing, the probability for various numbers of winners viewed as a random distribution will be as follows:

    090.68%
    18.87%
    20.43%
    30.01%

     

    The mixed linear/exponential model for powerball suggests, disregarding reserves and caps, the following probabilities for jackpot evolution:

    Average Jackpots$603,520,560.26$267,132,05126.06%0.31%
    $353 $469,060,003.20$207,616,72337.37%1.20%
    $300 $370,646,915.07$164,056,83148.65%3.22%
    $245 $298,617,346.50$132,174,89159.02%6.62%
    $208 $245,898,151.85$108,840,16667.98%11.21%
    $193 $207,312,421.86$91,761,23675.39%16.50%
    $173 $179,071,122.49$79,260,98981.32%21.88%
    $152 $158,401,020.09$70,111,92785.96%26.91%
    $126 $143,272,355.93$63,415,63385.66%31.30%
    $111 $127,799,409.28$56,566,95286.21%36.54%
    $99 $112,968,932.38$50,002,64286.77%42.38%
    $86 $98,780,925.24$43,722,70587.33%48.85%
    $75 $85,235,387.86$37,727,13987.89%55.93%
    $64 $72,332,320.23$32,015,94588.46%63.64%
    $54 $60,071,722.36$26,589,12389.03%71.94%
    $45 $48,453,594.24$21,446,67389.60%80.81%
    $34 $37,477,935.88$16,588,59590.18%90.18%

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      New Jersey
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      Posted: June 1, 2006, 6:18 am - IP Logged

      The powerball jackpot has rolled over.  The cash value is 21.3 million.  The advertised annuity value is $48M.

       The average number of tickets sold for a 5th drawing in this matrix is 15.3M.  If this is the number of tickets sold in this drawing, the probability for various numbers of winners viewed as a random distribution will be as follows:

      090.06%
      19.43%
      20.49%
      30.02%

      The mixed linear/exponential model for powerball suggests, disregarding reserves and caps, the following probabilities for jackpot evolution:

      Average Jackpots$603,612,793.79$267,172,87626.06%0.35%
      $353 $469,152,236.72$207,657,54737.37%1.33%
      $300 $370,739,148.59$164,097,65648.65%3.57%
      $245 $298,709,580.02$132,215,71659.02%7.34%
      $208 $245,990,385.37$108,880,99067.98%12.43%
      $193 $207,404,655.39$91,802,06175.39%18.29%
      $173 $179,163,356.01$79,301,81381.32%24.25%
      $152 $158,493,253.61$70,152,75285.96%29.83%
      $126 $143,364,589.46$63,456,45885.66%34.70%
      $111 $127,892,825.29$56,608,30086.21%40.50%
      $99 $113,061,918.40$50,043,80086.77%46.98%
      $86 $98,871,868.79$43,762,95887.33%54.15%
      $75 $85,322,676.46$37,765,77587.89%62.00%
      $64 $72,414,341.42$32,052,24988.45%70.55%
      $54 $60,146,863.66$26,622,38289.02%79.76%
      $45 $48,520,243.18$21,476,17389.59%89.59%

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        Posted: June 4, 2006, 12:15 pm - IP Logged

        The Powerball jackpot has rolled over.  The cash value is $26.9M, the advertised jackpot is $60M.

        The average number of tickets sold on a 6th drawing is 15.6M.  If this is how many tickets are sold, the probability of various numbers of winners will be as follows:

         

        089.87%
        19.60%
        20.51%
        30.02%

         

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          Posted: June 5, 2006, 8:55 pm - IP Logged

          The mixed linear/exponential modeling function predicts the following long term probabilities for jackpot evolution, ignoring reserves and caps:

          $353 $469,448,726.32$207,788,78137.37%1.49%
          $300 $371,035,638.19$164,228,88948.65%3.98%
          $245 $299,006,069.61$132,346,94959.02%8.18%
          $208 $246,286,874.97$109,012,22367.98%13.86%
          $193 $207,701,144.98$91,933,29475.39%20.39%
          $173 $179,459,845.61$79,433,04681.32%27.04%
          $152 $158,789,743.20$70,283,98585.96%33.25%
          $126 $143,661,079.05$63,587,69185.66%38.68%
          $111 $128,181,712.58$56,736,16886.20%45.16%
          $99 $113,340,093.36$50,166,92786.76%52.39%
          $86 $99,136,221.40$43,879,96787.31%60.38%
          $75 $85,570,096.68$37,875,28987.87%69.16%
          $64 $72,641,719.22$32,152,89288.43%78.70%
          $55 $60,351,089.01$26,712,77789.00%89.00%


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            Posted: June 6, 2006, 9:24 am - IP Logged

            Prob988, with PB rolling in the previous draw, it's now the current jackpot leader surpassing CA SLP. I would be surprised if both PB and CA SLP continue to roll.

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              Posted: June 8, 2006, 7:46 am - IP Logged

              The Powerball has rolled over.  The cash jackpot is $32.7M, the advertised annuity jackpot is $73M.  The average sales for 6th drawing is $15.9M.  If this is how many tickets are sold, the probabilities for various numbers of winners will be as follows:

               

              089.69%
              19.76%
              20.53%
              30.02%

               

              The mixed linear/exponential function gives the following model, ignoring caps and reserves, for jackpot evolution is as follows:

               

              Average Jackpots$604,123,614.19$267,398,97726.06%0.44%
              $353 $469,663,057.13$207,883,64837.37%1.67%
              $300 $371,249,969.00$164,323,75748.65%4.47%
              $245 $299,220,400.42$132,441,81759.02%9.18%
              $208 $246,501,205.78$109,107,09167.98%15.56%
              $193 $207,915,475.79$92,028,16175.39%22.88%
              $173 $179,674,176.42$79,527,91481.32%30.35%
              $152 $159,004,074.02$70,378,85285.96%37.32%
              $126 $143,875,409.86$63,682,55885.64%43.42%
              $111 $128,382,304.24$56,824,95486.19%50.70%
              $99 $113,526,196.46$50,249,30086.74%58.82%
              $86 $99,307,086.52$43,955,59687.30%67.81%
              $75 $85,724,974.43$37,943,84187.86%77.68%
              $66 $72,779,860.17$32,214,03688.42%88.42%

               

              The model is fairly accurate right now.  If it stays so, it suggests that there is about a 10% chance of hitting the cap.  There is a 90% chance of not hitting the cap.


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                Posted: June 11, 2006, 12:12 am - IP Logged

                Prob988, PB Jackpot has rolled to 86 million for 6/14.

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                  Posted: June 11, 2006, 8:37 am - IP Logged

                  The Powerball jackpot has rolled.  The cash value is $39M.  The advertised annuity jackpot is $86M.  Average sales for 8th drawings in a run are 17.1M.  If this is how many tickets are sold, the probability of various numbers of winners is as follows:

                  088.96%
                  110.41%
                  20.61%
                  30.02%

                  The mixed linear/exponential modelling function for Powerball jackpot evolution suggests, ignoring caps and reserves the following model evolution for the jackpot and probabilities for rollovers:

                   

                   

                   $769,897,866.67$349,139,73015.92%0.08%
                  Average Jackpots$590,587,777.77$267,824,69026.06%0.49%
                  $353 $459,348,848.17$208,309,36137.37%1.88%
                  $300 $363,293,702.88$164,749,47048.65%5.03%
                  $245 $292,989,937.34$132,867,53059.02%10.34%
                  $208 $241,533,875.98$109,532,80467.98%17.51%
                  $193 $203,872,646.46$92,453,87575.39%25.76%
                  $173 $176,307,998.65$79,953,62781.32%34.17%
                  $152 $156,133,144.60$70,804,56685.96%42.02%
                  $126 $141,366,957.90$64,108,27285.56%48.89%
                  $111 $126,148,779.36$57,207,00586.11%57.14%
                  $99 $111,555,618.76$50,589,17686.66%66.35%
                  $86 $97,587,476.11$44,254,78687.22%76.56%
                  $75 $84,244,351.41$38,203,83487.78%87.78%

                  Right now the model is functioning with reasonable accuracy.  It suggests that we have slightly less than even odds of seeing a jackpot of $70M cash, 156M advertised annuity.

                   


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                    Posted: June 14, 2006, 12:41 pm - IP Logged

                    I like these calculations. You probably need a computer to figure these out (a scientific calculator probably would not be as accurate).

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                      Posted: June 15, 2006, 7:53 am - IP Logged

                      I like these calculations. You probably need a computer to figure these out (a scientific calculator probably would not be as accurate).

                      I have built spreadsheets for these purposes.  They involved some work to set up, but they are easy to use now, if you know how to use them and maintain them.

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                        Posted: June 15, 2006, 8:00 am - IP Logged

                        The Powerball jackpot has rolled.  The cash value is $45.6M.  The advertised annuity jackpot is $100M.  Average sales for 8th drawings in a run are 19.8M.  If this is how many tickets are sold, the probability of various numbers of winners is as follows:

                        087.33%
                        111.83%
                        20.80%
                        30.04%

                        The mixed linear/exponential modelling programs suggests the following probability for long term jackpot evolutions:

                        Average Jackpots$587,565,399.78$267,929,82226.06%0.56%
                        $353 $457,049,328.43$208,414,49437.37%2.14%
                        $300 $361,523,250.65$164,854,60248.65%5.72%
                        $245 $291,606,715.15$132,972,66259.02%11.76%
                        $208 $240,434,071.51$109,637,93767.98%19.93%
                        $193 $202,980,278.39$92,559,00775.39%29.32%
                        $173 $175,567,455.44$80,058,76081.32%38.88%
                        $152 $155,503,723.60$70,909,69885.96%47.81%
                        $126 $140,818,868.40$64,213,40485.53%55.62%
                        $111 $125,651,996.96$57,297,31186.08%65.03%
                        $99 $111,109,119.29$50,665,75886.64%75.55%
                        $86 $97,190,235.39$44,318,74787.20%87.20%


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                          Posted: June 18, 2006, 2:05 am - IP Logged

                          Prob988, PB jackpot has reseted to 15 million for 6/21. Winning jackpot in PB was sold in Oklahoma. Once again, both MM and PB won one day apart.

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                            Posted: June 18, 2006, 11:13 am - IP Logged

                            The Powerball jackpot has been won.  The cash value is now $6.8M, the annuity is the base of $15M.

                            On average first draws sell 14.6 million tickets.  If this is how many tickets sell, the probability of various numbers of winners will be as follows:

                            090.49%
                            19.04%
                            20.45%
                            30.02%

                            The mixed linear/exponential model I have developed for the probability of long term jackpot evolution makes the following predictions, exclusive of jackpot minimums, reserves, and caps:

                            Average Jackpots$588,124,402.72$268,184,72826.06%0.23%
                            $353 $457,608,331.36$208,669,39937.37%0.90%
                            $300 $362,082,253.58$165,109,50848.65%2.40%
                            $245 $292,165,718.08$133,227,56759.02%4.93%
                            $208 $240,993,074.45$109,892,84267.98%8.35%
                            $193 $203,539,281.32$92,813,91275.39%12.28%
                            $173 $176,126,458.37$80,313,66581.32%16.29%
                            $152 $156,062,726.53$71,164,60385.96%20.03%
                            $126 $141,377,871.33$64,468,30985.44%23.30%
                            $111 $126,110,666.03$57,506,46486.00%27.27%
                            $99 $111,477,227.28$50,833,61686.57%31.71%
                            $86 $97,477,555.08$44,449,76587.13%36.63%
                            $75 $84,111,649.43$38,354,91287.70%42.03%
                            $66 $71,379,510.33$32,549,05788.28%47.93%
                            $55 $59,281,137.78$27,032,19988.86%54.29%
                            $46 $47,816,531.77$21,804,33889.44%61.10%
                            $35 $36,985,692.32$16,865,47690.03%68.31%
                            $27 $26,788,619.42$12,215,61090.62%75.88%
                            $20 $17,225,313.06$7,854,74391.21%83.74%
                            $15 $8,295,773.26$3,782,87391.81%91.81%


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                              Posted: June 18, 2006, 11:21 am - IP Logged

                              I would be surprised Prob988 to see PB's sales actually fall in this first drawing. However, I like the way PB announces guaranteed jackpots at the start like CA SLP.

                                 
                                Page 13 of 21