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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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United States
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Posted: September 25, 2006, 12:45 am - IP Logged

Prob988, congratulations to Iowa for winning the PB Jackpot in the last draw. The last PB jackpot was at 200.3 million (annunity). That's the 2nd straight PB Jackpot winner over 200 million (annunity). I would be shocked if PB wins their 2nd straight jackpot in a row in the next draw Prob988.


    United States
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    Posted: September 28, 2006, 11:15 am - IP Logged

    Prob988, PB Jackpot winner hit in Kansas in last draw. Still at 15 million for 9/30.

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      New Jersey
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      Posted: October 1, 2006, 1:21 am - IP Logged

      Powerball has been won for the third consecutive time.  My last entry is thus more or less applicable and I will not update it since it will not change very much.


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        Posted: October 1, 2006, 3:23 pm - IP Logged

        Prob988, it looks like PB finds a way to get three straight PB winners in a row after a string of 100+ jackpot winners.

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          Morrison, IL
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          Posted: October 1, 2006, 5:57 pm - IP Logged

          That could be good pulicity for the game.

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            New Jersey
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            Posted: October 5, 2006, 8:01 am - IP Logged

            Powerball has rolled over.  The cash jackpot is $9.7M, the advertised annuity $20M.  Sales on second round drawings average $14.0M.

            If average sales are obtained the distribution of probable numbers of winners is as follows:

             

            090.46%
            19.07%
            20.45%
            30.02%

             

            The projection model is as follows:

             

            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
            $560,640,221.97$271,910,50826.91%0.23%
            $353 $440,860,341.85$213,817,26637.77%0.87%
            $300 $352,021,999.49$170,730,67048.57%2.30%
            $245 $286,132,377.07$138,774,20358.53%4.73%
            $208 $237,263,361.42$115,072,73067.22%8.08%
            $193 $201,018,189.54$97,493,82274.48%12.02%
            $180 $174,135,870.19$84,455,89780.37%16.14%
            $159 $154,197,791.37$74,785,92983.91%20.08%
            $132 $138,190,581.65$67,022,43284.55%23.93%
            $119 $122,874,345.44$59,594,05885.19%28.31%
            $105 $108,249,082.77$52,500,80585.84%33.23%
            $92 $94,314,793.62$45,742,67586.49%38.71%
            $79 $81,071,478.00$39,319,66787.15%44.76%
            $68 $68,519,135.90$33,231,78187.81%51.36%
            $57 $56,657,767.34$27,479,01788.48%58.49%
            $47 $45,487,372.30$22,061,37689.15%66.10%
            $36 $35,007,950.78$16,978,85689.83%74.15%
            $27 $25,219,502.80$12,231,45990.51%82.54%
            $20 $16,122,028.34$7,819,18491.20%91.20%

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              Posted: October 8, 2006, 12:19 am - IP Logged

              Prob988, PB's jackpot for 10/11 is 27 million (estimated).

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                New Jersey
                United States
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                Posted: October 8, 2006, 1:23 am - IP Logged

                The Powerball jackpot has rolled.  The cash value is now $13.2M; the advertised annuity is $27.0M

                Third drawings average $14.9M.  If this is the number of tickets that sell on the next drawing, the randomized probability of various numbers of winners is as follows:

                 

                090.30%
                19.21%
                20.47%
                30.02%

                 

                The modeling program I use to estimate long term probabilities suggests the following jackpot evolution, ignoring reserves, minimums and caps:

                 

                Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                $556,327,378.75$271,982,27426.91%0.26%
                $353 $437,500,293.13$213,889,03237.77%0.95%
                $300 $349,368,619.40$170,802,43648.57%2.52%
                $245 $284,003,118.97$138,845,96958.53%5.18%
                $208 $235,522,834.14$115,144,49767.22%8.85%
                $193 $199,565,976.12$97,565,58874.48%13.17%
                $180 $172,897,493.40$84,527,66380.37%17.68%
                $159 $153,118,012.94$74,857,69583.93%22.00%
                $132 $137,258,380.86$67,104,09784.56%26.22%
                $119 $122,078,969.35$59,683,05285.20%31.00%
                $105 $107,579,778.40$52,594,55885.84%36.39%
                $92 $93,760,808.02$45,838,61786.49%42.39%
                $79 $80,622,058.20$39,415,22887.14%49.01%
                $68 $68,163,528.95$33,324,39287.80%56.25%
                $57 $56,385,220.26$27,566,10888.46%64.06%
                $47 $45,287,132.14$22,140,37689.13%72.42%
                $36 $34,869,264.58$17,047,19689.80%81.25%
                $27 $25,131,617.59$12,286,56990.48%90.48%
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                  New Jersey
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                  Posted: October 12, 2006, 8:25 am - IP Logged

                  The Powerball jackpot has rolled.  The cash value is now $18M; the advertised annuity is $37.0M

                  Fourth drawings average $15.2M.  If this is the number of tickets that sell on the next drawing, the randomized probability of various numbers of winners is as follows:

                   

                  090.11%
                  19.39%
                  20.49%
                  30.02%

                   

                  The mixed linear/exponential modeling function I use for powerball suggests the following jackpot evolution probabilities:

                   

                  Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover Probability
                  $559,076,488.52$271,983,15726.91%
                  $353 $439,662,602.49$213,889,91537.77%
                  $300 $351,095,710.61$170,803,31948.57%
                  $245 $285,407,417.59$138,846,85258.53%
                  $208 $236,687,723.94$115,145,37967.22%
                  $193 $200,553,301.19$97,566,47174.48%
                  $180 $173,753,122.26$84,528,54680.37%
                  $159 $153,875,965.36$74,858,57883.93%
                  $132 $137,938,162.80$67,105,05284.56%
                  $119 $122,683,891.89$59,684,05685.20%
                  $105 $108,113,152.61$52,595,58885.84%
                  $92 $94,225,944.97$45,839,64986.49%
                  $79 $81,022,268.98$39,416,23987.14%
                  $68 $68,502,124.62$33,325,35887.80%
                  $57 $56,665,511.90$27,567,00688.46%
                  $47 $45,512,430.82$22,141,18389.13%
                  $36 $35,042,881.38$17,047,88889.80%

                   

                   

                  As always, caps, minimums and reserves are ignored.

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                    New Jersey
                    United States
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                    Posted: October 15, 2006, 8:58 am - IP Logged

                    The Powerball jackpot has rolled.  The cash value is now $22.4M; the advertised annuity is $47.0M

                    Fifth drawings average $15.8M in sales.  If this is the number of tickets that sell on the next drawing, the randomized probability of various numbers of winners is as follows:

                     

                    089.76%
                    19.70%
                    20.52%
                    30.02%

                     

                    Lottoreport has not yet updated the sales figures for the last drawing and I will delay the long term probability files until they do so.

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                      New Jersey
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                      Posted: October 18, 2006, 7:24 am - IP Logged

                      Here are the long term jackpot evolution figures:

                       

                      Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                      $570,829,869.13$272,055,08726.91%0.31%
                      $353 $448,937,799.17$213,961,84537.77%1.17%
                      $300 $358,532,887.82$170,875,24948.57%3.10%
                      $245 $291,481,372.50$138,918,78258.53%6.37%
                      $208 $241,750,604.13$115,217,30967.22%10.89%
                      $193 $204,866,287.47$97,638,40174.48%16.20%
                      $180 $177,509,927.22$84,600,47680.37%21.75%
                      $159 $157,220,261.75$74,930,50883.93%27.06%
                      $132 $140,956,420.03$67,179,23084.56%32.25%
                      $119 $125,387,574.22$59,759,18485.20%38.13%
                      $105 $110,513,724.31$52,670,37185.84%44.76%
                      $92 $96,334,870.31$45,912,78986.48%52.14%
                      $79 $82,851,012.21$39,486,44087.13%60.29%
                      $68 $70,062,150.02$33,391,32387.79%69.19%
                      $57 $57,968,283.73$27,627,43788.45%78.82%
                      $47 $46,569,413.34$22,194,78489.11%89.11%
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                        New Jersey
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                        Posted: October 19, 2006, 7:19 am - IP Logged

                        The PB jackpot has rolled over.  The cash jackpot is $27.7M; the advertised annuity is $59M.

                        The average sales for a 6th draw are 16.7M.    This suggests a randomized probability for various numbers of winners as follows:

                         

                        089.22%
                        110.18%
                        20.58%
                        30.02%

                         

                        The long term linear/exponential function suggests the following probability for jackpot evolution, ignoring reserves, caps and minimums:

                         

                        Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                        $579,479,569.67$272,060,74726.91%0.35%
                        $353 $455,743,061.75$213,967,50537.77%1.31%
                        $300 $363,970,167.64$170,880,90948.57%3.47%
                        $245 $295,904,046.86$138,924,44258.53%7.15%
                        $208 $245,420,765.90$115,222,97067.22%12.22%
                        $193 $207,978,325.71$97,644,06174.48%18.18%
                        $180 $180,208,016.38$84,606,13780.37%24.41%
                        $159 $159,611,333.16$74,936,16883.93%30.37%
                        $132 $143,101,211.42$67,184,80684.56%36.18%
                        $119 $127,296,477.49$59,764,61785.20%42.79%
                        $105 $112,197,131.38$52,675,60285.84%50.22%
                        $92 $97,803,173.08$45,917,76186.48%58.51%
                        $79 $84,114,602.60$39,491,09387.13%67.65%
                        $68 $71,131,419.92$33,395,59987.79%77.64%
                        $57 $58,853,625.07$27,631,27888.45%88.45%
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                          New Jersey
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                          Posted: October 22, 2006, 8:56 am - IP Logged

                          The PB jackpot has rolled over.  The cash value is estimated at 32.6 million; the advertised annuity is $70M.    The average 7th drawing in Powerball sells 17.1M in tickets, implying that if the current draw sells the average number of tickets, and the tickets are chosen in a random fashion, then the probability of various numbers of winners for this drawing will be:

                           

                          088.95%
                          110.41%
                          20.61%
                          30.02%

                           

                           

                          Lottoreport has not yet posted the sales figures for Powerball's last draw.  I will update the long term values from the modelling function when they have done so.

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                            New Jersey
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                            Posted: October 22, 2006, 11:58 am - IP Logged

                            Here is the mixed linear/exponential modeling function I use to approximate the long term evolution of the probability of rollovers for PB.  The model is exclusive of caps, reserves and minimums.   

                             

                            Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                            $584,179,518.35$272,060,74726.91%0.40%
                            $353 $459,439,428.48$213,967,50537.77%1.48%
                            $300 $366,922,197.70$170,880,90948.57%3.93%
                            $245 $298,304,017.30$138,924,44258.53%8.09%
                            $208 $247,411,284.75$115,222,97067.22%13.82%
                            $193 $209,665,162.49$97,644,06174.48%20.55%
                            $180 $181,669,618.26$84,606,13780.37%27.60%
                            $159 $160,905,882.81$74,936,16883.93%34.34%
                            $132 $144,261,853.46$67,184,80684.56%40.91%
                            $119 $128,328,933.07$59,764,61785.20%48.38%
                            $105 $113,107,121.63$52,675,60285.84%56.78%
                            $92 $98,596,419.16$45,917,76186.48%66.15%
                            $79 $84,796,825.64$39,491,09387.13%76.49%
                            $68 $71,708,341.08$33,395,59987.79%87.79%
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                              New Jersey
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                              Posted: October 26, 2006, 9:14 am - IP Logged

                              The Powerball jackpot has rolled over.  The cash value of the jackpot is $38.8M.  The advertised annuity value is $83.0M.  Eighth draws average 18.4M 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:

                               

                              088.16%
                              111.11%
                              20.70%
                              30.03%

                               

                              The mixed linear/exponential model I use to suggest the probability of long term behavior of the Powerball, exclusive of reserves, caps and minimums, is operating in a region where it seems to be fairly accurate and predictive within 1 or 2 percent.    It suggests the following long term probability:

                               

                              Average Historical AnnuityCalculated AnnuityCalculated Cash Value ProjectionsSingle Draw Rollover ProbabilityOverall Probability from baseline
                              $582,033,448.00$272,083,10626.91%0.45%
                              $353 $457,761,822.38$213,989,86437.77%1.69%
                              $300 $365,592,042.18$170,903,26848.57%4.47%
                              $245 $297,231,558.91$138,946,80158.53%9.21%
                              $208 $246,529,955.18$115,245,32867.22%15.73%
                              $193 $208,925,589.35$97,666,42074.48%23.41%
                              $180 $181,035,183.03$84,628,49580.37%31.43%
                              $159 $160,349,426.26$74,958,52783.93%39.10%
                              $132 $143,763,317.58$67,205,02184.56%46.59%
                              $119 $127,885,798.48$59,782,75985.19%55.10%
                              $105 $112,716,868.94$52,691,74185.83%64.68%
                              $92 $98,256,528.98$45,931,96886.48%75.35%
                              $79 $84,504,778.58$39,503,43987.13%87.13%

                               

                              If the model continues to be accurate - generally it doesn't break down too badly unless the jackpots are very large or are relatively small - there is a better than even chance of seeing a jackpot of $144M as the advertised annuity.

                                 
                                Page 17 of 21