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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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June 5, 2002
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Posted: June 19, 2006, 5:49 pm - 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.

Mega Millions always starts at $12 million. It should be higher.

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    Morrison, IL
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    Posted: June 19, 2006, 10:48 pm - IP Logged

    Yeah, but remember the cash values of the two starting jackpots are roughly even now. Mega's cash value is also $6.8 million.

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      New Jersey
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      Posted: June 22, 2006, 5:39 am - IP Logged

      Powerball has rolled.  The cash prize is $9.1M, the advertised annuity is $20M.

      The average 2nd draw sells about 13.5M tickets.  If this is the number of tickets sold, the probability of numbers of winners is as follows:

       

      091.17%
      18.42%
      20.39%
      30.01%

      The long term probability function suggests the following jackpot evolution, caps, reserves, and minimums ignored:

       $2,419,184,970.48$1,103,148,3470.17%0.00%
      $1,797,780,713.22$819,788,0050.92%0.00%
      $1,342,968,437.65$612,393,6083.24%0.00%
      $1,010,086,575.96$460,599,4798.12%0.00%
      $766,446,859.55$349,499,76815.92%0.04%
      Average Jackpots$588,124,402.72$268,184,72826.06%0.25%
      $353 $457,608,331.36$208,669,39937.37%0.98%
      $300 $362,082,253.58$165,109,50848.65%2.61%
      $245 $292,165,718.08$133,227,56759.02%5.37%
      $208 $240,993,074.45$109,892,84267.98%9.09%
      $193 $203,539,281.32$92,813,91275.39%13.37%
      $173 $176,126,458.37$80,313,66581.32%17.74%
      $152 $156,062,726.53$71,164,60385.96%21.81%
      $126 $141,377,871.33$64,468,30985.44%25.38%
      $111 $126,110,666.03$57,506,46486.00%29.70%
      $99 $111,477,227.28$50,833,61686.57%34.53%
      $86 $97,477,555.08$44,449,76587.13%39.89%
      $75 $84,111,649.43$38,354,91287.70%45.78%
      $66 $71,379,510.33$32,549,05788.28%52.20%
      $55 $59,281,137.78$27,032,19988.86%59.13%
      $46 $47,816,531.77$21,804,33889.44%66.55%
      $35 $36,985,692.32$16,865,47690.03%74.41%
      $27 $26,788,619.42$12,215,61090.62%82.65%
      $20 $17,225,313.06$7,854,74391.21%91.21%


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        Posted: June 23, 2006, 1:40 am - IP Logged

        I hope PB and CA SLP continue to roll, but also hope that NY Lotto jackpot gets hit in next draw. In fact, CA SLP has been the highest jackpot in world when PB was hit twice during CA SLP run. CA SLP has tied the most number of rolls [no jackpot winners] with 20 and set a new roll 20 low of 82 million.

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          New Jersey
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          September 4, 2005
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          Posted: June 25, 2006, 12:35 am - IP Logged

          The powerball has rolled over.  The cash prize is $12.6M, advertised as a $28M annuity.  The MM has a slightly larger cash prize, but longer odds.

          The average number of tickets sold on 3rd draws is 15.0M.  If this is an average draw the probability for various numbers of winners will be as follows:

           

          090.24%
          19.26%
          20.48%
          30.02%

          The mixed linear/exponential model for jackpot evolution gives, irrespective of caps, reserves or minimums the following probability model for jackpot growth:

          Average Jackpots$588,237,447.74$268,236,27626.06%0.28%
          $353 $457,721,376.39$208,720,94837.37%1.07%
          $300 $362,195,298.61$165,161,05648.65%2.86%
          $245 $292,278,763.11$133,279,11659.02%5.88%
          $208 $241,106,119.47$109,944,39067.98%9.96%
          $193 $203,652,326.34$92,865,46175.39%14.65%
          $173 $176,239,503.40$80,365,21481.32%19.44%
          $152 $156,175,771.55$71,216,15285.96%23.90%
          $126 $141,490,916.36$64,519,85885.45%27.81%
          $111 $126,231,321.56$57,561,48386.01%32.54%
          $99 $111,602,396.78$50,890,69386.57%37.83%
          $86 $97,604,142.01$44,507,48987.13%43.70%
          $75 $84,236,557.27$38,411,87087.70%50.16%
          $66 $71,499,642.55$32,603,83788.27%57.19%
          $55 $59,393,397.84$27,083,38988.85%64.79%
          $46 $47,917,823.15$21,850,52789.43%72.92%
          $35 $37,072,918.48$16,905,25190.01%81.55%
          $27 $26,858,683.84$12,247,56090.60%90.60%

           

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            Morrison, IL
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            Posted: June 25, 2006, 1:39 am - IP Logged

            For some weird reason, at any given jackpot level, Powerball has higher sales for Saturday drawings than for Wednesday drawings.


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              Posted: June 28, 2006, 12:48 am - IP Logged

              I agree what you said ryanm. PB sales are doing well because they always win when it's at least 100+ million. MM has 4 winners under 100 million versus 0 for PB this year. I hope it rolls in PB and CA SLP, but NY Lotto jackpot gets hit. In the last PB run, did it reach 100 million Prob988 before jackpot was won?

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                Morrison, IL
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                Posted: June 28, 2006, 8:14 am - IP Logged

                That's the reverse of what's been happening at this time last year - last year Mega didn't get hit under $100 million this far into the year, while Powerball was won eight times under $100 million already.

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                  New Jersey
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                  Posted: June 29, 2006, 6:26 am - IP Logged

                  The powerball has rolled over.  The cash prize is $17.7, advertised as a $40M annuity. 

                  The average number of tickets sold on 3rd draws is 15.0M.  If this is an average draw the probability for various numbers of winners will be as follows:

                   

                  090.55%
                  18.99%
                  20.45%
                  30.01%

                   

                  The long term jackpot evolution from the mixed linear/exponential model, ignoring caps and reserves suggests the following:

                   

                  $353 $457,652,961.49$208,689,75037.37%1.18%
                  $300 $362,126,883.71$165,129,85948.65%3.16%
                  $245 $292,210,348.21$133,247,91959.02%6.49%
                  $208 $241,037,704.57$109,913,19367.98%11.00%
                  $193 $203,583,911.45$92,834,26475.39%16.18%
                  $173 $176,171,088.50$80,334,01681.32%21.46%
                  $152 $156,107,356.66$71,184,95585.96%26.39%
                  $126 $141,422,501.46$64,488,66185.45%30.70%
                  $111 $126,159,398.21$57,528,68686.01%35.93%
                  $99 $111,528,639.46$50,857,06086.57%41.78%
                  $86 $97,530,225.22$44,473,78387.13%48.26%
                  $75 $84,164,155.49$38,378,85587.70%55.38%
                  $66 $71,430,430.27$32,572,27688.28%63.15%
                  $55 $59,329,049.56$27,054,04788.85%71.53%
                  $46 $47,860,013.36$21,824,16689.43%80.51%
                  $35 $37,023,321.67$16,882,63590.02%90.02%
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                    New Jersey
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                    Posted: July 2, 2006, 1:06 am - IP Logged

                    The powerball has rolled over.  The cash prize is $22.5, advertised as a $50M annuity. 

                    The average number of tickets sold on 4rd draws is 15.7M.  If this is an average draw the probability 

                    089.80%
                    19.66%
                    20.52%
                    30.02%

                    The mixed linear exponential model predicts the following:

                     

                    $353 $457,888,155.04$208,796,99937.37%1.31%
                    $300 $362,362,077.26$165,237,10748.65%3.51%
                    $245 $292,445,541.76$133,355,16759.02%7.20%
                    $208 $241,272,898.12$110,020,44267.98%12.21%
                    $193 $203,819,104.99$92,941,51275.39%17.96%
                    $173 $176,406,282.05$80,441,26581.32%23.82%
                    $152 $156,342,550.21$71,292,20385.96%29.29%
                    $126 $141,657,695.01$64,595,90985.45%34.07%
                    $111 $126,397,607.06$57,637,30986.00%39.87%
                    $99 $111,765,751.84$50,965,18386.56%46.36%
                    $86 $97,762,129.35$44,579,53187.13%53.56%
                    $75 $84,386,739.60$38,480,35387.69%61.47%
                    $66 $71,639,582.58$32,667,65088.26%70.10%
                    $55 $59,520,658.29$27,141,42088.83%79.43%
                    $46 $48,029,966.74$21,901,66589.41%89.41%


                      United States
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                      Posted: July 2, 2006, 1:49 am - IP Logged

                      Prob988, if CA SLP doesn't roll after tonight's drawing, then PB takes the highest jackpot in USA. However, if CA SLP does roll after tonight's drawing, CA SLP still will have highest jackpot.


                        United States
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                        Posted: July 6, 2006, 1:00 am - IP Logged

                        Prob988, can you please use my quote when you post? PB Jackpot for 7/8 has rolled to 62 million.

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                          New Jersey
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                          Posted: July 28, 2006, 10:28 am - IP Logged

                          I accidentally placed this in the wrong thread.

                           

                          Powerball has rolled over.  The cash value is 70.7M, the annuity jackpot is $155M.    Although the upcoming roll is a 12th draw, the jackpot size is now equivalent to an average 13th draw.  The average sales for a thirteen draw are $28.9M.

                          If this is the number of tickets that sell, the randomized probability for various numbers of winner is:

                           

                           

                          082.04%
                          116.24%
                          21.61%
                          30.11%
                          40.01%

                           

                          A long term mixed linear/exponential model suggests that the jackpot may evolve in this way with the last column representing the probability of all the jackpots including that one rolling over:

                           

                          Average Jackpots$591,234,004.92$269,678,99526.06%0.84%
                          $353 $460,754,854.66$210,163,66637.37%3.22%
                          $300 $365,255,799.82$166,603,77448.65%8.62%
                          $245 $295,359,042.69$134,721,83459.02%17.72%
                          $208 $244,200,875.05$111,387,10967.98%30.03%
                          $193 $206,757,677.05$94,308,17975.39%44.17%
                          $173 $179,352,608.79$81,807,93281.32%58.58%
                          $152 $159,294,552.69$72,658,87084.58%72.04%

                           

                           

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                            July 19, 2005
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                            Posted: July 28, 2006, 8:35 pm - IP Logged

                            Prob988-

                            Thank you for posting these tables.

                            I look at them often,

                            I am happy you may have decided to continue posting them.

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                              New Jersey
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                              September 4, 2005
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                              Posted: July 30, 2006, 3:07 pm - IP Logged

                              Prob988-

                              Thank you for posting these tables.

                              I look at them often,

                              I am happy you may have decided to continue posting them.

                              Thanks.

                              I wasn't sure if I'd continue, or if anyone missed them, but here's today's comments on PB:

                               

                              The powerball has rolled over.  The cash value is $81M.  The advertised annuity jackpot is $178M.

                              The average sales for 14th draws are 33.5M.  If this is the number of tickets sold for this drawing, the randomized probability for various numbers of winners is:

                               

                              079.48%
                              118.25%
                              22.10%
                              30.16%
                              40.01%

                               

                               

                               The sales figures for last drawing have yet to be posted, and so the long term probability will have to wait.

                                 
                                Page 14 of 21