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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: September 30, 2005, 4:05 pm - IP Logged

If the cash value % stays below 50% of the annuity, a $340 million jackpot (which would trigger the Match 5 bonus) would yield a cash value SLIGHTLY LESS than what Jack won.

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    New Jersey
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    Posted: October 2, 2005, 12:46 am - IP Logged

    The powerball has rolled again.  The new reported cash value is said to be 88.7 million dollars, only 4.4 million more than the last jackpot.  This seems to be in error, since this would suggest that the lottery is expecting to sell only 13 million tickets after just having sales of 33.4 million.

    I will post the rollover odds for 33.4 million in sales, which assumes that the jackpot will sell just like the last one:

     

    079.56%
    118.19%
    22.08%
    30.16%
    40.01%


     

    I will update this post if there is clarification.

     

     

     

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      Morrison, IL
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      Posted: October 2, 2005, 1:28 am - IP Logged

        Yeah, the cash value option should have increased by at least $12 million.

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        New Jersey
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        Posted: October 4, 2005, 4:27 pm - IP Logged

        The powerball has rolled again.  The new reported cash value is said to be 88.7 million dollars, only 4.4 million more than the last jackpot.  This seems to be in error, since this would suggest that the lottery is expecting to sell only 13 million tickets after just having sales of 33.4 million.

        I will post the rollover odds for 33.4 million in sales, which assumes that the jackpot will sell just like the last one:

         

        079.56%
        118.19%
        22.08%
        30.16%
        40.01%


         

        I will update this post if there is clarification.

         

         

         

        Based on a change in the structure of the Powerball prizes, alertly caught by RyanM and posted on another thread, it is now possible to make a slight correction to the above post.  I estimated that the current jackpot would sell at about the same level as the last jackpot.  However from the new prize structure it is now possible to refine the expected sales as being around 34.4 million.

        If this should pan out, then the probabilities will be given in the following table.

        079.00%
        118.63%
        22.20%
        30.17%
        40.01%


        This is only slightly different than my last estimation.

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          New Jersey
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          Posted: October 6, 2005, 8:40 am - IP Logged

          The powerball has rolled over again with the cash value predicted to be $101.7M.  The calculated cash jackpot for the last run, using the rules pasted on the Iowa website (cash value = 0.2986451 of sales = 0.65771*0.493) was about $89.2M.  This suggests that the lottery expects to sell for this jackpot advertised at $205M annuity, $41.7M in tickets.  The probability distribution for the likely number of winners is given in the following table: 

          075.17%
          121.45%
          23.06%
          30.29%
          40.02%


            Jake649's avatar - scene sunovermountains.jpg

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            Posted: October 6, 2005, 9:09 am - IP Logged

            Interesting to note that the Powerball jackpot has rolled 16 times. The record Powerball jackpot of $314.9 million was set with 16 rolls.

            The Mega Millions lottery has rolled a maximum of only 15 times. It has rolled 15 times more than once though.

            Good luck,
            Jake

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              Posted: October 6, 2005, 11:04 am - IP Logged

              If one graphs the sales figures for powerball over the last 5 drawings, the growth is almost perfectly linear, with the $148M jackpot on 9/28 varying slightly from this linearity.  I've generated a few such graphs over the years and have noted that one of the signs of lotto fever is deviation from linearity in a way that suggests an exponential function, but thus far in this run, that has not happened.  The slope of this line is $3.7M and the y-intercept is $18.1 M.

              Assuming that linearity would remain constant - and this is probably not a good bet - it is likely that 6 more rollovers would be required to exceed Jack Whitaker's pot, with the final cash value reaching $178M, about $6M more than Whitaker won.  I would estimate the probability of this occurring, from the plotted values, at about 20%.

              This is just mathematical modelling however, and such models break down as conditions change, the changing condition being the onset of lotto fever.  It is difficult to predict when lotto fever might kick in and the linear pattern broken, since in past times, with a jackpot this size lotto fever would already be underway.  Still a non-quantitative guess suggests that it will happen soon and it will really not take 6 rollovers to beat Jack's pot, if indeed it happens.

               

               

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                Greenwich, CT
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                Posted: October 6, 2005, 11:16 am - IP Logged

                Great work on the graphing, Prob988.

                Yes, I think lotto fever will set in with the neeext draw, and it would take only three more rollovers to break the Christmas 2002 amount.

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                  Morrison, IL
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                  Posted: October 6, 2005, 12:48 pm - IP Logged

                  Interesting to note that the Powerball jackpot has rolled 16 times. The record Powerball jackpot of $314.9 million was set with 16 rolls.

                  The Mega Millions lottery has rolled a maximum of only 15 times. It has rolled 15 times more than once though.

                  Good luck,
                  Jake

                    Actually, when Mega Millions was the Big Game, it rolled 19 times in 2002, when it produced the second largest jackpot of $331 million.

                    Jake649's avatar - scene sunovermountains.jpg

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                    Posted: October 6, 2005, 1:38 pm - IP Logged

                    ryanm,

                    Yes that is true, but I consider the Mega Millions lottery not the same as the Big Game. Changes were made to the Big Game lottery when it was turned into the Mega Millions lottery.

                    Good luck,
                    Jake

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                      Posted: October 6, 2005, 1:55 pm - IP Logged

                      Great work on the graphing, Prob988.

                      Yes, I think lotto fever will set in with the neeext draw, and it would take only three more rollovers to break the Christmas 2002 amount.

                      I suspect you're right.  Of course we may not find out if someone wins the jackpot.  There is roughly a 1/4 chance of that happening this draw.

                      In the recent MM jackpot running to $250M annuity, the breakout occurred when the advertised jackpot reached $172M, so powerball is already late.

                       

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                        Posted: October 6, 2005, 10:30 pm - IP Logged

                        The model I've proposed above for the probability of exceeding Jack's jackpot is obviously unsatifying since it pretends that 6 linearly increasing jackpots would occur, whereas it is more likely that some kind of lotto fever will click in and result in non-linearity.

                        Of course the difficulty is that we are in new territory with the new Powerball odds, so we cannot really look at the past to model prospective futures.

                        However I did think of a model that is slightly more satisfying.  The most recent case of lotto fever was the recent Megamillions run which went up to $250M annuity.  This is the only super high jackpot of the super high odds era.  Graphing the sales of this run shows the slope of the line increased radically for the last three drawings, indicating some level of lotto fever.

                        The sales were not, of course, evenly distributed.  The first of the three rollovers accounted for 24% of the surge towards the final jackpot, the second, 31%, and the last,  44%.

                        To beat Jack, the cash jackpot would have to rise about $70 million, requiring $240M in sales.  If the distributions were the same in Powerball as in MM's last three in the lotto fever run, the sales would need to be respectively $57M, $75M and $108M.

                        Estimating the odds on three jackpots of these types gives a 40% chance of matching Jack's pot, and a roughly 20% chance of going beyond Jack's pot with an additional rollover.

                         

                         

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                          Posted: October 9, 2005, 2:07 am - IP Logged

                          The powerball jackpot has rolled again.  From the sales figures, the realized cash value of the recent drawing was approximately $104.2M, higher than advertised.  The new cash value is predicted to be around $117.7M.  Thus anticipated sales are expected to be $45.2M.  I suspect they may actually prove to be somewhat higher (the last draw had sales of nearly $50.1M) but the probability of various numbers of winners are given below for $45.2M.  These probabilities are:

                          073.39%
                          122.70%
                          23.51%
                          30.36%
                          40.03%


                           

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                            Posted: October 9, 2005, 11:16 am - IP Logged

                            Now I will review the probability of beating Jack's Jackpot.  Jack's jackpot was worth $170.5M cash value, and our current cash jackpot is $117.7.  The distance we still need to go is $52.8M cash value to match Jack. 

                            Graphing the sales figures, I see that the linearity in increases that held for the last 7 drawings has been broken.  There is evidence of some lotto fever now.

                            My guess is that this would require $176.8 in sales, three more drawings, and two more rollovers to beat Jack.  I will distribute, for the same reasons given by me two post ago, these two speculative jackpots so that the first gives a jump of $23 million in cash value at $76 million in sales, and the second a cash value jump of $30 million with $101M in sales.  (This would only be the second time that Powerball sold more than $100M in a single drawing, going back to 2002, that being for the drawing Jack won - that drawing had $163M in sales.)

                            If these assumptions about sales growth are correct, the probability of reaching Jack's Jackpot are roughly 44%.  The probability of rollover again once beyond that is about 22%.  Note that it is more likely that someone will win the jackpot before matching Jack than that someone will actually match him.

                            Again though, these are mathematical models depending on assumptions.  These assumptions could be wrong.

                             

                             

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                              Posted: October 13, 2005, 9:11 am - IP Logged

                              For the most recent rollovers, the probability distribution for winners looks like this:

                              065.00%
                              128.00%
                              26.03%
                              30.87%
                              40.09%
                              50.01%


                                 
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