OK, here is what I decided to try as a crude estimate of long term probability for rollovers. We'll see how it works, if the jackpot continues to roll and is not won.
I rejected all of the data points before and including data point #14, assuming that the post "lotto fever" jackpots would represent a new exponential function, different than that which so accurately represented the first 14 drawings. For data points 15 and 16 I used the average sales from previous jackpots (the mean of 3 and 2 values respectively) and for data point #17 the sales for the $315M jackpot.
I then reset the jackpot to equal the current cash value to generate a new function, which we'll try out. I have assumed that sales for this drawing will be close to $80M, which is consistent with drawings near this prize level. (It's almost as if a drawing was skipped on the previous function.)
Here is what this new equation generates for long term probability of rollovers:
$568,249,867.08 | $338,366,966 | 23.83% | 1.97% |
$433,676,591.39 | $258,234,698 | 34.05% | 8.25% |
$332,571,333.95 | $198,031,112 | 44.51% | 24.23% |
$256,610,687.02 | $152,800,000 | 54.43% | 54.43% |
The first column is advertised annuity jackpots, the second is cash value (the $152.8M figure being the reset applied in the formula) the third column being what the new equation predicts the probability of rollover for each drawing will be, and the 4th column represented what the probability of each jackpot up to and including the drawing described in a particular row, rolling as of today. Thus, if this equation is a good model, there is a 2% chance of 4 more rolls, an 8% chance of 3 more rolls, a 24 percent chance of two more rolls and a 54% of one more roll.
I have no evidence that this formula will prove correct, but the results look reasonable.
According to the formula, the jackpot obtained for 4 more rolls would represent a jack pot of almost 3/4 of a billion dollars annuity, with a cash value of $450M dollars. This is, however, very unlikely. As of today, there seems to be a 98% probability that this will not happen.