I have developed a modeling function that fits the experimental behavior of the Powerball pretty well, at least when one looks at it graphically. This function models the Powerball as a linear growth function to draw 12, and thereafter as an exponential function using the data points of average values from drawings 13 to 19.
The model does not fit perfectly the behavior of the recent run, which has been above average in performance overall. Still it is a useful approximation and I offer it for what it's worth:
$471,894,023.98 | $217,285,748 | 37.36% | 5.52% |
$372,555,343.88 | $171,544,802 | 48.68% | 14.77% |
$299,918,746.49 | $138,098,950 | 59.08% | 30.34% |
$246,806,753.52 | $113,643,292 | 68.05% | 51.36% |
$207,971,181.66 | $95,761,276 | 75.47% | 75.47% |
This model obviously ignores the cap, and says how the drawing would behave in the absense of the cap. Note that the potential exists for the cap to be pushed ever higher until it is essentially meaningless.
The first column is the (inflated) annuity value, the second column, the more meaningful cash value (which is what is directly calculated). The third column is the probability that a run of that size will rollover, and the fourth colum is the probability that all runs will rollover from this point. According to this model we have a roughly 30% of reaching the cap, which will easily exceed the cap point which is currently $365M. Note that the jackpot, according will not reach cap figure of $390, but will fall slightly short of it, if this model proves successful and relevant.
If my understanding of the rules is correct, this means that the jackpot might go like this: It reaches $372M and then (15% chance overall) it goes to $397M.