Here are the long term modelling results for probabilities of jackpots of various sizes derived from my curve fitting scheme. As I have discussed, I think, before, modeling gives better results in some areas than it does in others. It deviates widely in the first several drawing and it also deviates when the jackpots approach records. It is now operating in a region where it is very accurate though. This is satisfying to me.
(I keep the model updated by inserting new sales figures for each run that give sales averages for particular numbers of drawings.)
Here is the table of long term probabilities:
| $513,814,525.83 | $305,953,195 | 51.39% | 0.70% |
| $451,347,787.20 | $268,757,091 | 55.35% | 1.37% |
| $395,839,530.41 | $235,704,448 | 59.12% | 2.47% |
| $346,514,615.43 | $206,333,703 | 62.68% | 4.17% |
$315 | $302,684,248.96 | $180,234,712 | 66.03% | 6.66% |
$262 | $263,736,365.80 | $157,043,018 | 69.16% | 10.08% |
$225 | $229,127,081.77 | $136,434,762 | 72.06% | 14.58% |
$192 | $198,373,098.65 | $118,122,163 | 74.73% | 20.23% |
$165 | $171,044,955.23 | $101,849,496 | 77.20% | 27.07% |
$147 | $146,761,030.13 | $87,389,522 | 79.46% | 35.06% |
$128 | $125,182,212.66 | $74,540,318 | 81.52% | 44.13% |
$108 | $106,007,167.39 | $63,122,450 | 83.40% | 54.13% |
$90 | $88,968,126.13 | $52,976,475 | 85.10% | 64.91% |
$77 | $73,827,148.74 | $43,960,711 | 86.64% | 76.28% |
$65 | $60,372,800.39 | $35,949,258 | 88.04% | 88.04% |
As before, the first column is the actual jackpots from the last very large MM run. The second column is the annuity value predicted by the model. The third column is the cash value predicted. The fourth column is the probabilty that each individual drawing will rollover. The last column is the probability that a particular drawing and all of the drawings before it will roll over. The current jackpot is annuity $61M and cash $36.1M. (The annuity is a bit of a fudge, and the model actually calculates cash values without the extra possible error associated with extra data of annuity yield.
For anyone who may be interested in such a thing, the form of the equation is this C = $9,793,867*exp(0.118*N) where N is the drawing number with the reset jackpot being N = 1.