Here is the long term probability spreadsheet updated with the latest data.
| $513,994,723.76 | $306,060,495 | 51.46% | 0.92% |
| $451,651,912.87 | $268,938,184 | 55.40% | 1.79% |
| $396,232,427.14 | $235,938,400 | 59.16% | 3.23% |
| $346,967,413.99 | $206,603,324 | 62.71% | 5.46% |
$315 | $303,173,403.84 | $180,525,981 | 66.04% | 8.71% |
$262 | $264,242,828.12 | $157,344,593 | 69.16% | 13.19% |
$225 | $229,635,590.25 | $136,737,556 | 72.05% | 19.07% |
$192 | $198,871,572.76 | $118,418,982 | 74.72% | 26.47% |
$165 | $171,523,976.40 | $102,134,731 | 77.18% | 35.42% |
$147 | $147,213,399.05 | $87,658,888 | 79.43% | 45.90% |
$128 | $125,602,572.15 | $74,790,623 | 81.49% | 57.78% |
$108 | $106,391,681.67 | $63,351,410 | 83.36% | 70.91% |
$90 | $89,314,208.65 | $53,182,552 | 85.06% | 85.06% |
As before, the first column is the historical values in the run that went to $315M last year in this matrix. The second column is a calculated value of the annuity generally advertised. The third column is the cash values obtained as discussed below, the 4th column is the probability that each particular roll will rollover and the last column is the probability that a particular roll plus all other rolls between here and there will rollover. Thus we see we have a better than even chance of having a $147M annuity jackpot in this run and a slightly less than even chance that we will have a $170M annuity.
The actual advertised cash value right now is $51.9M and the actual annuity advertised value is $88M. The annuity value reached in the last jackpot was $44.5, about 0.5M from what the model predicted before update. (Updated with the new data, the program would have predicted $44.1 for that run.)
The data is the average of sales as listed on the lottoreport website for each drawing in a sequence until the jackpot is won. The data applied to generate the equation now generates the following equation for predicting sales, from which the jackpots are calculated:
S = $9,853,856*exp(0.112*N)
where exp() refers to the exponential function and N is the drawing in the sequence of starting (N=1) jackpots and rollover jackpots. The cash jackpot is calculated by summing all the predicted sales in the run and multiplying this sum by 0.318.
I am very happy with the way the model is performing right now. It seems fairly accurate.
For those with an interest in mathematics, the least squares model equations can be found here:
http://mathworld.wolfram.com/LeastSquaresFittingExponential.html