The Megamillions jackpot has rolled over and the cash value is now $52.4M. The cash value reached on the last drawing was $45.2M. The annuity value is now $88M, just shy of the $90M annuity record for this number of drawings in a prize building pool. The lottery is apparently predicting 22.6M in sales. If this proves to be correct, the probability of various numbers of winners is given in the following table:
0 | 87.93% |
1 | 11.31% |
2 | 0.73% |
3 | 0.03% |
I have updated the data fitted into my exponential modeling equation to reflect new average sales data since the change in the matrix in MM, including the sales on the current winless run. I have also adjusted for slight changes in the annuity/cash ratio reported by the Massachusetts lottery web site. (The annuity values are probably the least reliable pieces of data - since the annuity varies with financial markets and their volatility.) The model now seems to be operating within a few percent of the actual behavior of the lottery - something that I expect to prevail almost until we get into record breaking areas - if, in fact, we do so.
The following table gives the modeled probability for rollovers over the long term.
| $512,485,514.18 | $305,161,829 | 51.75% | 0.94% |
| $450,676,550.44 | $268,357,400 | 55.65% | 1.82% |
| $395,680,472.35 | $235,609,736 | 59.36% | 3.27% |
| $346,746,330.39 | $206,471,679 | 62.88% | 5.50% |
$315 | $303,205,948.38 | $180,545,360 | 66.18% | 8.75% |
$262 | $264,464,799.78 | $157,476,767 | 69.26% | 13.22% |
$225 | $229,993,889.65 | $136,950,907 | 72.12% | 19.09% |
$192 | $199,322,531.47 | $118,687,507 | 74.76% | 26.47% |
$165 | $172,031,920.08 | $102,437,189 | 77.20% | 35.40% |
$147 | $147,749,413.07 | $87,978,060 | 79.43% | 45.86% |
$128 | $126,143,442.50 | $75,112,686 | 81.48% | 57.73% |
$108 | $106,918,987.45 | $63,665,397 | 83.34% | 70.86% |
$90 | $89,813,545.66 | $53,479,884 | 85.03% | 85.03% |
The first column gives the historical annuity prizes posted on the last large run. The second prize give a calculated annuity prize for putative drawings. The third column gives cash value of the prize. Predicted sales are not shown in this table, but the probabilities are generated from these unshown modeled sales figures. The probability of a rollover for that single drawing is calculated and shown in column 5. The last column is that all drawing including that one and those before it will roll. The starting point is the current $88M annuity jackpot. Note that the model gives a rollover probability that is 2% lower than the figure obtained by using the MM's prediction of the cash prize.