The MM jackpot has rolled over. The cash value is now $8.6M and the advertised annuity jackpot is $15M.
The average number of tickets sold on a second draw is 15.2M. If this is the number of tickets sold, the distribution of probabilities for various numbers of winners is given as:
0 | 91.73% |
1 | 7.92% |
2 | 0.34% |
3 | 0.01% |
The long term probability for jackpot evolution as determined by an exponential curve fitted model is as follows:
$541,198,243.99 | $305,175,676 | 49.27% | 0.45% |
$471,058,240.59 | $265,624,508 | 53.62% | 0.92% |
(Average Annuity, M) | $409,293,967.11 | $230,796,320 | 57.76% | 1.71% |
$315 | $354,905,240.38 | $200,127,122 | 61.67% | 2.96% |
$262 | $307,011,313.54 | $173,120,268 | 65.34% | 4.81% |
$247 | $264,836,613.63 | $149,338,424 | 68.74% | 7.36% |
$217 | $227,698,182.32 | $128,396,475 | 71.89% | 10.70% |
$186 | $194,994,616.35 | $109,955,298 | 74.78% | 14.89% |
$158 | $166,196,328.73 | $93,716,263 | 77.42% | 19.91% |
$135 | $140,836,972.79 | $79,416,404 | 79.82% | 25.71% |
$115 | $118,505,890.39 | $66,824,155 | 82.00% | 32.21% |
$96 | $98,841,461.91 | $55,735,602 | 83.97% | 39.29% |
$84 | $81,525,250.34 | $45,971,183 | 85.74% | 46.79% |
$71 | $66,276,844.66 | $37,372,776 | 87.33% | 54.57% |
$57 | $52,849,318.95 | $29,801,144 | 88.75% | 62.49% |
$45 | $41,025,233.84 | $23,133,674 | 90.03% | 70.41% |
$35 | $30,613,115.35 | $17,262,396 | 91.16% | 78.21% |
$26 | $21,444,354.26 | $12,092,233 | 92.18% | 85.79% |
$17 | $13,370,475.74 | $7,539,463 | 93.08% | 93.08% |
There seems to be some concern about the failure of MM to produce an advertised annuity jackpot of more than $100M since early spring.
Calculating from the model function, we see that there is (now) a 47% probability of reaching a jackpot in that general area from this (second) draw. It can be shown that there is a 99% probability that any second draw will produce such a second jackpot in, on average, 7.3 rounds of runs.
To understand what this means properly, one should discard notions of the lottery thus being "due" to produce a large jackpot. In probability, the occurrence of past events does not influence future events, as much as one might like to believe otherwise. It means irrespective of previous events that 99 times out of 100, such a drawing will occur within 7 to 8 rounds of draws if we start from a second draw. (The probability is somewhat lower if we start from a reset jackpot.) However this is not the same as saying that it is a certainty, nor does the fact that we have gone since the end of March this year without such a jackpot have any effect on next two or three drawings. There is a 99% probability of such a run within 7 to 8 draws from this drawing.
The laws of probability dictate that the MM could never again reach $100M and also that every series of future jackpot could end up with a jackpot being over $100M. Either situation is highly improbable, however.