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# Probability of a MegaMillions rollover.

Topic closed. 352 replies. Last post 10 years ago by Prob988.

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New Jersey
United States
Member #21206
September 4, 2005
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 Posted: March 14, 2007, 9:20 am - IP Logged

The MM jackpot has rolled over.  The cash prize is \$16.7M; the advertised annuity is \$28M.  The average sales on a third drawing is 15.89M.  Sales as this level would approximately produce the following randomized probability for numbers of winners:

 0 91.35% 1 8.26% 2 0.37% 3 0.01%

As is often the case after a big jackpot has been run, the first drawing of the next run sold unusually high amounts of tickets.    For this reason, I will be treating the system as if one extra rollover had taken place and this is the fourth drawing.  Thus for the long term program - and I'm not sure that the recent behavior corresponds all that well to my exponential model - suggests the following for long term rollovers:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$736,586,531.75 \$440,531,359 30.87% 0.05% \$626,762,787.99 \$374,848,916 36.53% 0.15% \$532,677,501.39 \$318,579,194 42.20% 0.40% \$452,075,248.62 \$270,373,290 47.75% 0.96% \$315 \$383,023,823.20 \$229,075,605 53.09% 2.00% \$262 \$323,867,916.40 \$193,696,147 58.13% 3.77% \$247 \$273,189,436.00 \$163,386,796 62.83% 6.48% \$217 \$229,773,511.64 \$137,420,972 67.16% 10.32% \$180 \$192,579,371.76 \$115,176,220 71.10% 15.36% \$153 \$160,715,394.18 \$96,119,285 74.66% 21.61% \$130 \$133,417,731.94 \$79,793,334 77.86% 28.94% \$109 \$110,032,002.33 \$65,806,997 80.70% 37.17% \$92 \$89,997,599.97 \$53,824,993 83.22% 46.06% \$81 \$72,834,257.84 \$43,560,089 85.44% 55.35% \$67 \$58,130,534.32 \$34,766,212 87.39% 64.79% \$55 \$45,533,950.07 \$27,232,555 89.09% 74.14% \$45 \$34,742,538.32 \$20,778,520 90.58% 83.22% \$34 \$25,497,606.10 \$15,249,390 91.87% 91.87%

United States
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March 19, 2007
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 Posted: March 19, 2007, 9:47 pm - IP Logged

One of those key questions is:

The closest data is:

1- The odds of 1.63% for a similar estimated jackpot (\$394, see post from January 10 2007) as Overall Calculated Model Rollover Probability of the long term jackpot evolution model, which is significantly outphased with the observed (more precisely: official) evolution.

2- the distribution probability for zero winners for each round, IF an average number of tickets sells on that round, which normally Prob988 gives before each round. Multiplying all of them would give the information I asked for IF an average number of tickets would have been sold on each round.

This simple math will shed more light on the underlying question.

New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 20, 2007, 11:43 am - IP Logged

One of those key questions is:

The closest data is:

1- The odds of 1.63% for a similar estimated jackpot (\$394, see post from January 10 2007) as Overall Calculated Model Rollover Probability of the long term jackpot evolution model, which is significantly outphased with the observed (more precisely: official) evolution.

2- the distribution probability for zero winners for each round, IF an average number of tickets sells on that round, which normally Prob988 gives before each round. Multiplying all of them would give the information I asked for IF an average number of tickets would have been sold on each round.

This simple math will shed more light on the underlying question.

Based on actual sales during the run, the probability of a \$390 jackpot was about 4.5%.

This figure includes all of the rollovers, but not the final drawing, since the final draw was won.

When one says "reach \$390M," of course, one assumes that the final drawing will have sales similar to those actually obtained, about \$212M.

New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 21, 2007, 5:49 am - IP Logged

The MM Jackpot has been won.  The cash value is \$28.6M.    The advertised annuity is 48M.    The average 6th round jackpot sells 19.3M tickets.  If sales are average, the probability of various numbers of winners will be:

 0 89.61% 1 9.83% 2 0.54% 3 0.02%

The long term modelling program suggests the following:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$739,158,032.14 \$440,414,994 30.90% 0.05% \$629,028,264.35 \$374,796,008 36.56% 0.18% \$534,667,892.37 \$318,572,953 42.23% 0.48% \$453,818,908.68 \$270,400,433 47.77% 1.15% \$315 \$384,546,628.10 \$229,125,699 53.10% 2.40% \$262 \$325,193,391.52 \$193,761,062 58.14% 4.53% \$247 \$274,338,898.72 \$163,460,260 62.84% 7.78% \$217 \$230,766,221.21 \$137,498,207 67.16% 12.39% \$180 \$193,432,681.51 \$115,253,639 71.10% 18.45% \$153 \$161,444,902.33 \$96,194,254 74.66% 25.95% \$130 \$134,037,428.37 \$79,863,968 77.85% 34.75% \$109 \$110,554,409.30 \$65,872,002 80.69% 44.64% \$92 \$90,433,905.48 \$53,883,535 83.21% 55.33% \$81 \$73,194,440.94 \$43,611,688 85.43% 66.49% \$67 \$58,423,481.93 \$34,810,658 87.38% 77.83% \$55 \$45,767,565.06 \$27,269,841 89.08% 89.08%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 24, 2007, 2:09 pm - IP Logged

The MM has rolled over.    The cash prize is now \$35.6M.  The advertised annuity is \$60M.  Average sales for 6th round draws are 19.2M.  If this draw produces average sales, the probability of various numbers of winners will be as follows:

 0 89.61% 1 9.83% 2 0.54% 3 0.02%

The long term jackpot model program I use for long term evolution of jackpots suggests the following:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$742,173,213.03 \$440,356,106 30.92% 0.06% \$631,648,127.35 \$374,777,889 36.58% 0.20% \$536,940,044.38 \$318,584,426 42.24% 0.54% \$455,785,427.55 \$270,432,687 47.79% 1.29% \$315 \$386,244,670.03 \$229,171,838 53.11% 2.70% \$316 \$326,655,737.87 \$193,815,738 58.15% 5.08% \$254 \$275,594,447.16 \$163,519,372 62.84% 8.73% \$217 \$231,840,425.83 \$137,558,653 67.16% 13.90% \$179 \$194,347,946.58 \$115,313,115 71.10% 20.70% \$131 \$162,220,933.84 \$96,251,087 74.65% 29.11% \$113 \$134,691,547.46 \$79,916,985 77.84% 39.00% \$109 \$111,101,831.22 \$65,920,420 80.68% 50.10% \$92 \$90,887,987.56 \$53,926,873 83.20% 62.09% \$81 \$73,566,902.75 \$43,649,696 85.42% 74.63% \$67 \$58,724,600.42 \$34,843,263 87.37% 87.37% \$51 \$46,006,347.44 \$27,297,099 89.07% 100.00% \$44 \$35,108,175.76 \$20,830,851 90.56% 100.00% \$34 \$25,769,617.54 \$15,289,973 91.85% 100.00% \$25 \$17,767,479.91 \$10,542,038 92.98% 100.00% \$16 \$10,910,510.66 \$6,473,570 93.95% 100.00% \$12 \$5,034,827.24 \$2,987,331 94.79% 100.00%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 29, 2007, 8:09 am - IP Logged

The MM has rolled over.    The cash prize is now \$43.4M.  The advertised annuity is \$74M.  Average sales for 6th round draws are 21.2M.  If this draw produces average sales, the probability of various numbers of winners will be as follows:

 0 88.64% 1 10.69% 2 0.64% 3 0.03%

The long term probability model suggests the following:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$750,791,285.67 \$440,328,943 30.94% 0.07% \$639,023,541.25 \$374,778,671 36.59% 0.23% \$543,243,835.00 \$318,605,168 42.25% 0.62% \$461,165,126.35 \$270,467,115 47.79% 1.48% \$315 \$390,827,528.99 \$229,215,064 53.12% 3.09% \$262 \$330,551,512.43 \$193,863,995 58.15% 5.81% \$247 \$278,897,797.93 \$163,569,790 62.84% 9.99% \$217 \$234,632,991.23 \$137,609,079 67.16% 15.90% \$180 \$196,700,131.39 \$115,361,969 71.09% 23.68% \$153 \$164,193,452.55 \$96,297,241 74.65% 33.31% \$130 \$136,336,755.90 \$79,959,665 77.84% 44.62% \$109 \$112,464,875.55 \$65,959,130 80.68% 57.33% \$92 \$92,007,795.56 \$53,961,329 83.19% 71.06% \$81 \$74,477,039.05 \$43,679,777 85.41% 85.41%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 31, 2007, 12:07 pm - IP Logged

The MM jackpot has rolled.  The estimated cash jackpot is \$51.5M.  The advertised annuity is \$88M.

The average 8th draw in a run produces \$23.M  in sales.    (The Standard Deviation is 2.3M).

If an average number of tickets are sold, the randomized probability of various numbers of winners will be as follows:

 0 87.75% 1 11.47% 2 0.75% 3 0.03%

Here is the long term program model:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$752,400,386.12 \$440,325,226 30.96% 0.08% \$640,445,859.49 \$374,806,384 36.61% 0.27% \$544,497,290.79 \$318,654,664 42.26% 0.73% \$462,266,334.06 \$270,530,866 47.80% 1.73% \$315 \$391,791,804.46 \$229,287,249 53.12% 3.61% \$316 \$331,392,904.58 \$193,940,166 58.15% 6.80% \$186 \$279,629,137.91 \$163,646,598 62.84% 11.69% \$217 \$235,265,953.39 \$137,684,052 67.15% 18.61% \$179 \$197,245,301.75 \$115,433,330 71.09% 27.71% \$153 \$164,660,401.29 \$96,363,758 74.64% 38.98% \$130 \$136,734,111.44 \$80,020,531 77.83% 52.22% \$109 \$112,800,398.17 \$66,013,869 80.67% 67.10% \$92 \$92,288,449.24 \$54,009,717 83.18% 83.18%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
Offline
 Posted: April 4, 2007, 2:47 am - IP Logged

MM has rolled over.  The cash jackpot is \$61.3M; the advertised annuity is \$105M.  The average sales for a ninth draw is \$25.6M.

Every drawing on this run has produced above average sales though.

Even so, average sales would produce a probability distribution of number of winners as follows:

 0 86.43% 1 12.61% 2 0.92% 3 0.04%

The exponential model function, for what it's worth, predicts the following long range evolution of the jackpot:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$754,269,673.18 \$440,349,819 30.96% 0.10% \$642,065,550.66 \$374,843,983 36.61% 0.32% \$545,898,310.09 \$318,700,632 42.27% 0.88% \$463,475,864.71 \$270,581,624 47.80% 2.07% \$315 \$392,833,726.48 \$229,340,071 53.12% 4.34% \$316 \$332,288,183.67 \$193,993,006 58.15% 8.17% \$186 \$280,396,170.70 \$163,697,955 62.83% 14.05% \$217 \$235,920,873.51 \$137,732,853 67.15% 22.36% \$179 \$197,802,250.87 \$115,478,838 71.08% 33.30% \$153 \$165,131,768.97 \$96,405,499 74.63% 46.85% \$130 \$137,130,747.07 \$80,058,236 77.82% 62.77% \$109 \$113,131,798.10 \$66,047,421 80.66% 80.66%

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