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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
949 Posts
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 Posted: September 14, 2006, 2:07 am - IP Logged

MM has rolled over.    The cash value prize is estimated at \$94.7; the advertised annuity value is \$163M.

Because of slow sales early in the drawing, I will treat the up coming drawing as an 12th round drawing rather than as a 13th round drawing.

An eleventh round drawing sells on average sells 34.8M tickets.  If this is the number of tickets that sell, the randomized distribution of the probability of various numbers of winner is as follows:

 0 78.90% 1 18.70% 2 2.22% 3 0.17% 4 0.01%

Here's the long term model jackpot evolution figures:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$603,956,395.39 \$350,887,550 43.86% 0.75% \$524,686,711.42 \$304,833,323 48.53% 1.70% \$455,158,487.38 \$264,438,704 53.04% 3.50% \$394,174,594.21 \$229,008,184 57.34% 6.60% \$315 \$340,685,018.19 \$197,931,725 61.40% 11.51% \$262 \$293,768,781.87 \$170,674,255 65.19% 18.74% \$247 \$252,618,086.85 \$146,766,459 68.71% 28.75% \$217 \$216,524,405.13 \$125,796,694 71.95% 41.85% \$186 \$184,866,279.82 \$107,403,906 74.92% 58.16% \$158 \$157,098,624.90 \$91,271,410 77.63% 77.63%

United States
Member #16612
June 2, 2005
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 Posted: September 14, 2006, 11:08 am - IP Logged

Prob988, PB also rolled. However, MM jackpot (annunity) is now higher than PB. I hope MM continues to roll.

New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: September 16, 2006, 8:46 am - IP Logged

The MM jackpot has been won and the jackpot has been reset to \$7.0M cash and \$12M as an advertised annuity.

The average number of sales for a first round drawing is \$14.3M.  If this is how many tickets sell this draw, the probability distribution for numbers of winners is as follows:

 0 92.18% 1 7.51% 2 0.31% 3 0.01%

The long term proability model function, which ignores minimums and reserves suggests the following behavior:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$602,303,598.36 \$351,343,766 43.79% 0.19% \$523,209,412.78 \$305,205,491 48.47% 0.42% \$453,841,488.71 \$264,740,868 52.99% 0.88% \$393,003,781.68 \$229,252,206 57.29% 1.65% \$315 \$339,647,325.57 \$198,127,607 61.35% 2.88% \$262 \$292,852,146.27 \$170,830,419 65.15% 4.70% \$247 \$251,811,399.46 \$146,889,983 68.68% 7.22% \$217 \$215,817,458.97 \$125,893,518 71.92% 10.51% \$186 \$184,249,715.87 \$107,479,001 74.90% 14.61% \$158 \$156,563,877.91 \$91,328,929 77.61% 19.51% \$131 \$132,282,584.77 \$77,164,841 80.07% 25.13% \$111 \$110,987,177.44 \$64,742,520 82.29% 31.39% \$94 \$92,310,479.69 \$53,847,780 84.28% 38.15% \$82 \$75,930,467.14 \$44,292,773 86.07% 45.26% \$69 \$61,564,715.00 \$35,912,750 87.68% 52.59% \$56 \$48,965,528.39 \$28,563,225 89.10% 59.98% \$46 \$37,915,671.64 \$22,117,475 90.38% 67.31% \$35 \$28,224,622.69 \$16,464,363 91.51% 74.48% \$26 \$19,725,288.10 \$11,506,418 92.51% 81.39% \$17 \$12,271,122.00 \$7,158,155 93.40% 87.98% \$12 \$5,733,599.38 \$3,344,600 94.19% 94.19%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: September 20, 2006, 6:04 am - IP Logged

The MM jackpot has been won and the jackpot has been reset to \$7.0M cash and \$12M as an advertised annuity.

The average number of sales for a first round drawing is \$14.3M.  If this is how many tickets sell this draw, the probability distribution for numbers of winners is as follows:

 0 92.18% 1 7.51% 2 0.31% 3 0.01%

The long term proability model function, which ignores minimums and reserves suggests the following behavior:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$602,303,598.36 \$351,343,766 43.79% 0.19% \$523,209,412.78 \$305,205,491 48.47% 0.42% \$453,841,488.71 \$264,740,868 52.99% 0.88% \$393,003,781.68 \$229,252,206 57.29% 1.65% \$315 \$339,647,325.57 \$198,127,607 61.35% 2.88% \$262 \$292,852,146.27 \$170,830,419 65.15% 4.70% \$247 \$251,811,399.46 \$146,889,983 68.68% 7.22% \$217 \$215,817,458.97 \$125,893,518 71.92% 10.51% \$186 \$184,249,715.87 \$107,479,001 74.90% 14.61% \$158 \$156,563,877.91 \$91,328,929 77.61% 19.51% \$131 \$132,282,584.77 \$77,164,841 80.07% 25.13% \$111 \$110,987,177.44 \$64,742,520 82.29% 31.39% \$94 \$92,310,479.69 \$53,847,780 84.28% 38.15% \$82 \$75,930,467.14 \$44,292,773 86.07% 45.26% \$69 \$61,564,715.00 \$35,912,750 87.68% 52.59% \$56 \$48,965,528.39 \$28,563,225 89.10% 59.98% \$46 \$37,915,671.64 \$22,117,475 90.38% 67.31% \$35 \$28,224,622.69 \$16,464,363 91.51% 74.48% \$26 \$19,725,288.10 \$11,506,418 92.51% 81.39% \$17 \$12,271,122.00 \$7,158,155 93.40% 87.98% \$12 \$5,733,599.38 \$3,344,600 94.19% 94.19%

MM has been won on the first draw.

Since the last draw was also a first draw, the probabilities remain the same.

Morrison, IL
United States
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May 13, 2004
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 Posted: September 20, 2006, 8:02 am - IP Logged

All right; it's nice to see a PB or MM opening jackpot won. It conveys the message that the odds aren't insurmountable.

United States
Member #2338
September 17, 2003
2063 Posts
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 Posted: September 20, 2006, 9:40 am - IP Logged

For MM it means another long string of pathetic low jackpots IMO. No wonder I don't play it.

New Jersey
United States
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September 4, 2005
949 Posts
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 Posted: September 20, 2006, 10:33 pm - IP Logged

There have been 15 "first draws" since the matrix change.  Only one first drawing has been won, meaning that 93% of the time, the first jackpot has rolled over.

This is consistent with the figures I routinely give here when first jackpots crop up, close to what I predict for the likelyhood that the next first jackpot will roll over.

If no could ever win a first jackpot, no one would ever play it of course.  A single ticket playing in a \$300 million jackpot has the same probability of winning as a single ticket in a \$12 million dollar jackpot, although the expectation values are very different.

I would expect that out of every hundred sequences beginning with a first draw, two would give give jackpots over \$400 million annuity.

The average run gives about 8 drawings.  The run that ended recently went beyond average.

United States
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June 2, 2005
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 Posted: September 23, 2006, 3:24 am - IP Logged

After two straight MM jackpot winners Prob988, MM jackpot for 9/26 has rolled to 15 million.

New Jersey
United States
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September 4, 2005
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 Posted: September 23, 2006, 12:25 pm - IP Logged

The MM jackpot has rolled.  The cash value is \$8.8M.  The advertised annuity is \$15.0M.  The average number of tickets sold for a second draw in a series is \$14.0M.  If this is the number of tickets that sell, the probability of various numbers of winners is given as follows:

 0 92.33% 1 7.37% 2 0.29% 3 0.01%

The long term jackpot evolution model, an exponential function generating model sales, predicts the following probabilities for this run:

 Historical Average Advertised Annuity Jackpots Model Calculated Annuity Prize Model Calculated Cash Value Single Draw Calculated Model Rollover Probability Overall Calculated Model Rollover Probability \$598,727,859.65 \$351,253,678 43.82% 0.20% \$520,152,864.82 \$305,156,347 48.50% 0.45% \$451,232,662.79 \$264,723,162 53.01% 0.93% \$390,780,934.38 \$229,258,148 57.31% 1.75% \$315 \$337,757,127.71 \$198,150,848 61.37% 3.06% \$262 \$291,248,547.26 \$170,865,814 65.16% 4.99% \$247 \$250,454,643.72 \$146,933,391 68.68% 7.66% \$217 \$214,673,234.13 \$125,941,631 71.93% 11.15% \$186 \$183,288,415.30 \$107,529,204 74.90% 15.50% \$158 \$155,759,962.26 \$91,379,178 77.61% 20.69% \$131 \$131,614,029.47 \$77,213,564 80.06% 26.66% \$111 \$110,434,994.46 \$64,788,530 82.28% 33.30% \$94 \$91,858,303.82 \$53,890,205 84.28% 40.47% \$82 \$75,564,198.10 \$44,330,996 86.07% 48.03% \$69 \$61,272,207.88 \$35,946,362 87.67% 55.80% \$56 \$48,736,326.01 \$28,591,978 89.10% 63.65% \$46 \$37,740,773.13 \$22,141,254 90.37% 71.44% \$35 \$28,096,283.45 \$16,483,153 91.50% 79.05% \$26 \$19,636,846.98 \$11,520,284 92.51% 86.40% \$17 \$12,216,851.96 \$7,167,220 93.39% 93.39%
New Jersey
United States
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September 4, 2005
949 Posts
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 Posted: September 27, 2006, 7:51 am - IP Logged

The MM jackpot has been won.  The jackpot has been reset to \$7.1M cash, \$12M for the advertised annuity.

It happens that to have been won on a second draw, after a previous sequence in which the jackpot was won on the first draw was a 7 in 1000 shot.

The average sales for opening runs is 15.3M.  If this is how many tickets that sell, the randomized distribution probability for various numbers of winners is as follows:

 0 91.67% 1 7.98% 2 0.35% 3 0.01%

The long term exponential program for jackpot evolution 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 \$590,821,944.39 \$349,569,650 44.45% 0.19% \$514,252,435.83 \$304,266,025 49.03% 0.43% \$446,944,096.61 \$264,441,924 53.45% 0.88% \$387,776,777.75 \$229,434,594 57.65% 1.65% \$315 \$335,765,813.56 \$198,661,440 61.62% 2.86% \$262 \$290,045,634.78 \$171,610,334 65.34% 4.64% \$247 \$249,855,363.74 \$147,831,090 68.79% 7.10% \$217 \$214,526,151.79 \$126,927,973 71.98% 10.31% \$186 \$183,470,048.31 \$108,553,112 74.90% 14.33% \$158 \$156,170,215.95 \$92,400,711 77.56% 19.13% \$131 \$132,172,329.43 \$78,201,962 79.98% 24.67% \$111 \$111,077,014.64 \$65,720,567 82.17% 30.85% \$94 \$92,533,202.23 \$54,748,811 84.15% 37.54% \$82 \$76,232,285.06 \$45,104,102 85.92% 44.61% \$69 \$61,902,982.41 \$36,625,931 87.51% 51.92% \$56 \$49,306,825.25 \$29,173,205 88.94% 59.33% \$46 \$38,234,187.66 \$22,621,894 90.21% 66.71% \$35 \$28,500,798.21 \$16,862,972 91.34% 73.95% \$26 \$19,944,673.31 \$11,800,598 92.34% 80.96% \$17 \$12,423,421.46 \$7,350,524 93.24% 87.67% \$12 \$5,811,873.61 \$3,438,692 94.03% 94.03%
New Member

United States
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July 19, 2005
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 Posted: September 27, 2006, 8:57 pm - IP Logged

"It happens that to have been won on a second draw, after a previous sequence in which the jackpot was won on the first draw was a 7 in 1000 shot."

But if you look at it as 2 out of 3, the odds aren't so long.

I figure the odds of the MM being won in 2 of 3 draws after a reset is about 18 in 1000 or 1 in 56.

hit hit miss ~ 0.34%

hit miss hit ~ 0.72%

miss hit hit ~ 0.72%

Total ~ 1.78%

United States
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June 2, 2005
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 Posted: September 28, 2006, 1:47 am - IP Logged

Prob988, I'll be surprised if MM jackpot hits again in next draw.

New Jersey
United States
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September 4, 2005
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 Posted: September 30, 2006, 8:31 am - IP Logged

The MM jackpot has rolled.  The cash value is \$8.8M, the advertised annuity is \$15M.

Second round jackpots on average sell 15.0 M tickets.  If this is the number of tickets that sell, the distribution of probability of various numbers of winners will be:

 0 91.83% 1 7.82% 2 0.33% 3 0.01%

The mathematical model for jackpot evolution, which tends to be more accurate in later drawings 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 \$595,883,754.74 \$349,585,136 44.45% 0.20% \$518,649,521.98 \$304,274,386 49.03% 0.46% \$450,758,187.47 \$264,444,803 53.44% 0.94% \$391,079,556.18 \$229,433,340 57.65% 1.75% \$315 \$338,620,150.87 \$198,657,155 61.62% 3.04% \$262 \$292,506,673.64 \$171,603,915 65.34% 4.93% \$247 \$251,971,468.00 \$147,823,261 68.79% 7.55% \$217 \$216,339,739.60 \$126,919,314 71.97% 10.97% \$186 \$185,018,322.84 \$108,544,083 74.90% 15.24% \$158 \$157,485,806.42 \$92,391,673 77.56% 20.35% \$131 \$133,283,853.28 \$78,193,194 79.98% 26.24% \$111 \$112,009,570.66 \$65,712,281 82.17% 32.81% \$94 \$93,308,803.05 \$54,741,164 84.15% 39.93% \$82 \$76,870,236.58 \$45,097,205 85.92% 47.45% \$69 \$62,420,216.49 \$36,619,860 87.51% 55.22% \$56 \$49,718,191.59 \$29,168,006 88.94% 63.10% \$46 \$38,552,709.78 \$22,617,590 90.21% 70.95% \$35 \$28,737,897.96 \$16,859,567 91.34% 78.65% \$26 \$20,110,367.81 \$11,798,082 92.35% 86.10% \$17 \$12,526,495.80 \$7,348,878 93.24% 93.24%

United States
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June 2, 2005
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 Posted: October 4, 2006, 2:34 pm - IP Logged

Prob988, MM Jackpot for 10/6 is 25 million (rolled).

New Jersey
United States
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 Posted: October 4, 2006, 8:53 pm - IP Logged

The MM jackpot has rolled.  The cash value is \$14.7M.  The advertised annuity value is \$25M.

The average third draw sells \$14.7M.

If this draw sells this much, the randomized probability of various numbers of winners is as follows:

 0 91.95% 1 7.72% 2 0.32% 3 0.01%

The model for Jackpot growth predicts 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 \$594,544,263.46 \$349,592,027 44.44% 0.22% \$517,479,381.76 \$304,277,876 49.02% 0.49% \$449,737,562.34 \$264,445,687 53.44% 1.00% \$390,190,931.01 \$229,432,267 57.65% 1.88% \$315 \$337,848,060.19 \$198,654,659 61.62% 3.26% \$262 \$291,837,462.05 \$171,600,428 65.34% 5.29% \$247 \$251,393,078.53 \$147,819,130 68.79% 8.09% \$217 \$215,841,526.85 \$126,914,818 71.97% 11.77% \$186 \$184,590,887.89 \$108,539,442 74.90% 16.35% \$158 \$157,120,851.02 \$92,387,060 77.56% 21.83% \$131 \$132,974,051.13 \$78,188,742 79.98% 28.14% \$111 \$111,748,453.66 \$65,708,091 82.17% 35.19% \$94 \$93,090,660.91 \$54,737,309 84.15% 42.82% \$82 \$76,690,028.10 \$45,093,737 85.92% 50.89% \$69 \$62,273,491.25 \$36,616,813 87.52% 59.23% \$56 \$49,601,020.81 \$29,165,400 88.94% 67.67% \$46 \$38,461,625.21 \$22,615,436 90.21% 76.09% \$35 \$28,669,837.96 \$16,857,865 91.34% 84.35% \$26 \$20,062,629.74 \$11,796,826 92.35% 92.35%

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