Quick Links You last visited December 13, 2017, 5:46 pm All times shown are Eastern Time (GMT5:00)  Probability of a MegaMillions rollover.Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 4, 2006, 8:03 am  IP Logged  
The MM jackpot has rolled. The cash value is $30.4M ; the advertised annuity is $52M. Sixth round jackpots sell on average, 19.3M in tickets. If an average amount is sold, the randomized probability of various numbers of winners will be as follows: 0  89.56%  1  9.88%  2  0.54%  3  0.02% 
The long term probability model function is within 3% of actual events. It suggests that the probability of the jackpot growing is as follows: Historical Average Advertised Annuity Jackpots  Model Calculated Annuity Prize  Model Calculated Cash Value  Single Draw Calculated Model Rollover Probability  Overall Calculated Model Rollover Probability   $594,392,245.97  $348,633,914  44.89%  0.29%   $518,095,732.34  $303,883,074  49.40%  0.66%   $450,916,084.13  $264,479,626  53.74%  1.33%   $391,763,903.80  $229,784,597  57.88%  2.47%  $315  $339,679,968.69  $199,235,366  61.79%  4.27%  $262  $293,819,676.11  $172,336,541  65.45%  6.91%  $247  $253,439,347.10  $148,651,925  68.85%  10.56%  $217  $217,884,166.82  $127,797,444  71.99%  15.33%  $180  $186,577,565.91  $109,434,918  74.87%  21.30%  $153  $159,011,870.77  $93,266,578  77.51%  28.44%  $131  $134,740,070.99  $79,030,234  79.90%  36.70%  $111  $113,368,570.60  $66,495,027  82.08%  45.92%  $94  $94,550,805.43  $55,457,684  84.04%  55.95%  $82  $77,981,623.11  $45,739,221  85.80%  66.58%  $69  $63,392,334.73  $37,182,042  87.39%  77.60%  $52  $50,546,357.72  $29,647,383  88.80%  88.80% 
  
California United States Member #46824 October 1, 2006 270 Posts Offline  Posted: November 4, 2006, 11:38 am  IP Logged  
Prob988...quick question if I may. How did you calculate the figure for 0 winners, 89.56% in this instance? I tried taking the average number of tickets sold (19.3m) divided by total odds (175,711,536) and came up with a different number. What factors should I be using?
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 4, 2006, 1:41 pm  IP Logged  
I use what is called a Poisson distribution, assuming that all purchases are effectively random. When the number of tickets purchased is very small compared to the odds, a Poisson distribution will give numbers that are close to the numbers obtained by dividing the number of tickets purchased by the probability. However as the number of tickets purchased increases, there is a greater probability that each new purchaser will purchase a ticket with a set of numbers that has been already purchased by someone else. We all are intuitively aware that the larger the number of tickets that are sold, the more frequently we will see jackpots won by more than one person. These possibilities are measured by Poisson calculations. The mathematics of Poisson distributions are available on the internet and in many other places and I encourage you to investigate them. I have built a series of spreadsheets that do all of my calculations, and produce the results that I provide here from them. I have arranged it so that I merely enter the sales for each drawing in a box on these spreadsheets and all of the values pop out. I then cut and paste them here for informational purposes. Note that I only report values that have a probability of 1 hundredth of one percent. The probability of there being six winners in the upcoming draw is not zero. It is possible that there will be six winners, not very likely, but possible. Sources of error in my calculation include the fact that purchases are not always random. For instance people play their birthday numbers frequently, which tends to skew the probability of rollovers in someway by creating more doubly covered sets of numbers (those with all of the numbers being less than 31) and creating more uncovered sets (those which do not represent birthdays.) There are undoubtedly other such effects, however the Poisson calculations are a useful first approximation. The long term probabilities I post are based on a mathematical technique known as curve fitting. I have graphed the sales figures for various jackpot sizes, made an estimate of the type of curve that fits, for MM an exponential function, and for PB a linear function that switches at a certain point to an exponential function, and have calculated certain constants. These constants are automatically updated for each drawing by a series of linked spreadsheets. I hope you find them useful and I hope you find these comments useful.   
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 8, 2006, 4:00 am  IP Logged  
The MM jackpot has rolled. The cash value is $37.1M ; the advertised annuity is $63M. Seventh round jackpots sell on average, 21.7M in tickets. If an average amount is sold, the randomized probability of various numbers of winners will be as follows: 0  88.39%  1  10.90%  2  0.67%  3  0.03% 
The long term probability modelling function is pretty much on the money right now. It predicts as follows: Historical Average Advertised Annuity Jackpots  Model Calculated Annuity Prize  Model Calculated Cash Value  Single Draw Calculated Model Rollover Probability  Overall Calculated Model Rollover Probability   $592,026,467.62  $348,637,809  44.89%  0.33%   $516,018,875.83  $303,877,782  49.40%  0.74%   $449,095,861.20  $264,467,563  53.74%  1.50%   $390,171,617.16  $229,767,730  57.88%  2.78%  $315  $338,290,114.89  $199,215,290  61.79%  4.81%  $262  $292,609,592.02  $172,314,538  65.45%  7.78%  $247  $252,388,895.26  $148,629,016  68.85%  11.89%  $217  $216,975,455.44  $127,774,435  71.99%  17.27%  $180  $185,794,699.74  $109,412,434  74.88%  23.99%  $153  $158,340,729.41  $93,245,096  77.51%  32.03%  $131  $134,168,111.72  $79,010,110  79.91%  41.33%  $111  $112,884,652.93  $66,476,518  82.08%  51.72%  $94  $94,145,035.08  $55,440,965  84.04%  63.01%  $82  $77,645,213.28  $45,724,403  85.80%  74.98%  $69  $63,117,482.71  $37,169,184  87.39%  87.39% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 11, 2006, 1:24 am  IP Logged  
The MM jackpot has rolled. The cash value is $44.3M ; the advertised annuity is $75M. Eighth round jackpots sell on average, $23.2M in tickets. If the current drawing results in average sales the probability of various numbers of winner is as follows: 0  87.61%  1  11.59%  2  0.77%  3  0.03% 
The long term model, a curve fit exponential function now overestimates the jackpot by 3%. It is nonetheless useful for estimating the long term probability of the lottery going to higher jackpots. Here are the values: Historical Average Advertised Annuity Jackpots  Model Calculated Annuity Prize  Model Calculated Cash Value  Single Draw Calculated Model Rollover Probability  Overall Calculated Model Rollover Probability   $590,231,123.34  $348,629,850  44.88%  0.38%   $514,437,385.11  $303,861,015  49.39%  0.85%   $447,705,186.67  $264,444,530  53.74%  1.71%   $388,951,173.30  $229,740,493  57.88%  3.19%  $315  $337,221,511.06  $199,185,506  61.79%  5.50%  $262  $291,676,401.83  $172,283,528  65.45%  8.91%  $247  $251,576,449.81  $148,597,823  68.85%  13.61%  $217  $216,270,657.82  $127,743,869  71.99%  19.76%  $180  $185,185,858.84  $109,383,114  74.88%  27.45%  $153  $157,817,410.96  $93,217,484  77.51%  36.66%  $131  $133,721,004.88  $78,984,540  79.91%  47.30%  $111  $112,505,450.80  $66,453,220  82.08%  59.19%  $94  $93,826,327.73  $55,420,084  84.04%  72.11%  $82  $77,380,392.00  $45,706,018  85.81%  85.81% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 15, 2006, 11:38 pm  IP Logged  
The MM jackpot has been won. The cash prize is reset to $7.1M and the advertised annuity is $12M. Average 1st draws produce 15.2M in sales. Selling an average number of tickets would result in the following distribution for the probability of various numbers of winners: 0  91.71%  1  7.93%  2  0.34%  3  0.01% 
Here is the long term probability, which ignores minimums: Historical Average Advertised Annuity Jackpots  Model Calculated Annuity Prize  Model Calculated Cash Value  Single Draw Calculated Model Rollover Probability  Overall Calculated Model Rollover Probability   $589,189,237.47  $348,603,632  44.87%  0.20%   $513,513,969.88  $303,829,099  49.39%  0.44%   $446,888,401.17  $264,408,971  53.73%  0.88%   $388,230,314.51  $229,702,936  57.88%  1.64%  $315  $336,586,910.96  $199,147,256  61.79%  2.83%  $262  $291,119,332.98  $172,245,605  65.45%  4.58%  $247  $251,089,038.57  $148,561,014  68.85%  7.00%  $217  $215,845,805.02  $127,708,768  72.00%  10.17%  $180  $184,817,167.09  $109,350,157  74.88%  14.13%  $153  $157,499,118.36  $93,186,978  77.52%  18.87%  $131  $133,447,924.48  $78,956,689  79.91%  24.34%  $111  $112,272,915.51  $66,428,142  82.09%  30.46%  $94  $93,630,140.14  $55,397,833  84.05%  37.10%  $82  $77,216,778.81  $45,686,594  85.81%  44.15%  $69  $62,766,224.91  $37,136,683  87.40%  51.45%  $52  $50,043,754.25  $29,609,221  88.82%  58.87%  $43  $38,842,712.35  $22,981,938  90.08%  66.28%  $33  $28,981,157.70  $17,147,185  91.22%  73.57%  $25  $20,298,906.46  $12,010,186  92.22%  80.66%  $16  $12,654,930.49  $7,487,501  93.12%  87.46%  $12  $5,925,066.66  $3,505,664  93.92%  93.92% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 18, 2006, 8:43 am  IP Logged  
MM has rolled over. The cash jackpot is $9.4M. The advertised annuity value is $16M. Second round draws sell on average $14.9M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows: 0  91.85%  1  7.81%  2  0.33%  3  0.01% 
Lotteryreport has not yet posted the sales figures and I will update the long term jackpot evolution figures when she has done so.   
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 19, 2006, 12:41 am  IP Logged  
The sales figures for the last MM drawing are now available. Here is the long term probability model function data for the probability for the 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   $593,382,592.54  $348,612,273  44.87%  0.21%   $517,163,807.92  $303,833,737  49.38%  0.46%   $450,060,465.71  $264,410,524  53.73%  0.94%   $390,982,397.77  $229,702,159  57.88%  1.75%  $315  $338,969,815.43  $199,144,767  61.79%  3.02%  $262  $293,177,716.68  $172,241,909  65.45%  4.88%  $247  $252,862,158.13  $148,556,518  68.85%  7.46%  $217  $217,368,168.89  $127,703,799  72.00%  10.83%  $180  $186,119,109.77  $109,344,977  74.88%  15.04%  $153  $158,607,305.18  $93,181,792  77.52%  20.09%  $131  $134,385,795.39  $78,951,655  79.91%  25.92%  $111  $113,061,075.13  $66,423,382  82.09%  32.43%  $94  $94,286,700.69  $55,393,437  84.05%  39.51%  $82  $77,757,661.57  $45,682,626  85.81%  47.01%  $68  $63,205,425.22  $37,133,187  87.40%  54.78%  $56  $50,393,574.43  $29,606,225  88.82%  62.68%  $46  $39,113,966.49  $22,979,455  90.09%  70.57%  $34  $29,183,351.68  $17,145,219  91.22%  78.34%  $25  $20,440,396.15  $12,008,733  92.23%  85.88%  $16  $12,743,060.91  $7,486,548  93.12%  93.12%  $12  $5,966,294.22  $3,505,198  93.92%  100.00% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 19, 2006, 12:51 am  IP Logged  
The Powerball jackpot has rolled over. The cash value is $26.1M; the advertised annuity is $54M. On average, sixth drawings in a powerball jackpot run sell $16.89M in tickets. Were the average number of tickets to sell this time out, the randomized probability of various numbers of winners is as follows: 0  89.08%  1  10.30%  2  0.60%  3  0.02% 
The model function for the long term evolution of jackpots suggests the following: Average Historical Annuity  Calculated Annuity  Calculated Cash Value Projections  Single Draw Rollover Probability  Overall Probability from baseline   $563,775,073.13  $272,491,285  27.11%  0.35%  $353  $444,264,170.36  $214,727,682  37.86%  1.29%  $300  $355,325,804.62  $171,740,806  48.54%  3.41%  $245  $289,139,099.33  $139,750,565  58.39%  7.03%  $208  $239,883,866.00  $115,943,869  67.01%  12.04%  $193  $203,228,800.60  $98,227,254  74.24%  17.97%  $180  $175,950,606.43  $85,042,793  80.11%  24.21%  $159  $155,650,550.50  $75,231,099  83.87%  30.22%  $132  $139,545,043.85  $67,446,771  84.50%  36.03%  $119  $124,128,268.44  $59,995,330  85.14%  42.64%  $105  $109,400,224.25  $52,876,775  85.78%  50.08%  $92  $95,360,911.30  $46,091,107  86.43%  58.38%  $80  $82,010,329.57  $39,638,326  87.08%  67.55%  $68  $69,348,479.07  $33,518,432  87.74%  77.57%  $57  $57,375,359.80  $27,731,424  88.40%  88.40% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 22, 2006, 8:21 am  IP Logged  
MM has rolled over. The cash jackpot is $13.6M. The advertised annuity value is $23M. Second round draws sell on average $15.9M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows: 0  91.32%  1  8.29%  2  0.38%  3  0.01% 
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   $589,627,657.58  $348,649,398  44.86%  0.22%   $513,867,975.02  $303,852,368  49.37%  0.50%   $447,172,348.14  $264,414,954  53.72%  1.01%   $388,456,333.32  $229,695,919  57.87%  1.87%  $315  $336,765,232.15  $199,130,746  61.78%  3.24%  $262  $291,258,568.45  $172,222,458  65.45%  5.24%  $247  $251,196,422.46  $148,533,537  68.85%  8.01%  $217  $215,927,400.07  $127,678,810  71.99%  11.64%  $180  $184,878,041.39  $109,319,190  74.88%  16.16%  $153  $157,543,496.54  $93,156,154  77.52%  21.58%  $131  $133,479,316.98  $78,926,900  79.92%  27.84%  $111  $112,294,228.99  $66,400,066  82.09%  34.84%  $94  $93,643,771.71  $55,371,969  84.05%  42.44%  $82  $77,224,696.31  $45,663,299  85.82%  50.49%  $68  $62,770,035.34  $37,116,195  87.40%  58.84%  $56  $50,044,761.93  $29,591,685  88.82%  67.32%  $46  $38,841,968.32  $22,967,425  90.09%  75.79%  $34  $28,979,501.67  $17,135,705  91.22%  84.13%  $25  $20,297,002.31  $12,001,706  92.23%  92.23% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 25, 2006, 5:14 am  IP Logged  
MM has rolled over. The cash jackpot is $18.4M. The advertised annuity value is $31M. Fourth round draws sell on average $16.8M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows: 0  90.90%  1  8.67%  2  0.41%  3  0.01% 
The long term curve fitting model suggests the following for the probability for 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   $587,406,671.23  $348,654,282  44.85%  0.24%   $511,928,935.92  $303,854,594  49.37%  0.54%   $445,482,042.33  $264,415,148  53.72%  1.09%   $386,985,458.53  $229,694,595  57.87%  2.03%  $315  $335,487,937.26  $199,128,324  61.78%  3.51%  $262  $290,152,047.12  $172,219,280  65.44%  5.68%  $247  $250,240,554.60  $148,529,878  68.85%  8.69%  $217  $215,104,435.51  $127,674,891  71.99%  12.62%  $180  $184,172,320.80  $109,315,184  74.88%  17.52%  $153  $156,941,205.21  $93,152,199  77.52%  23.40%  $131  $132,968,267.59  $78,923,101  79.92%  30.19%  $111  $111,863,669.95  $66,396,501  82.09%  37.78%  $94  $93,284,218.03  $55,368,697  84.05%  46.02%  $82  $76,927,780.47  $45,660,360  85.82%  54.75%  $68  $62,528,375.64  $37,113,617  87.40%  63.80%  $56  $49,851,846.38  $29,589,483  88.82%  72.99%  $46  $38,692,052.20  $22,965,605  90.09%  82.18%  $34  $28,867,517.14  $17,134,268  91.22%  91.22% 
  
United States Member #16612 June 2, 2005 3493 Posts Offline
 Posted: November 26, 2006, 3:09 pm  IP Logged  
Prob988, I hope MM continues to roll and get up to 365+ million.   
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: November 29, 2006, 11:21 pm  IP Logged  
MM has rolled over. The cash jackpot is $23.9M. The advertised annuity value is $40M. Fifth round draws sell on average $18.6M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows: 0  89.94%  1  9.54%  2  0.51%  3  0.02% 
The long term curve fitting model suggests the following for the probability for 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   $583,563,750.38  $348,679,341  44.84%  0.26%   $508,557,733.71  $303,863,246  49.36%  0.59%   $442,529,465.60  $264,411,356  53.71%  1.20%   $384,404,366.01  $229,681,609  57.86%  2.23%  $315  $333,236,475.36  $199,108,794  61.78%  3.85%  $262  $288,193,059.48  $172,195,353  65.44%  6.23%  $247  $248,541,057.25  $148,503,282  68.85%  9.53%  $217  $213,635,150.36  $127,647,002  71.99%  13.83%  $180  $182,907,261.04  $109,287,088  74.88%  19.22%  $153  $155,857,306.86  $93,124,741  77.52%  25.66%  $131  $132,045,062.10  $78,896,925  79.92%  33.10%  $111  $111,082,993.32  $66,372,089  82.09%  41.42%  $94  $92,629,952.36  $55,346,397  84.05%  50.46%  $82  $76,385,624.37  $45,640,411  85.82%  60.03%  $68  $62,085,640.30  $37,096,170  87.41%  69.95%  $56  $49,497,274.41  $29,574,621  88.83%  80.03%  $46  $38,415,656.76  $22,953,355  90.09%  90.09% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: December 3, 2006, 10:12 am  IP Logged  
The MM jackpot has been won. The cash prize is reset to $7.2M and the advertised annuity is $12M. Average 1st draws produce 15.2M in sales. Selling an average number of tickets would result in the following distribution for the probability of various numbers of winners: 0  91.72%  1  7.93%  2  0.34%  3  0.01% 
Here is the long term probability, which ignores minimums, focusing on models generated from sales figures and what sales actually contribute to jackpots: Historical Average Advertised Annuity Jackpots  Model Calculated Annuity Prize  Model Calculated Cash Value  Single Draw Calculated Model Rollover Probability  Overall Calculated Model Rollover Probability   $589,340,718.90  $348,693,259  44.83%  0.19%   $513,574,074.30  $303,864,661  49.35%  0.43%   $446,878,967.66  $264,403,389  53.70%  0.88%   $388,169,264.02  $229,666,815  57.85%  1.64%  $315  $336,488,871.33  $199,089,249  61.77%  2.84%  $262  $290,996,170.42  $172,172,734  65.44%  4.59%  $247  $250,950,309.16  $148,478,933  68.85%  7.01%  $217  $215,699,137.59  $127,621,990  71.99%  10.19%  $180  $184,668,587.67  $109,262,248  74.88%  14.15%  $153  $157,353,324.52  $93,100,717  77.52%  18.90%  $131  $133,308,516.95  $78,874,206  79.92%  24.38%  $111  $112,142,593.43  $66,351,034  82.10%  30.50%  $94  $93,510,865.27  $55,327,262  84.06%  37.15%  $82  $77,109,913.33  $45,623,365  85.82%  44.20%  $68  $62,672,646.84  $37,081,316  87.41%  51.50%  $56  $49,963,953.81  $29,562,006  88.83%  58.92%  $46  $38,776,872.20  $22,942,983  90.10%  66.32%  $34  $28,929,219.51  $17,116,455  91.23%  73.61%  $25  $20,260,625.97  $11,987,537  92.24%  80.69%  $16  $12,629,922.85  $7,472,704  93.13%  87.48%  $12  $5,912,843.58  $3,498,432  93.93%  93.93% 
  
Thread Starter New Jersey United States Member #21206 September 4, 2005 954 Posts Offline  Posted: December 6, 2006, 9:48 am  IP Logged  
MM has rolled over. The cash jackpot is $9.0M. The advertised annuity value is $15M. Second round draws sell on average $14.9M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows: 0  91.87%  1  7.79%  2  0.33%  3  0.01% 
The long term modeling program I use, which does not account for jackpot minima, 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   $581,306,498.72  $348,783,899  44.80%  0.21%   $506,522,262.92  $303,913,358  49.32%  0.46%   $440,699,603.43  $264,419,762  53.68%  0.94%   $382,764,632.81  $229,658,780  57.84%  1.75%  $315  $331,772,150.20  $199,063,290  61.76%  3.02%  $262  $286,890,220.41  $172,134,132  65.43%  4.89%  $247  $247,386,601.10  $148,431,961  68.84%  7.47%  $217  $212,616,796.26  $127,570,078  71.99%  10.85%  $180  $182,013,541.44  $109,208,125  74.88%  15.08%  $153  $155,077,548.85  $93,046,529  77.52%  20.14%  $131  $131,369,361.56  $78,821,617  79.93%  25.97%  $111  $110,502,183.84  $66,301,310  82.10%  32.50%  $94  $92,135,570.62  $55,281,342  84.06%  39.58%  $82  $75,969,873.19  $45,581,924  85.83%  47.08%  $68  $61,741,350.48  $37,044,810  87.42%  54.86%  $56  $49,217,866.15  $29,530,720  88.84%  62.75%  $46  $38,195,101.31  $22,917,061  90.11%  70.64%  $34  $28,493,221.10  $17,095,933  91.24%  78.39%  $25  $19,953,940.73  $11,972,364  92.25%  85.92%  $16  $12,437,943.02  $7,462,766  93.14%  93.14% 
  
