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Probability of a Rollover in Powerball.

Topic closed. 310 replies. Last post 10 years ago by Prob988.

 Page 21 of 21
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: February 15, 2007, 2:54 pm - IP Logged

The Powerball jackpot has rolled.  The cash value is 27.5M; the advertised annuity, \$58M.  The average number of tickets sold on on sixth draws is 16.7M.

The average sales of this size produce a probability distribution for numbers of winners as follows:

 0 89.14% 1 10.25% 2 0.59% 3 0.02%

The long term jackpot evolution has been pretty accurate of late in Powerball (not so good in MM - which I am still modeling as a pure exponential).  Here is what it suggests for the long term behavior for this run:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$578,696,238.33 \$274,381,837 27.19% 0.34% \$353 \$457,144,193.15 \$216,749,402 37.72% 1.23% \$300 \$366,140,574.52 \$173,601,134 48.19% 3.27% \$245 \$298,007,960.30 \$141,296,878 57.90% 6.79% \$218 \$246,998,415.94 \$117,111,318 66.42% 11.73% \$196 \$208,808,576.24 \$99,004,066 73.61% 17.66% \$180 \$180,216,596.55 \$85,447,524 79.51% 23.99% \$158 \$158,810,345.33 \$75,298,009 83.84% 30.17% \$132 \$142,358,753.07 \$67,497,685 84.48% 35.98% \$119 \$126,613,062.79 \$60,032,056 85.12% 42.60% \$104 \$111,573,274.48 \$52,901,122 85.76% 50.05% \$92 \$97,239,388.14 \$46,104,882 86.41% 58.35% \$79 \$83,611,403.78 \$39,643,338 87.07% 67.53% \$67 \$70,689,321.40 \$33,516,489 87.73% 77.55% \$57 \$58,473,140.99 \$27,724,334 88.40% 88.40%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
Offline
 Posted: February 18, 2007, 11:41 am - IP Logged

Powerball has rolled over.  The cash jackpot is \$31.9 M, the advertised annuity value is \$67M.  The average sales for 7th draws is 17.1M.

Sales of 17.1M in this drawing would produce a probability distribution for numbers of winners as follows:

 0 88.93% 1 10.43% 2 0.61% 3 0.02%

The long term jackpot model suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$576,368,847.15 \$274,420,391 27.19% 0.38% \$353 \$455,322,666.60 \$216,787,956 37.72% 1.40% \$300 \$364,697,778.85 \$173,639,689 48.19% 3.70% \$245 \$296,848,712.96 \$141,335,432 57.90% 7.68% \$218 \$246,051,455.65 \$117,149,872 66.42% 13.26% \$196 \$208,020,551.07 \$99,042,621 73.61% 19.97% \$180 \$179,547,562.97 \$85,486,078 79.51% 27.12% \$158 \$158,230,398.41 \$75,336,563 83.84% 34.12% \$132 \$141,842,645.74 \$67,534,036 84.47% 40.69% \$119 \$126,157,590.33 \$60,066,077 85.11% 48.17% \$104 \$111,175,232.19 \$52,932,685 85.76% 56.60% \$92 \$96,895,571.30 \$46,133,862 86.41% 66.00% \$79 \$83,318,607.67 \$39,669,606 87.07% 76.38% \$67 \$70,444,341.30 \$33,539,918 87.73% 87.73%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: February 22, 2007, 7:45 am - IP Logged

Powerball has rolled over.  The cash jackpot is \$37.5M, the advertised annuity is \$78M.  Average sales for 8th round drawings are 18.3M.  Average sales would provide the following probability distribution for numbers of winners:

 0 88.20% 1 11.07% 2 0.69% 3 0.03%

The long term probability distribution model suggests the following for jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$570,972,780.08 \$274,506,144 27.19% 0.43% \$353 \$451,097,314.83 \$216,873,709 37.72% 1.59% \$300 \$361,348,918.54 \$173,725,442 48.19% 4.21% \$245 \$294,156,064.51 \$141,421,185 57.90% 8.74% \$218 \$243,850,100.07 \$117,235,625 66.42% 15.10% \$196 \$206,187,016.78 \$99,128,373 73.61% 22.74% \$180 \$177,989,409.22 \$85,571,831 79.51% 30.89% \$158 \$156,878,416.64 \$75,422,316 83.82% 38.85% \$132 \$140,632,056.86 \$67,611,566 84.46% 46.35% \$119 \$125,082,161.96 \$60,135,655 85.10% 54.88% \$104 \$110,228,731.94 \$52,994,583 85.74% 64.49% \$92 \$96,071,766.79 \$46,188,349 86.40% 75.21% \$79 \$82,611,266.52 \$39,716,955 87.05% 87.05%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: February 25, 2007, 11:35 pm - IP Logged

The powerball jackpot has rolled over.  The new cash prize is \$43.2M; the advertised annuity is \$90M.  The average sales for a 9th drawing are 21.1M.  Average sales would produce a winner distribuiton probability like this:

 k, number of winners p(m,k) 0 86.57% 1 12.49% 2 0.90% 3 0.04%

The long term models suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$571,990,745.54 \$274,555,558 27.19% 0.50% \$353 \$451,923,172.17 \$216,923,123 37.72% 1.82% \$300 \$362,030,948.32 \$173,774,855 48.19% 4.84% \$245 \$294,730,413.44 \$141,470,598 57.90% 10.04% \$218 \$244,343,830.47 \$117,285,039 66.42% 17.34% \$196 \$206,620,389.67 \$99,177,787 73.61% 26.10% \$180 \$178,377,593.64 \$85,621,245 79.51% 35.46% \$158 \$157,232,769.34 \$75,471,729 83.81% 44.60% \$132 \$140,946,828.33 \$67,654,478 84.45% 53.22% \$119 \$125,359,406.09 \$60,172,515 85.09% 63.02% \$104 \$110,470,502.62 \$53,025,841 85.73% 74.06% \$92 \$96,280,117.91 \$46,214,457 86.39% 86.39%

United States
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June 2, 2005
3493 Posts
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 Posted: February 26, 2007, 7:41 pm - IP Logged

I hope PB continues to roll and reaches between 365 and 390 million on this run.

New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 1, 2007, 11:54 pm - IP Logged

Powerball has rolled.  The cash jackpot is \$50.2M, the advertised annuity is \$105M.  Tenth round jackpots sell  21.9 M tickets.  If this is the nubmer that sell, the distribution of winners will be as follows:

 0 86.07% 1 12.91% 2 0.97% 3 0.05%

Here is the long term model of the run:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$574,228,336.77 \$274,535,833 27.19% 0.57% \$353 \$453,682,406.54 \$216,903,398 37.72% 2.11% \$300 \$363,432,046.34 \$173,755,131 48.19% 5.60% \$245 \$295,863,381.83 \$141,450,874 57.90% 11.62% \$218 \$245,276,055.51 \$117,265,314 66.42% 20.07% \$196 \$207,402,322.12 \$99,158,063 73.61% 30.22% \$180 \$179,047,004.98 \$85,601,520 79.51% 41.06% \$158 \$157,817,938.35 \$75,452,005 83.81% 51.64% \$132 \$141,473,902.14 \$67,637,999 84.45% 61.61% \$119 \$125,830,565.07 \$60,158,994 85.09% 72.96% \$104 \$110,887,927.12 \$53,014,990 85.74% 85.74%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 4, 2007, 9:55 pm - IP Logged

Not that anybody is noticing, Powerball has rolled and has quite an impressive jackpot.  The cash value is \$57.6M, the advertised annuity is \$120M.  Tenth draws average about 21.9M in sales.  This suggests the following probability distribution for numbers of winners:

 0 86.07% 1 12.91% 2 0.97% 3 0.05%

The long term model suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$572,275,012.31 \$274,692,006 27.19% 0.67% \$353 \$452,207,438.95 \$217,059,571 37.72% 2.46% \$300 \$362,315,215.09 \$173,911,303 48.19% 6.52% \$245 \$295,014,680.21 \$141,607,046 57.90% 13.53% \$218 \$244,628,097.24 \$117,421,487 66.42% 23.38% \$196 \$206,904,656.44 \$99,314,235 73.61% 35.19% \$180 \$178,661,860.41 \$85,757,693 79.51% 47.81% \$158 \$157,517,036.11 \$75,608,177 83.77% 60.13% \$132 \$141,184,317.03 \$67,768,472 84.41% 71.79% \$119 \$125,554,268.61 \$60,266,049 85.05% 85.05%
New Jersey
United States
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September 4, 2005
949 Posts
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 Posted: March 11, 2007, 3:37 pm - IP Logged

The powerball jackpot has rolled.  The cash value is \$79.5M.  The advertised annuity is \$165M.

Average ticket sales for 12th drawings are 27.4M.  If this is the number of tickets that sell, the probability of various numbers of winners is:

 0 82.90% 1 15.55% 2 1.46% 3 0.09%
rural lowcountry, south carolina
United States
Member #31677
February 2, 2006
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 Posted: March 11, 2007, 3:44 pm - IP Logged

I hope PB continues to roll and reaches between 365 and 390 million on this run.

Me too!

New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 15, 2007, 10:35 am - IP Logged

The Powerball jackpot has rolled.  The cash value is \$88.2M, the annuity is advertised at \$183M.  Thirteen round draws sell on average 31.4M tickets.  (Recent draws have been above average though).

Here is the probability for various numbers of winners:

 0 80.66% 1 17.34% 2 1.86% 3 0.13% 4 0.01%

The long term model function suggests the following for jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$571,390,249.50 \$275,391,366 27.19% 1.11% \$353 \$451,812,747.87 \$217,758,931 37.72% 4.09% \$300 \$362,287,431.05 \$174,610,663 48.19% 10.85% \$245 \$295,261,592.23 \$142,306,407 57.90% 22.51% \$218 \$245,080,668.78 \$118,120,847 66.42% 38.87% \$196 \$207,511,201.21 \$100,013,595 73.61% 58.53% \$180 \$179,383,681.90 \$86,457,053 79.51% 79.51%
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: March 30, 2007, 12:02 am - IP Logged

Powerball has rolled.  The cash jackpot is 19.1M, the advertised annuity is \$41M.

Fourth round drawings sell 15.4M tickets on average.  The probabilities in an average run for various numbers of winners is as follows:

 0 89.97% 1 9.51% 2 0.50% 3 0.02%

The long term model suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$590,800,138.12 \$275,226,406 27.19% 0.26% \$353 \$467,086,533.74 \$217,593,971 37.72% 0.96% \$300 \$374,464,598.37 \$174,445,703 48.19% 2.56% \$245 \$305,120,382.33 \$142,141,446 57.90% 5.30% \$218 \$253,203,735.58 \$117,955,887 66.42% 9.16% \$196 \$214,334,766.21 \$99,848,635 73.61% 13.79% \$180 \$185,234,335.54 \$86,292,093 79.51% 18.73% \$158 \$163,447,417.09 \$76,142,577 83.43% 23.56% \$132 \$146,242,225.46 \$68,127,476 84.11% 28.24% \$119 \$129,809,086.06 \$60,472,038 84.80% 33.58% \$104 \$114,147,998.90 \$53,176,263 85.49% 39.60% \$92 \$99,258,963.96 \$46,240,152 86.19% 46.31% \$79 \$85,141,981.26 \$39,663,703 86.89% 53.73% \$67 \$71,797,050.79 \$33,446,919 87.60% 61.84% \$57 \$59,224,172.55 \$27,589,797 88.32% 70.59% \$46 \$47,423,346.55 \$22,092,339 89.04% 79.93% \$36 \$36,394,572.77 \$16,954,545 89.77% 89.77%

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