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# Probability of a Rollover in Powerball.

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

 Page 15 of 21
New Jersey
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 Posted: July 31, 2006, 11:46 pm - IP Logged

Here is the probability table for the jackpot evolution of powerball:

 \$353 \$461,830,178.89 \$210,654,153 37.37% 4.47% \$300 \$366,331,124.05 \$167,094,261 48.65% 11.97% \$245 \$296,434,366.92 \$135,212,321 59.02% 24.60% \$208 \$245,276,199.27 \$111,877,595 67.98% 41.68% \$193 \$207,833,001.28 \$94,798,666 75.39% 61.31% \$173 \$180,427,933.02 \$82,298,418 81.32% 81.32%
New Jersey
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 Posted: August 3, 2006, 7:51 am - IP Logged

The Powerball jackpot has rolled.  The cash value is \$92.7M; the advertised annuity jackpot is \$204M.  The average number of tickets sold on a 15th draw is 40M.  If this is the number of tickets that sell, the probability distribution for numbers of winners is:

 0 76.58% 1 20.43% 2 2.73% 3 0.24% 4 0.02%

The long term probability looks like this, ignoring caps:

 Average Jackpots \$592,077,809.46 \$270,063,878 26.37% 1.44% \$353 \$462,750,509.21 \$211,073,942 37.53% 5.47% \$300 \$367,667,252.13 \$167,703,708 48.65% 14.57% \$245 \$297,760,699.09 \$135,817,300 58.88% 29.95% \$208 \$246,364,414.30 \$112,373,962 67.74% 50.87% \$193 \$208,577,140.09 \$95,138,089 75.10% 75.10%

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 Posted: August 4, 2006, 12:40 am - IP Logged

Prob988, I hope PB continues to roll, set new roll records, and hit the cap annunity value of 390 million.

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 Posted: August 6, 2006, 2:16 am - IP Logged

Prob988, I hope PB continues to roll, set new roll records, and hit the cap annunity value of 390 million.

Prob988, PB Jackpot for 8/9 has reseted to 15 million. Someone in Wisconsin won jackpot.

New Jersey
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 Posted: August 7, 2006, 8:57 am - IP Logged

The Powerball jackpot has been won, and the cash value has been reset at \$6.9M, and the advertised set annuity value is now \$15M.  First drawing Powerball Sales average 14.5M.  If this is how many tickets sell, the probability for randomized tickets of total numbers of winners is as follows:

 0 90.52% 1 9.01% 2 0.45% 3 0.01%

Long term jackpot evolution, ignoring minimums, caps and reserves, is modelled by a mixed linear/exponential function that suggests the following:

 Average Jackpots \$592,612,786.04 \$270,307,897 26.78% 0.22% \$353 \$464,787,607.25 \$212,003,122 37.71% 0.83% \$300 \$370,156,459.57 \$168,839,108 48.57% 2.20% \$245 \$300,099,416.05 \$136,884,056 58.59% 4.54% \$208 \$248,234,998.62 \$113,227,190 67.32% 7.74% \$193 \$209,838,890.81 \$95,713,610 74.60% 11.50% \$173 \$181,413,601.02 \$82,748,010 80.50% 15.41% \$152 \$160,369,876.92 \$73,149,357 84.35% 19.15% \$126 \$143,858,001.05 \$65,617,811 84.96% 22.70% \$112 \$128,042,080.44 \$58,403,710 85.57% 26.72% \$102 \$112,922,115.07 \$51,507,055 86.19% 31.23% \$90 \$98,498,104.95 \$44,927,845 86.81% 36.23% \$78 \$84,770,050.07 \$38,666,081 87.43% 41.74% \$67 \$71,737,950.45 \$32,721,762 88.06% 47.74% \$56 \$59,401,806.07 \$27,094,888 88.69% 54.21% \$46 \$47,761,616.94 \$21,785,460 89.33% 61.12% \$36 \$36,817,383.06 \$16,793,477 89.98% 68.42% \$27 \$26,569,104.42 \$12,118,940 90.62% 76.04% \$20 \$17,016,781.03 \$7,761,848 91.28% 83.91% \$15 \$8,160,412.89 \$3,722,201 91.93% 91.93%
New Jersey
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 Posted: August 8, 2006, 9:48 am - IP Logged

Here is a slightly different way of looking at the long term probability, by rejecting any modelling function and looking at the actual accumulated sales data since the matrix change.  When one does this this is what the data looks like, ignoring the presence of caps, minimum and reserves:

 Drawing Number Calculated Annuity Cash Value Averages Single Draw Rollover Probability Overall Probability from baseline 19 \$460,038,075.25 \$209,836,722.07 32.69% 0.87% 18 \$351,544,295.82 \$160,349,559.45 52.87% 2.67% 17 \$289,706,256.33 \$132,143,434.34 64.38% 5.05% 16 \$246,987,847.66 \$112,658,327.93 71.52% 7.84% 15 \$214,467,262.07 \$97,824,744.70 76.58% 10.96% 14 \$188,580,927.76 \$86,017,236.08 77.64% 14.32% 13 \$164,024,357.05 \$74,816,271.25 81.23% 18.44% 12 \$143,858,001.05 \$65,617,810.80 83.40% 22.70% 11 \$126,245,498.10 \$57,584,236.88 85.04% 27.22% 10 \$110,520,530.77 \$50,411,622.74 86.61% 32.01% 9 \$96,578,358.57 \$44,052,193.23 86.82% 36.96% 8 \$82,866,263.65 \$37,797,708.65 88.48% 42.57% 7 \$70,992,010.15 \$32,381,516.89 89.07% 48.11% 6 \$59,764,774.30 \$27,260,448.67 89.46% 54.01% 5 \$48,961,535.70 \$22,332,777.90 89.85% 60.37% 4 \$38,575,439.90 \$17,595,378.07 90.33% 67.19% 3 \$28,705,422.66 \$13,093,376.66 90.32% 74.39% 2 \$18,828,544.33 \$8,588,245.70 90.98% 82.36% 1 \$9,659,027.24 \$4,405,762.75 90.52% 90.52%

The annuity calculations are the weakest, since they depend on financial factors not affected by sales.  (An Argentine style collapse of the US currency under a spiral of debt accumulated for arbitrary wars, for instance, would affect interest rates.)

We see that on averate we have a chance that is slightly lower than half a chance on any reset jackpot of reaching an eigth draw, which on average compares to a \$37.78M cash jackpot.

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 Posted: August 10, 2006, 11:09 am - IP Logged

Powerball has rolled over.  The cash value is \$9.2M, the advertised annuity is \$20M.  Second drawings have sold at an average of \$13.8M.  If this is how many tickets sell, the distribution of winners will have the following probability:

 0 90.98% 1 8.60% 2 0.41% 3 0.01%

The long term mixed linear/exponential modeling function gives the following predictions for jackpot evolution:

 Average Jackpots \$592,590,519.86 \$270,297,740 26.78% 0.24% \$353 \$464,765,341.07 \$211,992,965 37.71% 0.90% \$300 \$370,134,193.39 \$168,828,951 48.57% 2.40% \$245 \$300,077,149.87 \$136,873,900 58.59% 4.93% \$208 \$248,212,732.44 \$113,217,033 67.32% 8.42% \$193 \$209,816,624.63 \$95,703,454 74.60% 12.51% \$173 \$181,391,334.84 \$82,737,854 80.50% 16.77% \$152 \$160,347,610.74 \$73,139,201 84.35% 20.83% \$126 \$143,831,281.64 \$65,605,623 84.95% 24.70% \$112 \$128,011,935.45 \$58,389,960 85.57% 29.07% \$102 \$112,889,572.19 \$51,492,211 86.18% 33.98% \$90 \$98,464,191.84 \$44,912,377 86.81% 39.42% \$78 \$84,735,794.41 \$38,650,456 87.43% 45.41% \$67 \$71,704,379.90 \$32,706,449 88.06% 51.94% \$56 \$59,369,948.30 \$27,080,357 88.70% 58.98% \$46 \$47,732,499.63 \$21,772,179 89.34% 66.50% \$36 \$36,792,033.87 \$16,781,915 89.98% 74.44% \$27 \$26,548,551.02 \$12,109,565 90.63% 82.73% \$20 \$17,002,051.10 \$7,755,129 91.28% 91.28%

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 Posted: August 13, 2006, 12:27 pm - IP Logged

Prob988, PB's estimated jackpot for 8/16 has rolled to 29 million.

New Jersey
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 Posted: August 14, 2006, 10:36 pm - IP Logged

The Powerball jackpot has rolled.  The cash value is \$13.2M and the advertised annuity value is \$29M.

The average 3rd draw jackpot has sales of 14.9M.  If this is the number of tickets that sell, the randomized probability distribution for numbers of winners is as follows:

 0 90.32% 1 9.19% 2 0.47% 3 0.02%

The mixed linear/exponential modeling function suggests the following long term probabilities, ignoring reserves, minimums and caps:

 Average Jackpots \$592,747,107.53 \$270,369,165 26.78% 0.26% \$353 \$464,921,928.74 \$212,064,389 37.71% 0.99% \$300 \$370,290,781.05 \$168,900,376 48.57% 2.62% \$245 \$300,233,737.54 \$136,945,324 58.59% 5.40% \$208 \$248,369,320.11 \$113,288,458 67.32% 9.22% \$193 \$209,973,212.29 \$95,774,878 74.60% 13.70% \$173 \$181,547,922.51 \$82,809,278 80.50% 18.36% \$152 \$160,504,198.40 \$73,210,625 84.37% 22.80% \$126 \$144,009,467.60 \$65,686,899 84.97% 27.03% \$112 \$128,206,112.47 \$58,478,530 85.58% 31.81% \$102 \$113,094,133.00 \$51,585,517 86.19% 37.17% \$90 \$98,673,529.20 \$45,007,861 86.80% 43.13% \$78 \$84,944,301.07 \$38,745,562 87.43% 49.69% \$67 \$71,906,448.60 \$32,798,619 88.05% 56.83% \$56 \$59,559,971.80 \$27,167,032 88.68% 64.55% \$46 \$47,904,870.67 \$21,850,802 89.31% 72.79% \$36 \$36,941,145.20 \$16,849,929 89.95% 81.49% \$27 \$26,668,795.40 \$12,164,412 90.60% 90.60%

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 Posted: August 17, 2006, 12:42 am - IP Logged

Prob988, PB Jackpot for 8/19 has rolled to 40 million.

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 Posted: August 17, 2006, 6:27 am - IP Logged

Powerball has rolled.  The new cash jackpot is \$18.4M.  The advertised annuity is \$40M.  The average sales for 4th round drawing is 14.9M.  If this is how many tickets the randomized distribution of winners is as follows:

 0 90.30% 1 9.21% 2 0.47% 3 0.02%

The mixed linear/exponential model gives the following results:

 Average Jackpots \$592,764,980.11 \$270,377,317 26.78% 0.29% \$353 \$464,939,801.32 \$212,072,542 37.71% 1.09% \$300 \$370,308,653.63 \$168,908,528 48.57% 2.90% \$245 \$300,251,610.12 \$136,953,476 58.59% 5.96% \$208 \$248,387,192.68 \$113,296,610 67.32% 10.18% \$193 \$209,991,084.87 \$95,783,030 74.60% 15.12% \$173 \$181,565,795.08 \$82,817,430 80.50% 20.26% \$152 \$160,522,070.98 \$73,218,777 84.37% 25.17% \$126 \$144,028,805.15 \$65,695,720 84.97% 29.83% \$112 \$128,226,441.68 \$58,487,803 85.58% 35.11% \$102 \$113,114,980.59 \$51,595,027 86.19% 41.03% \$90 \$98,694,421.86 \$45,017,391 86.80% 47.60% \$78 \$84,964,765.51 \$38,754,896 87.42% 54.84% \$67 \$71,926,011.52 \$32,807,542 88.05% 62.73% \$56 \$59,578,159.91 \$27,175,328 88.68% 71.24% \$46 \$47,921,210.66 \$21,858,255 89.31% 80.34% \$36 \$36,955,163.79 \$16,856,323 89.95% 89.95%

These projections ignore caps, reserves and minimums.

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 Posted: August 20, 2006, 12:06 am - IP Logged

PB has rolled to 51 million Prob988. I hope it continues to roll and set new records.

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 Posted: August 22, 2006, 11:42 pm - IP Logged

Powerball, as we know, rolled last Saturday night.  The cash jackpot is \$23.3M and the advertised annuity jackpot is \$51M.

Powerball's fifth drawings average 15.6M in sales.  The randomized probability of various numbers of winners will be, if this is the number of tickets sold:

 0 89.85% 1 9.62% 2 0.51% 3 0.02%

The mixed linear/exponential modeling function suggests the following probabilities of jackpot evolution:

 Average Jackpots \$592,994,190.94 \$270,481,866 26.78% 0.32% \$353 \$465,169,012.15 \$212,177,091 37.71% 1.21% \$300 \$370,537,864.46 \$169,013,078 48.57% 3.22% \$245 \$300,480,820.95 \$137,058,026 58.59% 6.62% \$208 \$248,616,403.51 \$113,401,160 67.32% 11.30% \$193 \$210,220,295.70 \$95,887,580 74.60% 16.79% \$173 \$181,795,005.91 \$82,921,980 80.50% 22.51% \$152 \$160,751,281.81 \$73,323,327 84.37% 27.96% \$126 \$144,265,178.81 \$65,803,536 84.97% 33.14% \$112 \$128,465,845.78 \$58,597,002 85.58% 39.00% \$102 \$113,353,282.71 \$51,703,723 86.18% 45.57% \$90 \$98,927,489.60 \$45,123,700 86.80% 52.87% \$78 \$85,188,466.46 \$38,856,933 87.41% 60.92% \$67 \$72,136,213.28 \$32,903,421 88.03% 69.69% \$56 \$59,770,730.06 \$27,263,165 88.66% 79.16% \$47 \$48,092,016.81 \$21,936,165 89.29% 89.29%

As usual this ignores caps, reserves and minimums.

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 Posted: August 24, 2006, 11:33 am - IP Logged

Prob988, PB Jackpot is now 64 million for 8/26. What's your probability stats now?

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 Posted: August 24, 2006, 4:17 pm - IP Logged

The powerball jackpot has rolled.  The cash value is \$29.4M, the advertised annuity is \$64 million dollars.

The average 6th round drawing sells 16.3M tickets.  If this is how many tickets sell on this drawing the distribution of winners will have the following random probability:

 0 89.46% 1 9.96% 2 0.55% 3 0.02%

My model of jackpot evolution gives the following probability:

 Average Jackpots \$580,995,539.01 \$270,526,048 26.78% 0.36% \$353 \$455,777,230.07 \$212,221,273 37.71% 1.36% \$300 \$363,075,992.34 \$169,057,259 48.57% 3.60% \$245 \$294,447,693.90 \$137,102,207 58.59% 7.41% \$208 \$243,641,000.68 \$113,445,341 67.32% 12.65% \$193 \$206,027,944.04 \$95,931,761 74.60% 18.80% \$173 \$178,182,360.31 \$82,966,162 80.50% 25.20% \$152 \$157,567,802.44 \$73,367,508 84.37% 31.30% \$126 \$141,416,501.22 \$65,847,058 84.97% 37.10% \$112 \$125,936,983.51 \$58,639,408 85.57% 43.66% \$102 \$111,129,249.30 \$51,744,557 86.18% 51.02% \$90 \$96,993,298.59 \$45,162,505 86.79% 59.20% \$78 \$83,529,131.40 \$38,893,252 87.41% 68.21% \$67 \$70,736,747.70 \$32,936,798 88.03% 78.04% \$56 \$58,616,147.52 \$27,293,144 88.65% 88.65%

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