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# Probability of a Rollover in Powerball.

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

 Page 16 of 21

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 Posted: August 27, 2006, 12:33 am - IP Logged

Prob988, PB Jackpot has rolled to 75 million for 8/30.

New Jersey
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 Posted: August 27, 2006, 11:12 am - IP Logged

The Powerball jackpot has rolled.  The cash value jackpot is estimated at \$34.9M, and the advertised annuity value is \$75M.    Note that the difference between the MM jackpot and the Powerball jackpot is 5 million in both annuity and in cash, but the cash value of powerball is lower by 5 million while the advertised annuity is higher than MM.

Thus you win more money with MM, but need to beat longer odds.

The number of  tickets sold on 7th draws averages 16.9M.  If this is the number of tickets sold, the randomized probability for various numbers of winners is as follows:

 0 89.07% 1 10.31% 2 0.60% 3 0.02%

Lottoreport has not posted the sales figures for the most recent drawing as of yet, and I will therefore not post long term jackpot evolution model figures.

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 Posted: August 29, 2006, 8:29 pm - IP Logged

The data on sales of the most recent drawing is now available.

Here is what the mixed linear exponential model predicts for jackpot evolution:

 Average Historical Annuity Drawing Number Calculated Annuity Cash Value Averages Single Draw Rollover Probability Overall Probability from baseline \$353 19 \$451,408,146.95 \$210,186,918.42 32.69% 1.81% \$300 18 \$345,126,992.33 \$160,699,755.80 52.87% 5.55% \$245 17 \$284,550,079.35 \$132,493,630.70 64.38% 10.49% \$208 16 \$242,702,870.95 \$113,008,524.29 71.52% 16.30% \$193 15 \$210,845,510.99 \$98,174,941.06 76.58% 22.79% \$173 14 \$185,487,103.22 \$86,367,432.44 77.64% 29.76% \$152 13 \$161,431,339.82 \$75,166,467.60 81.23% 38.33% \$126 12 \$141,676,256.98 \$65,968,007.16 83.40% 47.19% \$112 11 \$124,422,943.85 \$57,934,433.23 85.04% 56.58% \$102 10 \$109,018,671.89 \$50,761,819.10 86.61% 66.54% \$90 9 \$95,360,836.70 \$44,402,389.59 86.82% 76.82% \$78 8 \$81,928,386.58 \$38,147,905.00 88.48% 88.48%

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 Posted: August 31, 2006, 12:25 am - IP Logged

Prob988, PB Jackpot for 9/2 is 89 million. Everyone, I think the annunity jackpot is running higher than expected for each run because it keeps rolling to at least 100+ Million.

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 Posted: August 31, 2006, 1:20 am - IP Logged

PB has rolled.  The cash value is \$41.3M.  The advertised annuity is \$89M.  The average 8th draw produces sales of \$17.9M.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

 0 88.48% 1 10.83% 2 0.66% 3 0.03%

A modelling program that I have written, not very accurate right now, suggests the following jackpot evolution:

 \$583,391,611.73 \$270,719,928 26.78% 0.47% \$457,746,939.00 \$212,415,153 37.71% 1.74% \$364,730,056.92 \$169,251,139 48.57% 4.61% \$295,868,081.62 \$137,296,087 58.59% 9.48% \$244,888,393.45 \$113,639,221 67.32% 16.18% \$207,147,265.71 \$96,125,641 74.60% 24.04% \$179,206,868.79 \$83,160,041 80.50% 32.23% \$158,522,119.09 \$73,561,388 84.35% 40.03% \$142,286,471.12 \$66,027,317 84.94% 47.46% \$126,724,429.62 \$58,805,831 85.55% 55.87% \$111,835,994.59 \$51,896,928 86.15% 65.31% \$97,621,166.03 \$45,300,609 86.76% 75.81% \$84,079,943.93 \$39,016,873 87.38% 87.38%
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 Posted: September 3, 2006, 9:51 pm - IP Logged

PB has rolled.  The cash value is \$47.9M.  The advertised annuity is \$102M.  The average 9th draw produces sales of \$17.9M.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

 0 86.82% 1 12.27% 2 0.87% 3 0.04%

The model function developed for this game shows the following jackpot evolution, for what it's worth:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline Average Jackpots \$583,796,182.73 \$270,907,667 26.78% 0.46% \$353 \$458,151,510.00 \$212,602,892 37.71% 1.73% \$300 \$365,134,627.93 \$169,438,878 48.57% 4.59% \$245 \$296,272,652.62 \$137,483,826 58.59% 9.46% \$208 \$245,292,964.45 \$113,826,960 67.32% 16.14% \$193 \$207,551,836.72 \$96,313,380 74.60% 23.97% \$173 \$179,611,439.79 \$83,347,780 80.50% 32.14% \$152 \$158,926,690.10 \$73,749,127 84.30% 39.92% \$126 \$142,637,809.10 \$66,190,354 84.90% 47.36% \$112 \$127,026,219.94 \$58,945,875 85.50% 55.78% \$102 \$112,091,922.61 \$52,015,690 86.11% 65.23% \$92 \$97,834,917.10 \$45,399,799 86.73% 75.75%
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 Posted: September 7, 2006, 6:04 am - IP Logged

PB has rolled.  The cash value is \$55.8.  The advertised annuity is \$119M.  The average 10th draw produces sales of \$23.7.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

 0 83.93% 1 14.70% 2 1.29% 3 0.08%

The long term mixed linear modeling function, ignoring caps, reserves and minimums and is running about 6% behind the actual run.  Nevertheless this is what it predicts for long term jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$578,117,065.63 \$271,083,464 26.78% 0.61% \$353 \$453,775,340.95 \$212,778,689 37.71% 2.28% \$300 \$361,723,053.42 \$169,614,675 48.57% 6.05% \$245 \$293,575,183.82 \$137,659,624 58.59% 12.45% \$208 \$243,124,160.21 \$114,002,757 67.32% 21.26% \$193 \$205,774,411.82 \$96,489,178 74.60% 31.58% \$173 \$178,123,759.65 \$83,523,578 80.50% 42.33% \$152 \$157,653,512.92 \$73,924,925 84.24% 52.58% \$126 \$141,471,855.43 \$66,337,223 84.85% 62.41% \$112 \$125,965,941.97 \$59,066,383 85.46% 73.56% \$102 \$111,135,772.54 \$52,112,404 86.07% 86.07%
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 Posted: September 10, 2006, 9:32 am - IP Logged

PB has rolled.  The cash value is \$64.5.  The advertised annuity is \$137M.  The average 11th draw produces sales of \$26.5M.  It this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

 0 83.40% 1 15.14% 2 1.37% 3 0.08%

The long term probability modelling function is lagging on this draw, because sales are running ahead of the average values.  Nonetheless here is what the model predicts for long term jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$576,517,226.03 \$271,425,993 26.78% 0.71% \$353 \$452,676,075.82 \$213,121,218 37.71% 2.64% \$300 \$360,994,372.05 \$169,957,204 48.57% 7.00% \$245 \$293,120,851.90 \$138,002,153 58.59% 14.41% \$208 \$242,872,933.83 \$114,345,286 67.32% 24.60% \$193 \$205,673,547.92 \$96,831,707 74.60% 36.54% \$173 \$178,134,211.65 \$83,866,107 80.50% 48.97% \$152 \$157,746,373.96 \$74,267,453 84.12% 60.84% \$126 \$141,487,901.12 \$66,612,917 84.73% 72.33% \$112 \$125,916,784.34 \$59,281,990 85.36% 85.36%
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 Posted: September 14, 2006, 1:57 am - IP Logged

PB has rolled.  The cash value is \$73.9.  The advertised annuity is \$157M.  These figures are more consistent with a 13th draw in an average run, rather than a 12th.  I will therefore treat it as a 13th draw.  The average 13th draw produces sales of \$30.4M.  If this is how many tickets sell, the randomized distribution of probability of various numbers of winners is as follows:

 0 81.23% 1 16.88% 2 1.75% 3 0.12% 4 0.01%

The modeling function predicts the following for jackpot evolution, ignoring caps, reserves and minimums:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$576,963,808.21 \$271,577,232 26.78% 0.98% \$353 \$453,095,747.45 \$213,272,457 37.71% 3.65% \$300 \$361,394,121.34 \$170,108,443 48.57% 9.67% \$245 \$293,505,852.34 \$138,153,392 58.59% 19.91% \$208 \$243,247,015.46 \$114,496,525 67.32% 33.98% \$193 \$206,039,546.15 \$96,982,946 74.60% 50.48% \$173 \$178,494,225.62 \$84,017,346 80.50% 67.66% \$152 \$158,101,957.67 \$74,418,692 84.05% 84.05%

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 Posted: September 14, 2006, 11:09 am - IP Logged

Prob988, I'm happy that PB rolled. However, MM's annunity jackpot is higher than PB in the next draw. I hope PB continues to roll and follow MM.

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 Posted: September 17, 2006, 1:53 am - IP Logged

The Powerball jackpot has rolled.  The cash value is now \$83.5M.  The advertised annuity value is represented as being \$179M.    The lottery has been selling above average sales on this run.  Although in a temporal sense, the upcoming draw is the 13th in this series, the jackpots are better reflected by an average 14th draw.  I will therefore treat the system as if it were a 14th draw.  The average number of sales on a 14th draw is about \$40.0M tickets.  If this is the number of sales realized on the next draw the randomized probability distribution of winners will be as follows:

 0 77.64% 1 19.65% 2 2.49% 3 0.21% 4 0.01%

The long term jackpot evolution as predicted by my mixed linear/exponential modeling function predicts the following jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$582,891,434.82 \$271,907,457 26.78% 1.16% \$353 \$457,902,755.27 \$213,602,682 37.71% 4.34% \$300 \$365,371,516.07 \$170,438,668 48.57% 11.51% \$245 \$296,869,070.43 \$138,483,617 58.59% 23.69% \$208 \$246,155,548.16 \$114,826,750 67.32% 40.43% \$193 \$208,611,467.55 \$97,313,171 74.60% 60.06% \$173 \$180,816,947.96 \$84,347,571 80.50% 80.50%

These numbers ignore minimums, reserves and caps.

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 Posted: September 17, 2006, 12:50 pm - IP Logged

I hope PB continues to roll and set records Prob988. If it does, it reaches at least 200+ million for Saturday 9/26.

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 Posted: September 21, 2006, 10:05 am - IP Logged

The Powerball jackpot has rolled.  The cash value is now \$94.5M.  The advertised annuity value is represented as being \$203M.    The lottery has been selling above average sales on this run.  Although in a temporal sense, the upcoming draw is the 14th in this series, the jackpots are better reflected by an average 15th draw.  I will therefore treat the system as if it were a 15th draw.  The average number of sales on a 14th draw is about \$39.0M tickets.  If this is the number of sales realized on the next draw the randomized probability distribution of winners will be as follows:

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

The long term jackpot evolution modeling program suggests the following, ignoring caps, reserves, and minimums:

 Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$584,024,547.01 \$271,873,496 26.91% 1.45% \$459,231,657.10 \$213,780,254 37.77% 5.38% \$366,675,265.59 \$170,693,658 48.57% 14.23% \$298,028,040.46 \$138,737,191 58.53% 29.30% \$247,113,766.01 \$115,035,719 67.22% 50.07% \$209,351,666.56 \$97,456,810 74.48% 74.48%

Note that the cash value estimated beforehand by the Powerball lottery in the last run, \$83.5M, was exceeded in the actual event.  The last cash jackpot reached \$85.6M.

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 Posted: September 21, 2006, 10:19 pm - IP Logged

Prob988, I'm happy that PB's annunity jackpot rolled to over 200+ million. I hope it continues to roll.

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 Posted: September 24, 2006, 8:01 am - IP Logged

Powerball has been one and the the jackpot has been reset at \$7.2M cash and \$15 million as an advertised annuity.

A first round draw produces on average, 14.5M in sales.  If this is the number of tickets that sell, the randomized distribution of winners will be as follows:

 0 90.55% 1 8.99% 2 0.45% 3 0.01%

The long term model equation for the evolution of Powerball jackpots suggests this:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$551,094,924.37 \$271,873,496 26.91% 0.21% \$353 \$433,338,353.05 \$213,780,254 37.77% 0.80% \$300 \$346,000,658.35 \$170,693,658 48.57% 2.11% \$245 \$281,224,036.31 \$138,737,191 58.53% 4.35% \$208 \$233,180,510.80 \$115,035,719 67.22% 7.43% \$193 \$197,547,588.44 \$97,456,810 74.48% 11.06% \$180 \$171,119,362.32 \$84,418,885 80.37% 14.84% \$159 \$151,518,075.38 \$74,748,917 83.90% 18.47% \$132 \$135,766,252.99 \$66,978,018 84.54% 22.01% \$119 \$120,697,194.91 \$59,543,949 85.18% 26.04% \$105 \$106,310,901.12 \$52,446,711 85.83% 30.57% \$92 \$92,607,371.65 \$45,686,303 86.49% 35.62% \$79 \$79,586,606.47 \$39,262,726 87.15% 41.18% \$68 \$67,248,605.60 \$33,175,979 87.82% 47.25% \$57 \$55,593,369.03 \$27,426,062 88.49% 53.81% \$47 \$44,620,896.77 \$22,012,976 89.16% 60.81% \$36 \$34,331,188.81 \$16,936,720 89.84% 68.20% \$27 \$24,724,245.15 \$12,197,294 90.53% 75.91% \$20 \$15,800,065.80 \$7,794,699 91.22% 83.85% \$15 \$7,558,650.75 \$3,728,934 91.92% 91.92%

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