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# Probability of a Rollover in Powerball.

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

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New Jersey
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September 4, 2005
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 Posted: January 14, 2007, 9:51 pm - IP Logged

The Powerball jackpot has rolled over.  The cash value is \$86; the advertised annuity value is \$180M.  Fourteenth round drawings sell on average 31.0M tickets.  If this is the number that sell, the randomized probability for various numbers of winners will be as follows:

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

The modeling function, which moves on the 14th draw to an exponential form, being linear for 1 through 13, suggests the following for jackpot evolution, ignoring potential caps:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$570,222,427.33 \$272,439,604 27.19% 1.16% \$353 \$449,603,021.81 \$214,810,333 37.90% 4.26% \$300 \$359,734,073.99 \$171,872,946 48.53% 11.25% \$245 \$292,776,126.81 \$139,881,927 58.36% 23.19% \$208 \$242,888,297.94 \$116,046,631 66.95% 39.73% \$193 \$205,718,767.29 \$98,287,855 74.16% 59.35% \$180 \$178,025,158.65 \$85,056,465 80.03% 80.03%
New Jersey
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 Posted: January 18, 2007, 1:08 am - IP Logged

The Powerball jackpot has rolled over.  The cash value is \$86; the advertised annuity value is \$180M.  Fourteenth round drawings sell on average 31.0M tickets.  If this is the number that sell, the randomized probability for various numbers of winners will be as follows:

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

The modeling function, which moves on the 14th draw to an exponential form, being linear for 1 through 13, suggests the following for jackpot evolution, ignoring potential caps:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$570,222,427.33 \$272,439,604 27.19% 1.16% \$353 \$449,603,021.81 \$214,810,333 37.90% 4.26% \$300 \$359,734,073.99 \$171,872,946 48.53% 11.25% \$245 \$292,776,126.81 \$139,881,927 58.36% 23.19% \$208 \$242,888,297.94 \$116,046,631 66.95% 39.73% \$193 \$205,718,767.29 \$98,287,855 74.16% 59.35% \$180 \$178,025,158.65 \$85,056,465 80.03% 80.03%

The long term program did spectactularly well on predicting the new jack pot which is \$98.3 cash, \$205M advertised.

Update tomorrow.

California
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 Posted: January 18, 2007, 10:23 am - IP Logged

The long term program did spectactularly well on predicting the new jack pot which is \$98.3 cash, \$205M advertised.

Update tomorrow.

Prob988...it looks like your predictions were "right on the money."

If you could only come up with a way to predict those 6 little numbers, now that would be special!!!!

New Jersey
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 Posted: January 18, 2007, 11:39 pm - IP Logged

Prob988...it looks like your predictions were "right on the money."

If you could only come up with a way to predict those 6 little numbers, now that would be special!!!!

It would be indeed.  Of course, if I could do that, I wouldn't be posting it here, but using it to win the lottery.

However it is not possible to predict the numbers since they don't really depend on external factors, but it is reasonable to estimate the probability of jackpot growth since they follow regular patterns.

My modelling programs are not always accurate particularly  the low range and high range, but they do give a good idea of what one might expect.

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 Posted: January 19, 2007, 8:08 am - IP Logged

The sales figures at lottoreport for the last drawing are still not available so the long term estimates will not be updated from the last one until they come out.

The Powerball has, though rolled over.  The cash jackpot for powerball is \$98.3M.  The advertised annuity is \$205M.  At 15th drawing sells on average \$40M tickets.    The randomized probability for various numbers of winners is as follows:

 0 76.58% 1 20.43% 2 2.73% 3 0.24% 4 0.02%
New Jersey
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 Posted: January 21, 2007, 8:54 am - IP Logged

The Powerball jackpot has rolled.  The cash value is \$114M.  The advertised annuity is \$240M.  The average 16th PB draw sells 49.0M tickets.  If this is the number that sell, the randomized distribution probability for various numbers of winners is as follows:

 0 71.52% 1 23.97% 2 4.02% 3 0.45% 4 0.04%

Lottoreport has posted sales figures and the long term projection program, which ignores caps, suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$574,443,881.71 \$272,860,844 27.24% 1.94% \$353 \$453,295,480.20 \$215,315,353 37.88% 7.14% \$300 \$362,862,050.78 \$172,359,474 48.45% 18.84% \$245 \$295,356,371.35 \$140,294,276 58.22% 38.88% \$208 \$244,965,528.22 \$116,358,626 66.78% 66.78%

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 Posted: January 21, 2007, 2:19 pm - IP Logged

Judging from the sales its very close to the drawing for 340 million on 10/20/05.

If it rolls it would be closer to 240, 300, 390 (the cap + 5-10 million in the match 5 bonus). Both the 365 (which had less sales at this point) and the 340 roll would have broken 400+ if it weren't for the cap.

New Jersey
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 Posted: January 22, 2007, 8:31 am - IP Logged

Judging from the sales its very close to the drawing for 340 million on 10/20/05.

If it rolls it would be closer to 240, 300, 390 (the cap + 5-10 million in the match 5 bonus). Both the 365 (which had less sales at this point) and the 340 roll would have broken 400+ if it weren't for the cap.

I would not be surprised, in the unlikely case that the jackpot rolls toward the cap, if it rises faster than historical data suggests.  It's been a long time since there's been a jackpot this high, meaning higher excitement.

The last drawing gave sales 10M above the previous average.

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 Posted: January 22, 2007, 6:53 pm - IP Logged

According to the Powerball E-mail the actual jackpot on Saturday, Jan 20 was\$212,300,000 Annuity/\$100,700,000 cash.

A  jackpot of \$390,000,000 annuity would have a \$185,000,000 cash value at Saturday's ratio.

185.0-100.7=84.3

30.28855% of Powerball Sales go to the jackpot.

84.3/.3028855 ~ 280

\$280,000,000 in sales for three draws seems likely (assuming no winner).

The limited sales history at the current jackpot levels indicates sales should be at least 50, 90, and 140 million tickets.

New Jersey
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 Posted: January 25, 2007, 4:22 pm - IP Logged

The Powerball jackpot has been won and is reset to \$7.1M cash, \$15M advertised annuity.  The average sales for first drawings is 14.7M.

If this is how many tickets sell, the randomized probability of various numbers of winners is as follows:

 0 90.41% 1 9.11% 2 0.46% 3 0.02%

The long term model for jackpot evolution, ignoring minimums and caps suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$579,469,194.57 \$274,282,085 27.19% 0.20% \$353 \$457,710,528.63 \$216,649,650 37.72% 0.75% \$300 \$366,552,217.11 \$173,501,383 48.19% 1.98% \$245 \$298,303,787.37 \$141,197,126 57.90% 4.11% \$250 \$208 \$247,207,534.22 \$117,011,566 66.42% 7.11% \$200 \$193 \$208,952,777.35 \$98,904,315 73.61% 10.70% \$172 \$180 \$180,312,195.46 \$85,347,773 79.51% 14.54% \$150 \$159 \$158,869,556.73 \$75,198,257 83.83% 18.28% \$131 \$132 \$142,375,405.69 \$67,391,025 84.47% 21.81% \$111 \$119 \$126,593,490.64 \$59,920,919 85.11% 25.82% \$97 \$105 \$111,523,811.57 \$52,787,937 85.76% 30.34% \$84 \$92 \$97,166,368.49 \$45,992,081 86.42% 35.37% \$72 \$79 \$83,521,161.39 \$39,533,350 87.08% 40.93% \$61 \$68 \$70,588,190.27 \$33,411,743 87.75% 47.00% \$51 \$57 \$58,367,455.13 \$27,627,262 88.42% 53.56% \$41 \$47 \$46,858,955.99 \$22,179,906 89.09% 60.58% \$32 \$36 \$36,062,692.82 \$17,069,675 89.78% 68.00% \$23 \$27 \$25,978,665.64 \$12,296,568 90.46% 75.74% \$15 \$20 \$16,606,874.44 \$7,860,587 91.15% 83.73% \$12 \$15 \$7,947,319.23 \$3,761,731 91.85% 91.85%
New Jersey
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 Posted: January 29, 2007, 10:45 am - IP Logged

The Powerball jackpot has been won and is reset to \$7.1M cash, \$15M advertised annuity.  The average sales for first drawings is now 14.8M, having risen slightly in the last jackpot run, because of record sales on the first drawing for this matrix.

If an average number of tickets sell this time, the randomized probability of various numbers of winners is as follows:

 0 90.34% 1 9.18% 2 0.47% 3 0.02%

The long term model for jackpot evolution, ignoring minimums and caps suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$579,534,429.33 \$274,312,963 27.19% 0.20% \$353 \$457,775,763.38 \$216,680,528 37.72% 0.75% \$300 \$366,617,451.87 \$173,532,261 48.19% 1.98% \$245 \$298,369,022.13 \$141,228,004 57.90% 4.11% \$208 \$247,272,768.97 \$117,042,444 66.42% 7.10% \$193 \$209,018,012.11 \$98,935,192 73.61% 10.69% \$180 \$180,377,430.22 \$85,378,650 79.51% 14.53% \$159 \$158,934,791.49 \$75,229,135 83.84% 18.27% \$132 \$142,453,687.40 \$67,428,079 84.48% 21.79% \$119 \$126,681,808.46 \$59,962,723 85.12% 25.80% \$105 \$111,619,154.68 \$52,833,067 85.77% 30.30% \$92 \$97,265,726.04 \$46,039,110 86.42% 35.33% \$79 \$83,621,522.55 \$39,580,854 87.08% 40.89% \$68 \$70,686,544.21 \$33,458,298 87.74% 46.95% \$57 \$58,460,791.02 \$27,671,441 88.41% 53.51% \$47 \$46,944,262.97 \$22,220,284 89.08% 60.53% \$36 \$36,136,960.08 \$17,104,828 89.76% 67.94% \$27 \$26,038,882.34 \$12,325,071 90.45% 75.69% \$20 \$16,650,029.74 \$7,881,014 91.13% 83.69% \$15 \$7,970,402.30 \$3,772,657 91.83% 91.83%
New Jersey
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 Posted: February 1, 2007, 11:08 pm - IP Logged

The Powerball jackpot has rolled.  The cash jackpot is \$9.3M.  The advertised annuity is \$20M.  An average 2nd PB draw sells \$14.2M in tickets.  If this is the amount that sells in the next drawing, the randomized probability of a a rollover we be as follows:

 0 90.37% 1 9.15% 2 0.46% 3 0.02%

The modeling program I developed suggests the following for jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$589,892,946.93 \$274,300,220 27.19% 0.22% \$353 \$465,952,226.04 \$216,667,785 37.72% 0.81% \$300 \$373,160,253.03 \$173,519,518 48.19% 2.16% \$245 \$303,688,733.15 \$141,215,261 57.90% 4.48% \$218 \$251,676,776.53 \$117,029,701 66.42% 7.74% \$196 \$212,736,450.55 \$98,922,450 73.61% 11.65% \$180 \$183,582,596.58 \$85,365,907 79.51% 15.82% \$158 \$161,755,681.17 \$75,216,392 83.83% 19.90% \$132 \$144,973,735.98 \$67,412,787 84.47% 23.74% \$119 \$128,914,990.87 \$59,945,471 85.12% 28.10% \$104 \$113,579,445.85 \$52,814,442 85.77% 33.01% \$92 \$98,967,100.90 \$46,019,702 86.42% 38.49% \$79 \$85,077,956.03 \$39,561,250 87.08% 44.54% \$67 \$71,912,011.25 \$33,439,085 87.74% 51.15% \$57 \$59,469,266.54 \$27,653,209 88.41% 58.29% \$46 \$47,749,721.92 \$22,203,621 89.09% 65.93% \$36 \$36,753,377.37 \$17,090,320 89.77% 74.00% \$27 \$26,480,232.91 \$12,313,308 90.45% 82.44% \$20 \$16,930,288.52 \$7,872,584 91.14% 91.14%
New Jersey
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 Posted: February 4, 2007, 8:06 am - IP Logged

Powerball has rolled over.  The cash jackpot is \$12.9M; the annuity value advertised is \$27M.  Third drawings sell 15.0M tickets on average.  The randomized probability of various numbers of winners - if average sales are obtained - is:

 0 90.24% 1 9.27% 2 0.48% 3 0.02%

The mathematical model I use to predict the long term probabilities of rollovers within a particular run suggests the following:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$587,823,153.61 \$274,317,472 27.19% 0.24% \$353 \$464,325,078.15 \$216,685,036 37.72% 0.89% \$300 \$371,864,505.04 \$173,536,769 48.19% 2.37% \$245 \$302,641,097.73 \$141,232,512 57.90% 4.91% \$218 \$250,814,898.11 \$117,046,952 66.42% 8.49% \$196 \$212,013,644.72 \$98,939,701 73.61% 12.78% \$180 \$182,963,911.65 \$85,383,159 79.51% 17.36% \$158 \$161,214,949.51 \$75,233,643 83.84% 21.83% \$132 \$144,498,038.77 \$67,432,418 84.48% 26.04% \$119 \$128,500,421.49 \$59,966,863 85.12% 30.82% \$104 \$113,222,097.67 \$52,836,979 85.77% 36.21% \$92 \$98,663,067.32 \$46,042,765 86.42% 42.22% \$79 \$84,823,330.43 \$39,584,221 87.08% 48.85% \$67 \$71,702,887.00 \$33,461,347 87.74% 56.10% \$57 \$59,301,737.04 \$27,674,144 88.41% 63.94% \$46 \$47,619,880.54 \$22,222,611 89.08% 72.32% \$36 \$36,657,317.50 \$17,106,748 89.76% 81.18% \$27 \$26,414,047.93 \$12,326,556 90.44% 90.44%
New Jersey
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 Posted: February 9, 2007, 1:22 am - IP Logged

The powerball jackpot has rolled over and is now valued at \$17.5M cash and is advertised as a \$37M annuity.  Fourth drawings average 15.3 M in sales.  If the next drawing is average, the probability of various numbers of winers is as follows:

 0 90.06% 1 9.42% 2 0.49% 3 0.02%

The long term model suggests this for jackpot evolution:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$579,980,981.21 \$274,315,329 27.19% 0.27% \$353 \$458,129,546.75 \$216,682,894 37.72% 0.99% \$300 \$366,901,781.29 \$173,534,626 48.19% 2.62% \$245 \$298,601,352.74 \$141,230,370 57.90% 5.43% \$218 \$247,466,169.11 \$117,044,810 66.42% 9.38% \$196 \$209,182,265.77 \$98,937,558 73.61% 14.13% \$180 \$180,519,862.48 \$85,381,016 79.51% 19.19% \$158 \$159,060,886.50 \$75,231,500 83.84% 24.14% \$132 \$142,566,477.94 \$67,430,091 84.48% 28.79% \$119 \$126,781,895.34 \$59,964,410 85.12% 34.08% \$104 \$111,707,138.70 \$52,834,457 85.77% 40.04% \$92 \$97,342,208.02 \$46,040,234 86.42% 46.68% \$79 \$83,687,103.30 \$39,581,738 87.08% 54.01% \$67 \$70,741,824.53 \$33,458,971 87.74% 62.03% \$57 \$58,506,371.72 \$27,671,933 88.41% 70.70% \$46 \$46,980,744.87 \$22,220,623 89.08% 79.96% \$36 \$36,164,943.98 \$17,105,041 89.76% 89.76%
New Jersey
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 Posted: February 11, 2007, 5:21 pm - IP Logged

Powerball rolled over.  The cash jackpot is \$22M.  The advertised annuity is \$46M.

Fifth draws sell on average 15.9M tickets.

If the sales are average the randomized probability of various numbers of winners will be as follows:

 0 89.68% 1 9.76% 2 0.53% 3 0.02%

The long term model suggests the following for jackpot development:

 Average Historical Annuity Calculated Annuity Calculated Cash Value Projections Single Draw Rollover Probability Overall Probability from baseline \$573,662,519.79 \$274,360,336 27.19% 0.30% \$353 \$453,158,337.07 \$216,727,900 37.72% 1.10% \$300 \$362,939,232.40 \$173,579,633 48.19% 2.92% \$245 \$295,393,968.30 \$141,275,376 57.90% 6.05% \$218 \$244,824,161.40 \$117,089,816 66.42% 10.45% \$196 \$206,963,544.45 \$98,982,565 73.61% 15.73% \$180 \$178,618,047.34 \$85,426,023 79.51% 21.37% \$158 \$157,396,332.77 \$75,276,507 83.84% 26.88% \$132 \$141,087,235.59 \$67,476,504 84.48% 32.06% \$119 \$125,478,419.58 \$60,011,418 85.12% 37.95% \$104 \$110,569,884.73 \$52,881,249 85.77% 44.58% \$92 \$96,361,631.03 \$46,085,997 86.42% 51.98% \$79 \$82,853,658.50 \$39,625,663 87.07% 60.15% \$67 \$70,045,967.13 \$33,500,245 87.74% 69.08% \$57 \$57,938,556.91 \$27,709,745 88.40% 78.74% \$46 \$46,531,427.86 \$22,254,161 89.07% 89.07%

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