Probability of a MegaMillions rollover.

Reply #352

Prob988 — Wed, 04 Apr 2007 06:47:18 GMT

MM has rolled over. The cash jackpot is $61.3M; the advertised annuity is $105M. The average sales for a ninth draw is $25.6M.

Every drawing on this run has produced above average sales though.

Even so, average sales would produce a probability distribution of number of winners as follows:

086.43%

112.61%

20.92%

30.04%

The exponential model function, for what it's worth, predicts the following long range evolution of the jackpot:

Historical Av... [ More ]

Reply #351

Prob988 — Sat, 31 Mar 2007 16:07:29 GMT

The MM jackpot has rolled. The estimated cash jackpot is $51.5M. The advertised annuity is $88M.

The average 8th draw in a run produces $23.M in sales. (The Standard Deviation is 2.3M).

If an average number of tickets are sold, the randomized probability of various numbers of winners will be as follows:

087.75%

111.47%

20.75%

30.03%

Here is the long term program model:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity Prize... [ More ]

Reply #350

Prob988 — Thu, 29 Mar 2007 12:09:47 GMT

The MM has rolled over. The cash prize is now $43.4M. The advertised annuity is $74M. Average sales for 6th round draws are 21.2M. If this draw produces average sales, the probability of various numbers of winners will be as follows:

088.64%

110.69%

20.64%

30.03%

The long term probability model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Roll... [ More ]

Reply #349

Prob988 — Sat, 24 Mar 2007 18:09:56 GMT

The MM has rolled over. The cash prize is now $35.6M. The advertised annuity is $60M. Average sales for 6th round draws are 19.2M. If this draw produces average sales, the probability of various numbers of winners will be as follows:

089.61%

19.83%

20.54%

30.02%

The long term jackpot model program I use for long term evolution of jackpots suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calcula... [ More ]

Reply #348

Prob988 — Wed, 21 Mar 2007 09:49:27 GMT

The MM Jackpot has been won. The cash value is $28.6M. The advertised annuity is 48M. The average 6th round jackpot sells 19.3M tickets. If sales are average, the probability of various numbers of winners will be:

089.61%

19.83%

20.54%

30.02%

The long term modelling program suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOv... [ More ]

Reply #347

Prob988 — Tue, 20 Mar 2007 15:43:09 GMT

Based on actual sales during the run, the probability of a $390 jackpot was about 4.5%.

This figure includes all of the rollovers, but not the final drawing, since the final draw was won.

When one says reach $390M, of course, one assumes that the final drawing will have sales similar to those actually obtained, about $212M.

Reply #346

MattMatt — Tue, 20 Mar 2007 01:47:25 GMT

One of those key questions is:

What are the odds the Jackpot reached $390 million?

The closest data is:

1- The odds of 1.63% for a similar estimated jackpot ($394, see post from January 10 2007) as Overall Calculated Model Rollover Probability of the long term jackpot evolution model, which is significantly outphased with the observed (more precisely: official) evolution.

2- the distribution probability for zero winners for each round, IF an average number of tickets sells on th... [ More ]

Reply #345

Prob988 — Wed, 14 Mar 2007 13:20:48 GMT

The MM jackpot has rolled over. The cash prize is $16.7M; the advertised annuity is $28M. The average sales on a third drawing is 15.89M. Sales as this level would approximately produce the following randomized probability for numbers of winners:

091.35%

18.26%

20.37%

30.01%

As is often the case after a big jackpot has been run, the first drawing of the next run sold unusually high amounts of tickets. For this reason, I will be treating the system as if one

Reply #344

Prob988 — Sun, 11 Mar 2007 19:44:01 GMT

The MM jackpot has rolled over. The cash value is $11.3M, the advertised annuity, $19M. Second round drawings produce sales typically of 14.8M in sales. If this is how many tickets sell, the probability of various numbers of winners will be as follows:

082.90%

115.55%

21.46%

30.09%

The long term model, which ignores minimums, predicts the following for long term evolution of the jackpot:

Historical Average Advertised Annuity JackpotsModel Calculated A... [ More ]

Reply #343

Prob988 — Thu, 08 Mar 2007 12:52:47 GMT

The final sales for the recent drawing were 212M:

This gives this kind of probability:

029.78%

136.07%

221.85%

38.82%

42.67%

50.65%

60.13%

70.02%

There was about a 1 in 5 chance of the result.

Reply #342

LckyLary — Wed, 07 Mar 2007 03:23:35 GMT

One thing that determines the # of winners is the kind of numbers that come out, if they were system-friendly or if they are low numbers (ages of children, birthdays, etc.) that increases the chance of multiple winners. A while back 100 people came one # away from sharing the PB jackpot 100-ways because they used the same fortune cookie numbers that came out all but the bonus ball.

Always when they did the drawing on Times Square someone would win somewhere...

Reply #341

dvdiva — Wed, 07 Mar 2007 03:01:22 GMT

If it rolls at this point I will be shocked. I'm still shocked that it would have such a high chance of a rollover. If it does roll I'm curious if two winners would be more likely than one winner.

Reply #340

Prob988 — Tue, 06 Mar 2007 22:59:45 GMT

Probably the last update. A $221M cash prize suggests sales of 177M. Probability for various numbers of winners:

036.50%

136.79%

218.54%

36.23%

41.57%

50.32%

60.05%

70.01%

The most probable outcome is now one winner. There still, however, is a decent chance of a rollover. A rollover is more unlikely than ever, but it is possible.

Reply #339

Prob988 — Tue, 06 Mar 2007 18:12:58 GMT

$180M in sales would be close to the odds against winning the lottery. In this case the rollover probability falls to 33%. This would still not eliminate the probability of a rollover, but of course it would make the likelihood of a winner 67%.

A rollover is still possible. Unlikely, but possible. I'd like to see it, just to see everyone go crazy. Of course I wouldn't like to see it as much as I would like to win the existing jackpot.

Reply #338

KY Floyd — Tue, 06 Mar 2007 17:29:16 GMT

We're closing in on $180 milion in sales. I'm going to have to forget probability and just cross my fingers that it rolls. This roll has seen more than a 60% jump in sales over the previous jackpot, and a similar increase for another roll would mean a single winner would also be a matter of luck rather than probability.

FWIW, a similar jump in sales would push the annuity value to about 525 and the cash to about 310.

Reply #337

CA LotteryGuy — Tue, 06 Mar 2007 16:45:31 GMT

Prob988....thanks for the updates

Reply #336

Prob988 — Tue, 06 Mar 2007 13:12:57 GMT

Actually, if the jackpot stays at $212M cash/$355M annuity, 148M tickets will be sold. This would lead to the following distribution of probabilty for various numbers of winners:

043.00%

136.29%

215.31%

34.31%

40.91%

50.15%

60.02%

It seems thus that while a rollover is the single most probable outcome, one or more winners combined is more likely. Thus you'd be better guessing that there will be at least one winner. Note that there is a 1% chance of 4... [ More ]

Reply #335

Prob988 — Mon, 05 Mar 2007 23:15:00 GMT

With the jackpot rising, it doesn't seem that my 134M sales figure was that far off.

Reply #334

Prob988 — Sat, 03 Mar 2007 18:28:07 GMT

In my previous analysis, I used a figure of $134M for sales - based on some extrapolation of sales figures from the previous draws in this run.

However the lottery is apparently estimating - until the jackpot is announced as being higher - sales of about 116M. The lottery's figure will give the following rollover probability:

051.45%

134.19%

211.36%

32.52%

40.42%

50.06%

60.01%

I think in any case, there is a fairly decent chance - close to e... [ More ]

Reply #333

Prob988 — Sat, 03 Mar 2007 13:58:11 GMT

The $202M cash, $340M jackpot changes the rules, and my estimates will be crude and somewhat ad hoc. For what it's worth, here is what I see for the current drawing in terms of winner distribution:

046.54%

135.60%

213.61%

33.47%

40.66%

50.10%

60.01%

Long term - and probably it won't go much further:

Model Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Proba... [ More ]

Reply #332

Prob988 — Thu, 01 Mar 2007 03:18:09 GMT

The field is 50% covered at about 122 million tickets sold, according to the Poisson distribution.

The MM jackpot, has of course, rolled over. The cash value is $158M. The advertised annuity is $267M.

The average number of tickets sold on 15th drawings is $72.0M. However there are only three such drawings involved in this average, but the last of them produced sales of $96M. This series of drawings from early in 2006, ending in February, closely followed the tragectory of the curre... [ More ]

Reply #331

KY Floyd — Wed, 28 Feb 2007 20:41:47 GMT

It happens when exactly 87,855,768 of the possible combinations have been played, but what that is in terms of actual sales is difficult to say. It doesn't even come close to happening with sales of only 100 to 110 million tickets as can be expected for the current drawing. Selling 50% of the possible combinations would require selling about 160 million tickets if the combinations were all picked randomly. Since a lot of people don't pick their combinations randomly there are even more repeat... [ More ]

Reply #330

dvdiva — Wed, 28 Feb 2007 14:10:35 GMT

I'm curious at what sales point does the probability of a rollover hit 50%.

Reply #329

Just6ntlc — Wed, 28 Feb 2007 06:47:30 GMT

Prob988, MM Jackpot has rolled to 267 million for 3/2. Lets see how the probability rolls down this time.

Reply #328

Just6ntlc — Wed, 28 Feb 2007 02:55:48 GMT

Prob988, I hope MM continues to roll until it reaches between 315 and 365 million and one ticket hits the jackpot.

Reply #327

Prob988 — Wed, 28 Feb 2007 02:51:19 GMT

There are only three examples of 15th draws, two examples of 16th draws, and one example of 17th draws in MM. In 14th draws (4 examples) the numbers have been all over the place, ranging from 48M to 76M. One 15th draw had sales of 96M, another of 58M.

I don't have any idea what would happen with a rollover and I think you're right on as usual - I don't think any one knows.

There is still some probability of a rollover, so maybe we'll find out.

Reply #326

KY Floyd — Tue, 27 Feb 2007 07:12:05 GMT

Even the people running the lottery have trouble estimating how many tickets will be sold at these levels. For the levels that are seen commonly they've got good data to work with and a 10% error is insignificant in real dollars. That make sit pretty easy for them to make a relaible estimate When advertised jackpots go over $200 million there's not much data to work with and there's a lot more unpredictability. For a $50 million jackpot there's a small but dependable minority who will spend $2... [ More ]

Reply #325

Prob988 — Tue, 27 Feb 2007 03:37:06 GMT

I expect that if the jackpot continues to roll, my model will be less predictive in terms of the actual jackpot. In fact, hidden in these tables is the fact that I am not actually predicting jackpots so much as sales.

The higher the jackpot goes, of course, the fewer instances there are of previous sales and the weaker the model is at approximating it. There are many factors at different times, jackpot fatigue, competing jackpots, economic conditions, even weather.

Graphically the

Reply #324

dvdiva — Sun, 25 Feb 2007 17:53:09 GMT

I always look forward to your predictions.

Just curious if you would do a spread as the jackpots get higher. A low-high estimates for a spread. I think the jackpot would go 217-265(or 270)-315 assuming it rolls at all. Sales seem very high (on level with pre-matrix 2004 levels) as the game grows due to the dearth of large jackpots recently.

Reply #323

Prob988 — Sat, 24 Feb 2007 22:35:19 GMT

The MM jackpot has rolled over. The cash jackpot is is 126.9M. The advertised annuity is $216M. Fourteenth draws sell on average 61.7M tickets. This suggests the following probability for various numbers of winners:

070.78%

124.46%

24.23%

30.49%

40.04%

The long term probability model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollove... [ More ]

Reply #322

Prob988 — Sun, 18 Feb 2007 16:37:02 GMT

The MM jackpot has rolled over. The cash value is now $88.3M. The advertised annuity is $150M. The averages sales for 12th round drawings is 41.6M. Sales at this level would produce the following probabilities for various numbers of winner:

078.90%

118.70%

22.22%

30.17%

40.01%

The long range model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculate... [ More ]

Reply #321

Prob988 — Thu, 15 Feb 2007 04:02:14 GMT

The MM jackpot has rolled over. The cash jackpot is now $75.6M. The advertised annuity jackpot is $130M. The average number of tickets sold on an 11th round draw is 35.6M. If this is the number of tickets that are sold, the randomized probability of various numbers of winners is:

081.65%

116.55%

21.68%

30.11%

40.01%

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollo... [ More ]

Reply #320

Prob988 — Sat, 10 Feb 2007 16:09:26 GMT

The MM jackpot has rolled over. The cash jackpot is now $61.9M. The advertised annuity is $106M.

Tenth round draws sell on average $31.5M in sales. If this drawing produces average sales, the probability of various numbers of winners resulting is as follows:

083.57%

115.00%

21.35%

30.08%

The long term exponential form modelling equation for MM suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Ca... [ More ]

Reply #319

Prob988 — Wed, 07 Feb 2007 17:27:09 GMT

The MM jackpot has rolled over. The cash jackpot is now $52.8M. The jackpot's advertised annuity value is $91M.

The average sales for a ninth drawing are 25.6M.

The randomized probability of various numbers of winners for this amount of sales is as follows:

086.43%

112.61%

20.92%

30.04%

The expectation value is 0.47.

The long term probability rollover model gives the following projection:

Historical Average Advertised Annuity JackpotsModel Cal... [ More ]

Reply #318

Prob988 — Sat, 03 Feb 2007 18:17:12 GMT

MM has rolled over. The cash prize is $44.7M, the advertised annuity is $7M. Eight round drawings in MM sell on average 23.1M tickets. This suggests that the probability of various numbers of winners is as follows:

087.67%

111.54%

20.76%

30.03%

The long term model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated

Reply #317

Prob988 — Wed, 31 Jan 2007 12:57:16 GMT

MM has rolled over. The cash prize is $37.5M, the advertised annuity is $65M. Seventh round drawings in MM sell on average 21.1M tickets. This suggests that the probability of various numbers of winners is as follows:

088.67%

110.66%

20.64%

30.03%

The long term model for jackpot evolution is as follows:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover Probab... [ More ]

Reply #316

Prob988 — Wed, 24 Jan 2007 06:06:54 GMT

MM has rolled over. The cash jackpot is now $25.0M; the advertised annuity is $43M.

On average, 5th round draws sell 18.4M tickets.

If the sales are average on this drawing the randomized probability of various numbers of winners is as follows:

090.05%

19.44%

20.49%

30.02%

The long term model suggests the following evolution of the jackpot:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Dr... [ More ]

Reply #315

Prob988 — Mon, 22 Jan 2007 00:04:05 GMT

MM has rolled over. The jackpot is $19.2M cash. The advertised annuity is $33M. Third round sales have averaged 15.89M in sales. If this is how many tickets sell, the randomized probability distribution for numbers of winners is as follows:

091.35%

18.26%

20.37%

30.01%

The long term evolution probabilities as modeled by least squares curve fitting to an exponential function suggest the following:

Historical Average Advertised Annuity Ja... [ More ]

Reply #314

Prob988 — Wed, 17 Jan 2007 13:12:43 GMT

MM has rolled over. The cash jackpot is $14.5M; the advertised annuity value is $25M. Third round draws sell on average 15.9M tickets.

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

091.36%

18.26%

20.37%

30.01%

The long term modelling function, which does not account for early minimums predicts the following behavior for jackpot evolution:

Historical Average Advertised Annuity JackpotsModel Calculated... [ More ]

Reply #313

Prob988 — Sat, 13 Jan 2007 15:17:02 GMT

MM has rolled over. The cash jackpot is $9.3M. 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:

091.89%

17.77%

20.33%

30.01%

The long term projection program, which ignores minimums and does not accurately predict prizes (although it does predict sales in making the calculations) suggests the following

Reply #312

Just6ntlc — Sat, 13 Jan 2007 04:05:29 GMT

Prob988, if MM jackpot will roll on this run, it'll be 16 million.

Reply #311

Prob988 — Wed, 10 Jan 2007 18:16:40 GMT

The MM jackpot has been won. The value of the prize is reset to $7.0M cash, $12.0M annuity. First draws average $15.1, although the drawing beginning the last run was the lowest recorded since the matrix change.

If an average number of tickets sell on this round, the distribution probability for various numbers of winners is as follows:

091.76%

17.89%

20.34%

30.01%

The long term jackpot evolution model, which ignores minimums predicts the following

Reply #310

Prob988 — Sat, 06 Jan 2007 14:31:55 GMT

MM has rolled over. The cash jackpot is $71.6M. The advertised annuity value is $122M. Eleventh round draws sell on average $34.9M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

083.57%

115.00%

21.35%

30.08%

For the last draw, sales were above average. However for the entire run, sales a running just above historical lows for an 11 draw run. The modeling function I use, which is ba... [ More ]

Reply #309

Prob988 — Thu, 04 Jan 2007 13:22:45 GMT

MM has rolled over. The cash jackpot is $59.7M. The advertised annuity value is $102M. Seventh round draws sell on average $30.8M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

083.93%

114.70%

21.29%

30.08%

This run has lower than average sales overall, although the pace for the last several draws has been near average. The mathematical projection model shows a jackpot that is about

Reply #308

Just6ntlc — Thu, 04 Jan 2007 06:18:15 GMT

Prob988, MM Jackpot for 1/5/07 has rolled to 102 million, up from 84 million in last draw (roll) on 1/2/07.

Reply #307

Prob988 — Thu, 28 Dec 2006 14:39:37 GMT

I didn't change all of the numbers in the opening paragraph of my last post. Here is the corrected post:

MM has rolled over. The cash jackpot is $42.7M. The advertised annuity value is $72M. Seventh round draws sell on average $23.1 tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

087.68%

111.53%

20.76%

30.03%

The long term projections, based on a mathematical model generated... [ More ]

Reply #306

Prob988 — Wed, 27 Dec 2006 16:10:11 GMT

MM has rolled over. The cash jackpot is $35.6M. The advertised annuity value is $60M. Seventh round draws sell on average $21.6M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

087.68%

111.53%

20.76%

30.03%

Note that the MM has been running below average in sales on this run.

The long term projections, based on a mathematical model generated from average sales gives the following pro... [ More ]

Reply #305

Prob988 — Sat, 23 Dec 2006 07:00:39 GMT

MM has rolled over. The cash jackpot is $35.6M. The advertised annuity value is $60M. Seventh round draws sell on average $21.6M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

088.45%

110.86%

20.67%

30.03%

The long term model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Mode... [ More ]

Reply #304

Prob988 — Wed, 20 Dec 2006 07:17:55 GMT

MM has rolled over. The cash jackpot is $29/7M. The advertised annuity value is $60M. Sixth round draws sell on average $19.4M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

089.60%

19.84%

20.54%

30.02%

The long term model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Mo... [ More ]

Reply #303

Prob988 — Sat, 16 Dec 2006 15:31:47 GMT

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:

089.97%

19.51%

20.50%

30.02%

The long term model for jackpot evolution suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle D... [ More ]

Reply #302

Prob988 — Thu, 14 Dec 2006 03:13:54 GMT

MM has rolled over. The cash jackpot is $17.9M. The advertised annuity value is $30M. Fourth round draws sell on average $16.7M tickets. If this is the number of tickets that sell, the probability of various numbers of winners is distributed as follows:

090.94%

18.64%

20.41%

30.01%

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

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated

Reply #301

Prob988 — Sat, 09 Dec 2006 07:59:55 GMT

MM has rolled over. The cash jackpot is $13.1M. The advertised annuity value is $22M. Third 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:

091.33%

18.28%

20.38%

30.01%

The modeling fuction suggests the following for the long term evolution of the jackpot:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calcul... [ More ]

Reply #300

Just6ntlc — Sat, 09 Dec 2006 06:35:11 GMT

Prob988, MM Jackpot for 12/12 has rolled to 22 million according to usamega.com

Reply #299

Prob988 — Wed, 06 Dec 2006 14:48:29 GMT

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:

091.87%

17.79%

20.33%

30.01%

The long term modeling program I use, which does not account for jackpot minima, suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity P... [ More ]

Reply #298

Prob988 — Sun, 03 Dec 2006 15:12:40 GMT

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:

091.72%

17.93%

20.34%

30.01%

Here is the long term probability, which ignores minimums, focusing on models generated from sales figures and what sales actually contribute to jackpots:

Hi... [ More ]

Reply #297

Prob988 — Thu, 30 Nov 2006 04:21:22 GMT

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:

089.94%

19.54%

20.51%

30.02%

The long term curve fitting model suggests the following for the probability for evolution of the jackpot:

Historical Average Advertised Annuity JackpotsModel Calculated An... [ More ]

Reply #296

Just6ntlc — Sun, 26 Nov 2006 20:09:49 GMT

Prob988, I hope MM continues to roll and get up to 365+ million.

Reply #295

Prob988 — Sat, 25 Nov 2006 10:14:17 GMT

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:

090.90%

18.67%

20.41%

30.01%

The long term curve fitting model suggests the following for the probability for evolution of the jackpot.

Historical Average Advertised Annuity JackpotsModel Calculated Annuit... [ More ]

Reply #294

Prob988 — Wed, 22 Nov 2006 13:21:36 GMT

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:

091.32%

18.29%

20.38%

30.01%

The long term probability model suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calcu... [ More ]

Reply #293

Prob988 — Sun, 19 Nov 2006 05:51:33 GMT

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:

089.08%

110.30%

20.60%

30.02%

The model function for the long term evolution of jackpots suggests the following:

Average Historical AnnuityCalculat... [ More ]

Reply #292

Prob988 — Sun, 19 Nov 2006 05:41:49 GMT

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 JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Rollover ProbabilityOverall Calculated Model Rollover Probability

$593,382,592.54$348,612,27344.87%0.21%

$517,163,807.92$303,833,73749.38%0.46%

$450,060,465.71$264,410,52453.73... [ More ]

Reply #291

Prob988 — Sat, 18 Nov 2006 13:43:03 GMT

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:

091.85%

17.81%

20.33%

30.01%

Lotteryreport has not yet posted the sales figures and I will update the long term jackpot evolution figures when she has done so.

Reply #290

Prob988 — Thu, 16 Nov 2006 04:38:06 GMT

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:

091.71%

17.93%

20.34%

30.01%

Here is the long term probability, which ignores minimums:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Ca... [ More ]

Reply #289

Prob988 — Sat, 11 Nov 2006 06:24:23 GMT

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:

087.61%

111.59%

20.77%

30.03%

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 h... [ More ]

Reply #288

Prob988 — Wed, 08 Nov 2006 09:00:37 GMT

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:

088.39%

110.90%

20.67%

30.03%

The long term probability modelling function is pretty much on the money right now. It predicts as follows:

Historical Average Advertised Annuity JackpotsModel Calculated Ann... [ More ]

Reply #287

Prob988 — Sat, 04 Nov 2006 18:41:09 GMT

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 purch... [ More ]

Reply #286

CA LotteryGuy — Sat, 04 Nov 2006 16:38:13 GMT

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

Reply #285

Prob988 — Sat, 04 Nov 2006 13:03:51 GMT

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:

089.56%

19.88%

20.54%

30.02%

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

Reply #284

Prob988 — Wed, 01 Nov 2006 09:52:51 GMT

The MM jackpot has rolled. The cash value is $24.6M ; the advertised annuity is $42M. Third round jackpots sell on average, 18.7M in tickets.

If an average amount is sold, the randomized probability of various numbers of winners will be as follows:

089.92%

19.55%

20.51%

30.02%

The long term modeling function suggests the following probabilities of jackpot evolution:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calcula... [ More ]

Reply #283

Prob988 — Sat, 28 Oct 2006 14:16:22 GMT

The MM jackpot has rolled. The cash value is $18.7M; the advertised annuity is $32M. Third round jackpots sell on average, 16.8M in tickets.

If an average amount is sold, the randomized probability of various numbers of winners will be as follows:

090.85%

18.71%

20.42%

30.01%

The long term modeling function suggests the following probabilities of jackpot evolution:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeMode... [ More ]

Reply #282

Prob988 — Wed, 25 Oct 2006 06:04:52 GMT

The MM jackpot has rolled. The cash value is $13.8M; the advertised annuity is $24M. Third round jackpots sell on average, 15.9M in tickets.

If an average amount is sold, the randomized probability of various numbers of winners will be as follows:

091.31%

18.30%

20.38%

30.01%

The long term modeling function suggests the following probabilities of jackpot evolution:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Cal... [ More ]

Reply #281

Prob988 — Sat, 21 Oct 2006 12:53:03 GMT

The MM jackpot has rolled. The cash value is $9.2M; the advertised annuity is $16M. Second round jackpots sell on average, 15.0M in tickets.

If an average amount is sold, the randomized probability of various numbers of winners will be as follows:

091.81%

17.84%

20.34%

30.01%

The long term modeling function suggests the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculat... [ More ]

Reply #280

Prob988 — Thu, 19 Oct 2006 18:30:06 GMT

That is a probable outcome.

Reply #279

ryanm — Thu, 19 Oct 2006 11:58:16 GMT

One more jackpot winner before 2007, and Mega Millions will tie Powerball's record of fourteen jackpots awarded in one year from either multi-state game. Powerball set that record just last year (2005).

Reply #278

Prob988 — Thu, 19 Oct 2006 11:07:13 GMT

The MM jackpot has been won and the jackpot has been reset to $6.9M cash and $12M as an advertised annuity.

The average number of sales for a first round drawing is $14.3M. If this is how many tickets sell this draw, the probability distribution for numbers of winners is as follows:

091.67%

17.97%

20.35%

30.01%

The exponential modeling function gives giving the probability of a number of future rollovers:

Historical Average Advertised Annuity JackpotsMod... [ More ]

Reply #277

Prob988 — Sat, 14 Oct 2006 05:59:00 GMT

The MM jackpot has rolled. The cash value is $31.8M. The advertised annuity is $55M.

Average sixth round draws sell 19.5M tickets. If this is the number of tickets that sell that the probability of various numbers of winners is given in the following table:

089.49%

19.94%

20.55%

30.02%

The exponential modeling function gives giving the probability of a number of future rollovers:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity... [ More ]

Reply #276

Prob988 — Wed, 11 Oct 2006 14:26:03 GMT

It depends on what you mean by a long string of low level wins and a large jackpot. There are several ways to interpret your question, and I will give you just one based on recent events.

Between April 21 and August 1 of this year, we had a string of runs in which the jackpot never passed $100M in advertised annuity value. The lengths of the runs in this period were 8 (about average) followed by below average length runs of 5, 4, 3, 6 and 4 draws.

Working from my modeling program,

Reply #275

Prob988 — Wed, 11 Oct 2006 06:45:37 GMT

The MM jackpot has rolled over, and the cash value is now $26.2M. The advertised annuity value is $45M. The average 5th draw produces 18.6M in sales. If the next drawing sells an average number of tickets, the randomized Poisson probability for various numbers of winners is as follows:

089.94%

19.54%

20.51%

30.02%

The exponential modelling function gives the following long term probability for the long term evolution of the jackpot:

Historical Average

Reply #274

dvdiva — Wed, 11 Oct 2006 05:09:35 GMT

I would say you are far more than just competent, I always look forward to your pobabilty outcomes.

Of course when it comes to Mega breaking 100 million vs a bunch of low level winners it always seems to go in one direction. On this run it looks like if it can survive until Nov 17th it would be over 300.

I wonder if a string of low level wins is more probable than a large jackpot (something I can't answer myself).

Reply #273

Prob988 — Sun, 08 Oct 2006 02:14:46 GMT

The averages refer to all drawings since the last change of matrices, which coincided with the addition of California. It would not make sense to refer to a time other than the conditions under which the lottery now operates.

I'm reasonably competent in mathematics, but I assure you I'm no genius. This stuff is pretty straight forward.

Reply #272

Just6ntlc — Sat, 07 Oct 2006 17:51:54 GMT

I think MM jackpots are higher than expected in this current run because of lower gas prices and the interest rates are steady. Also, I think the string of jackpot winners made it possible.

Reply #271

CA LotteryGuy — Sat, 07 Oct 2006 16:27:58 GMT

Prob988...thanks for the explanation of how the modeling function calculates jackpots. Still not sure if I totally understand, but then that's why you are a math genuis!!

Was wondering, how far back do you go to get the average drawing sales? Is it a rolling year or is it when California joined and they changed the jackpot minimum level?

On Wednesday and Saturday mornings after checking the numbers and realizing I don't need to choose between lump sum and annuity, my next step is to loo... [ More ]

Reply #270

Prob988 — Sat, 07 Oct 2006 07:52:01 GMT

The MegaMillions jackpot has rolled. The cash value is now $19.8M whereas the advertised annuity value is reported at $34M.

Fourth round drawings in MM sell on average $16.9M in tickets. If this is how many sell at this time, then the randomized probability distribution for numbers of winners will be as follows:

090.82%

18.74%

20.42%

30.01%

The modelling function calculates jackpots based on sales using the model formula S = C exp(a *N), where S is sales,... [ More ]

Reply #269

Prob988 — Thu, 05 Oct 2006 00:53:35 GMT

The MM jackpot has rolled. The cash value is $14.7M. The advertised annuity value is $25M.

The average third draw sells $14.7M.

If this draw sells this much, the randomized probability of various numbers of winners is as follows:

091.95%

17.72%

20.32%

30.01%

The model for Jackpot growth predicts the following:

Historical Average Advertised Annuity JackpotsModel Calculated Annuity PrizeModel Calculated Cash ValueSingle Draw Calculated Model Ro... [ More ]

Reply #268

Just6ntlc — Wed, 04 Oct 2006 18:34:36 GMT

Prob988, MM Jackpot for 10/6 is 25 million (rolled).

Reply #267

Prob988 — Sat, 30 Sep 2006 12:31:04 GMT

The MM jackpot has rolled. The cash value is $8.8M, the advertised annuity is $15M.

Second round jackpots on average sell 15.0 M tickets. If this is the number of tickets that sell, the distribution of probability of various numbers of winners will be:

091.83%

17.82%

20.33%

30.01%

The mathematical model for jackpot evolution, which tends to be more accurate in later drawings suggests the following:

Historical Average Advertised Annuity JackpotsModel... [ More ]

Reply #266

Just6ntlc — Thu, 28 Sep 2006 05:47:27 GMT

Prob988, I'll be surprised if MM jackpot hits again in next draw.

Reply #265

Homeydogg — Thu, 28 Sep 2006 00:57:04 GMT

It happens that to have been won on a second draw, after a previous sequence in which the jackpot was won on the first draw was a 7 in 1000 shot.

But if you look at it as 2 out of 3, the odds aren't so long.

I figure the odds of the MM being won in 2 of 3 draws after a reset is about 18 in 1000 or 1 in 56.

hit hit miss ~ 0.34%

hit miss hit ~ 0.72%

miss hit hit ~ 0.72%

Total ~ 1.78

Reply #264

Prob988 — Wed, 27 Sep 2006 11:51:44 GMT

The MM jackpot has been won. The jackpot has been reset to $7.1M cash, $12M for the advertised annuity.

It happens that to have been won on a second draw, after a previous sequence in which the jackpot was won on the first draw was a 7 in 1000 shot.

The average sales for opening runs is 15.3M. If this is how many tickets that sell, the randomized distribution probability for various numbers of winners is as follows:

091.67%

17.98%

20.35%

30.01%

The long ter... [ More ]

Reply #263

Prob988 — Sat, 23 Sep 2006 16:25:47 GMT

The MM jackpot has rolled. The cash value is $8.8M. The advertised annuity is $15.0M. The average number of tickets sold for a second draw in a series is $14.0M. If this is the number of tickets that sell, the probability of various numbers of winners is given as follows:

092.33%

17.37%

20.29%

30.01%

The long term jackpot evolution model, an exponential function generating model sales, predicts the following probabilities for this run:

Historical Ave... [ More ]

Reply #262

Just6ntlc — Sat, 23 Sep 2006 07:24:59 GMT

After two straight MM jackpot winners Prob988, MM jackpot for 9/26 has rolled to 15 million.

Reply #261

Prob988 — Thu, 21 Sep 2006 02:33:57 GMT

There have been 15 first draws since the matrix change. Only one first drawing has been won, meaning that 93% of the time, the first jackpot has rolled over.

This is consistent with the figures I routinely give here when first jackpots crop up, close to what I predict for the likelyhood that the next first jackpot will roll over.

If no could ever win a first jackpot, no one would ever play it of course. A single ticket playing in a $300 million jackpot has the same probability of winn... [ More ]

Reply #260

dvdiva — Wed, 20 Sep 2006 13:40:56 GMT

For MM it means another long string of pathetic low jackpots IMO. No wonder I don't play it.

Reply #259

ryanm — Wed, 20 Sep 2006 12:02:16 GMT

All right; it's nice to see a PB or MM opening jackpot won. It conveys the message that the odds aren't insurmountable.

Reply #258

Prob988 — Wed, 20 Sep 2006 10:04:12 GMT

MM has been won on the first draw.

Since the last draw was also a first draw, the probabilities remain the same.

Reply #257

Prob988 — Sat, 16 Sep 2006 12:46:19 GMT

The MM jackpot has been won and the jackpot has been reset to $7.0M cash and $12M as an advertised annuity.

The average number of sales for a first round drawing is $14.3M. If this is how many tickets sell this draw, the probability distribution for numbers of winners is as follows:

092.18%

17.51%

20.31%

30.01%

The long term proability model function, which ignores minimums and reserves suggests the following behavior:

Historical Average Advertised Annu... [ More ]

Reply #256

Just6ntlc — Thu, 14 Sep 2006 15:08:00 GMT

Prob988, PB also rolled. However, MM jackpot (annunity) is now higher than PB. I hope MM continues to roll.

Reply #255

Prob988 — Thu, 14 Sep 2006 06:07:55 GMT

MM has rolled over. The cash value prize is estimated at $94.7; the advertised annuity value is $163M.

Because of slow sales early in the drawing, I will treat the up coming drawing as an 12th round drawing rather than as a 13th round drawing.

An eleventh round drawing sells on average sells 34.8M tickets. If this is the number of tickets that sell, the randomized distribution of the probability of various numbers of winner is as follows:

078.90%

118.70%

22.22%

30.17

Reply #254

Prob988 — Sat, 09 Sep 2006 13:30:39 GMT

MM has rolled over. The cash value prize is estimated at $78.8; the advertised annuity value is $135M.

Because of slow sales early in the drawing, I will treat the up coming drawing as an 11th round drawing rather than as a 12th round drawing.

An eleventh round drawing sells on average sells 34.8M tickets. If this is the number of tickets that sell, the randomized distribution of the probability of various numbers of winner is as follows:

082.01%

116.27%

21.61%

30.11

Reply #253

Prob988 — Wed, 06 Sep 2006 11:04:40 GMT

MM has rolled over. The cash value prize is estimated at $66.5; the advertised annuity value is $114M.

Although this is an eleventh drawing coming up, it is more typical of an average 10th drawing, as sales have been lower for this run than on average. Possibly the long run without an annuity jackpot over $100M played a roll.

A tenth round drawing sells on average (including this recent draw). sells 30.7M tickets. If this is the number of tickets that sell, the randomized distributi... [ More ]