29-44-53-54-55- Red: 12

Quote:sodawaterYeah... I understand your thinking. I agree that if it doesn't hit tonight, the next drawing is going to be well over 50%.

By the way, just for the sake of correctness, if you thought it would have a 50% chance of winning each drawing, a fair price would be 3 to 1 that it wouldn't hit either one. If you had a 25% shot at 4 to 1 you'd have a huge edge.

They just released some numbers and the combination of numbers for tonight's drawing reached around 70% 'possible' combination. Definitely need to give him better odds :P

ETA drawing in 3minutes.

My body is ready.

Quote:Soft17They just released some numbers and the combination of numbers for tonight's drawing reached around 70% 'possible' combination. Definitely need to give him better odds :P

ETA drawing in 3minutes.

My body is ready.

If I would have successfully survived the bet without a winner tonight, the probability of a winner would have jumped to about 90% for the next individual drawing.

.3 * .1 = .03 = 1/.03 = 33.33:1 fair odds, in my opinion.

Quote:Mission146If I would have successfully survived the bet without a winner tonight, the probability of a winner would have jumped to about 90% for the next individual drawing.

.3 * .1 = .03 = 1/.03 = 33.33:1 fair odds, in my opinion.

Wasn't the bet for tonight, friday, and tuesday (christmas eve)?

I wouldn't have taken the bet, because there will obviously be a winner tonight.

The winner being me.

Quote:Mission146I did not buy a ticket, and I am quite confident I would not have won!

29-44-53-54-55- Red: 12

My theoretical ticket has performed as expected, same result, except I got to keep my $1.00!!!

Quote:Mission146My theoretical ticket has performed as expected, same result, except I got to keep my $1.00!!!

With the possible exception of a fleeting glance from a high heeled lady on stage, what is a dollar really going to get you?

When the lottery gets big, people go out and play. A lot more people than normal played the last draw. Even more played this one. Will people that just shelled out $10 or something on a bunch of tickets twice in one week really go back for a third time? At some point, the novelty of such a high jackpot may not be able to sustain continuing interest.

Quote:AsswhoopermcdaddyYou AP players will love these numbers for sure.

http://www.businessinsider.com/you-should-buy-a-mega-million-ticket-2013-12

That is a terrible article, especially the title. They gloss over the effect of taxes and jackpot sharing. I should analyze the odds properly to show it is still an awful bet.

Quote:bbbbccccAt some point, the novelty of such a high jackpot may not be able to sustain continuing interest.

I have to disagree there. When I analyzed the Powerball, in an old thread, I showed that ticket sales are exponentially correlated to jackpot size.

I would have been better off giving the money to the cashier to kick me in the nuts for 20 bucks.Atleast that way I would have saved $56.

Bedtime with a pillow full of tears.

KB1

Quote:Wizard

I have to disagree there. When I analyzed the Powerball, in an old thread, I showed that ticket sales are exponentially correlated to jackpot size.

Very true, but the mega millions has gone to much larger odds. You really only get the full blown media treatment at around $300 million. There has never been more than 2 consecutive draws above that level. With the longer odds, we are getting to the point where you may see 3 or even 4. Do people really go out to throw money at something for the 3rd or 4th time in two weeks like they do when it is something that happens only once or twice a year at best? We haven't seen such a situation to know for sure yet.

Of course it probably helps sales that it is Christmas week.

Quote:bbbbccccAlso, I think that going forward, there may be a reduction in ticket sales, expecially if it is true that there is only a 70% chance of a hit tonight.

When the lottery gets big, people go out and play. A lot more people than normal played the last draw. Even more played this one. Will people that just shelled out $10 or something on a bunch of tickets twice in one week really go back for a third time? At some point, the novelty of such a high jackpot may not be able to sustain continuing interest.

If by some chance it didn't hit tonight, ticket sales for friday will shatter records. you couldn't be more wrong on this

Good luck... 2/5 on one ticket no MB, and no loot here... -$3.

Sorry for the confusion... I will bust the post above.

Quote:98ClubsWinning numbers just b'cast.... 8-14-17-20-35 MB=7

Good luck... 2/5 on two tickets no MB, and no loot here... -$3.

you hit a total of 4 numbers on 3 tickets? you did way better than expected.

I should have offered Mission a lot better than 4:1

too bad... would have been fun to have a 900m jackpot on friday

FWIW 8-14 on QP and 8-"35" on the other. So three at first blush, but only apparently two.

Note: 2/5 is more difficult than 0/5 + MB ... 2 in 63 vs. 3 in 63. So I dun good... no loot.

Quote:bbbbccccWith the possible exception of a fleeting glance from a high heeled lady on stage, what is a dollar really going to get you?

A dollar will get me more than the absence of a dollar will.

If I had more time on my hands, maybe I could start gambling on the outcome, like Mission. Unfortunately, there's not enough data with this new game to make informed decisions.

Quote:AsswhoopermcdaddyYou AP players will love these numbers for sure.

http://www.businessinsider.com/you-should-buy-a-mega-million-ticket-2013-12

I hope you're happy, I just spent all morning refuting that article.

First, the author claims the probability of hitting one number, plus the Mega Ball is 0.017857143.

The number of combinations of hitting one ball, plus the mega ball, is:

Number of combinations to win the one ball * Number of combinations of four losing balls * Number of combinations of winning Mega Ball =

5 * combin(70,4) * 1 = 4,584,475.

The total number of combinations is:

Number of ways to choose 5 out of 75 * number of ways to choose 1 out of 15 =

combin(75,5) * 15 = 258,890,850.

So, the probability of hitting one number, plus the Mega Ball is 4,584,475/258,890,850 = 0.017708138. Not the 0.017857143 claimed by the author.

However, that is a minor differece. I mainly bring it up to impugn the math of Business Insider.

Before considering the annuity, taxes and jackpot sharing, we are in near agreement. They get an expected profit of 163.20% and I get 163.09%.

Assuming a single winner takes a lump sum of $341 million, we're still very close. They get an expected profit of 49.255% and I get 49.139%.

Then the article says:

Quote:Business InsiderSo, as long as there are fewer than 730 million tickets sold, a fairly likely situation right now, the expected value of a ticket should be positive, and so you should consider buying a Mega Millions ticket today.

What if the reader quit reading there? He would be making a terrible bet. However, the article continues:

Quote:Business InsiderBear in mind that there are many caveats to this analysis. Taxes will likely hurt your expected winnings pretty severely — the Feds will take about 40%, and your home state will claim anywhere from 0% to around 13%.

Those are some pretty big caveats! The highest marginal federal tax rate is 39.6%. Let's assume 6% for state tax. That leaves us with a jackpot of $185,504,000 . However, we still need to factor in the dreaded jackpot sharing.

In the case of the December 17, 2013 drawing there were $336,545,306 in ticket sales (source: lottoreport.com). This does not include Megaplier sales, as stated in the state by state sales.

At $1 each, we can assume 336,545,306 tickets sold. This would equate to 72.75% combinations covered, assuming every ticket was a quick pick.

Then again, according to ABC news, between 65% and 70% of combinations were covered. Let's split the difference and say 67.5%. That would equate to 290,975,218 tickets sold, for an expected number of winners of 290,975,218/258,890,850 =1.124. However, this article was published before the drawing. Maybe more tickets were sold since publication. I'm going to go with lottoreport.com, and assume 336,545,306 tickets sold.

The following table shows the probability of 0 to 10 other winners, how much of the share you will get if you win, and your expected share if you win. The lower right cell shows that after jackpot sharing you can expect to keep about 56% of it, and lose 44% to other winners.

Other winners | Probability | Jackpot share | Expected share |
---|---|---|---|

10 | 0.000001 | 0.090909 | 0.000000 |

9 | 0.000008 | 0.100000 | 0.000001 |

8 | 0.000055 | 0.111111 | 0.000006 |

7 | 0.000339 | 0.125000 | 0.000042 |

6 | 0.001827 | 0.142857 | 0.000261 |

5 | 0.008431 | 0.166667 | 0.001405 |

4 | 0.032429 | 0.200000 | 0.006486 |

3 | 0.099786 | 0.250000 | 0.024946 |

2 | 0.230283 | 0.333333 | 0.076761 |

1 | 0.354295 | 0.500000 | 0.177148 |

0 | 0.272545 | 1.000000 | 0.272545 |

Total | 1.000000 | 0.559602 |

So, after the lump sum, federal taxes, state taxes, and jackpot sharing we're left with an expected win of $103,808,379 if you do win. The following table calculates the expected value, all prizes considered. To make things easy, I'm assuming no taxes on all fixed wins.

Catch | Mega Ball | Pays | Combinations | Probability | Return |
---|---|---|---|---|---|

5 | Yes | $103,808,379 | 1 | 0.0000000039 | 0.400974 |

5 | No | $1,000,000 | 14 | 0.0000000541 | 0.054077 |

4 | Yes | $5,000 | 350 | 0.0000013519 | 0.006760 |

4 | No | $500 | 4,900 | 0.0000189269 | 0.009463 |

3 | Yes | $50 | 24,150 | 0.0000932826 | 0.004664 |

3 | No | $5 | 338,100 | 0.0013059558 | 0.006530 |

2 | Yes | $5 | 547,400 | 0.0021144046 | 0.010572 |

1 | Yes | $2 | 4,584,475 | 0.0177081384 | 0.035416 |

0 | Yes | $1 | 12,103,014 | 0.0467494854 | 0.046749 |

Loser | 0 | $0 | 241,288,446 | 0.9320083966 | 0.000000 |

Total | 0 | $0 | 258,890,850 | 1.0000000000 | 0.575205 |

The lower right cell shows the player will get back 57.52 cents for every dollar bet. In other words, a house edge of 42.48%.

Sorry Business Week, but your advice was terrible. I give that an article a D-.

If anyone can dig up the actual number of tickets sold, please let me know.

"LOS ANGELES - Two tickets with five numbers in Tuesday's multi-state Mega Millions draw, but missing the Mega number, were sold in San Diego County, and are each worth $2,621,916.

One ticket was sold at Fuller Liquor and Deli in San Diego, the other at Square Bottle Liquor in Chula Vista, the California Lottery announced.

There were 18 other tickets sold with five numbers, but missing the Mega number. They are each worth $1 million...."

Full article link:

http://www.10news.com/news/u-s-world/winning-mega-millions-numbers-for-tuesdays-636m-jackpot-unveiled-121713

edit to add that CNN has this in one of their articles, so maybe the article above is incorrect:

" Twenty ticket holders will win $1 million after matching all the numbers except the Megaball."

Full article link:

http://www.cnn.com/2013/12/18/us/mega-millions/

Quote:AlanCan someone explain why two of the tickets mentioned in this article are worth more than the other 18? Five numbers drawn, but no Mega number, so seems they should all be worth the same amount.

"LOS ANGELES - Two tickets with five numbers in Tuesday's multi-state Mega Millions draw, but missing the Mega number, were sold in San Diego County, and are each worth $2,621,916.

One ticket was sold at Fuller Liquor and Deli in San Diego, the other at Square Bottle Liquor in Chula Vista, the California Lottery announced.

There were 18 other tickets sold with five numbers, but missing the Mega number. They are each worth $1 million...."

Full article link:

http://www.10news.com/news/u-s-world/winning-mega-millions-numbers-for-tuesdays-636m-jackpot-unveiled-121713

edit to add that CNN has this in one of their articles, so maybe the article above is incorrect:

" Twenty ticket holders will win $1 million after matching all the numbers except the Megaball."

Full article link:

http://www.cnn.com/2013/12/18/us/mega-millions/

It's because all prizes in California are pari-mutual, not fixed.

http://www.megamillions.com/how-to-play

Quote:sodawater

It's because all prizes in California are pari-mutual, not fixed.

Thank you.

Quote:wudgedIn California winning tickets that are not the full jackpot are parimutuel.

http://www.megamillions.com/how-to-play

Thank you.

Quote:Wizard

In the case of the December 17, 2013 drawing there were $336,545,306 in ticket sales (source: lottoreport.com). This does not include Megaplier sales, as stated in the state by state sales.

Actually, that website says that this number did not include the Megaplier sales. Also, it doesn't include sales for CT and TN. I would guess about 11-12 million in sales from those two combined.

Quote:WizardI hope you're happy, I just spent all morning refuting that article.

<snip>

The following table shows the probability of 0 to 10 other winners, how much of the share you will get if you win, and your expected share if you win. The lower right cell shows that after jackpot sharing you can expect to keep about 56% of it, and lose 44% to other winners.

Other winners Probability Jackpot share Expected share 10 0.000001 0.090909 0.000000 9 0.000008 0.100000 0.000001 8 0.000055 0.111111 0.000006 7 0.000339 0.125000 0.000042 6 0.001827 0.142857 0.000261 5 0.008431 0.166667 0.001405 4 0.032429 0.200000 0.006486 3 0.099786 0.250000 0.024946 2 0.230283 0.333333 0.076761 1 0.354295 0.500000 0.177148 0 0.272545 1.000000 0.272545 Total 1.000000 0.559602

So, after the lump sum, federal taxes, state taxes, and jackpot sharing we're left with an expected win of $103,808,379 if you do win. The following table calculates the expected value, all prizes considered. To make things easy, I'm assuming no taxes on all fixed wins.

Catch Mega Ball Pays Combinations Probability Return 5 Yes $103,808,379 1 0.0000000039 0.400974 5 No $1,000,000 14 0.0000000541 0.054077 4 Yes $5,000 350 0.0000013519 0.006760 4 No $500 4,900 0.0000189269 0.009463 3 Yes $50 24,150 0.0000932826 0.004664 3 No $5 338,100 0.0013059558 0.006530 2 Yes $5 547,400 0.0021144046 0.010572 1 Yes $2 4,584,475 0.0177081384 0.035416 0 Yes $1 12,103,014 0.0467494854 0.046749 Loser 0 $0 241,288,446 0.9320083966 0.000000 Total 0 $0 258,890,850 1.0000000000 0.575205

The lower right cell shows the player will get back 57.52 cents for every dollar bet. In other words, a house edge of 42.48%.

Sorry Business Week, but your advice was terrible. I give that an article a D-.

If anyone can dig up the actual number of tickets sold, please let me know.

Wiz, I think you're being pretty hard on that grade. They do go on to mention taxes and jackpot sharing. Sure it's toward the end and the article title is misleading. But I'd probably give them a D+ or maybe or a C :).

I would like to highly encourage you to put all that math into an article on WoO. Even better would be a graph showing the expected value correlated to the jackpot size. It would go up with jackpot size until the craze started kicking in, and then go back down due to the higher probability of sharing. Considering all relevant variables (taxes, jackpot sharing, and the cash discount being key among them), the EV should never go positive.

Also, some kudos for refraining from using the word "annuity" in these analyses (as you used to). The "annuity" option means you get the full jackpot amount, over 30 years. If you're going to use the "cash option" in your numbers, as you are, much better to use the term "cash option" or "lump sum," as it reads above. Much better.

A whole different article could be written on which is better, considering prudent investment. I've come around on that one; I used to say a smart person who can handle deferred gratification should always take the annuity for the whole jackpot amount. But given inflation and a reasonable estimation of investment returns, I think I'm in agreement that the cash option is better. If you have no self control, then the annuity probably still wins.

I succumb to the lottery craze when the "theoretical" EV goes positive, even though I know (thanks to this site) that the realistic EV never goes positive. I fell victim to a work pool for the last drawing. So a succinct page with all of the math that says "NO!" would help me.

Quote:AcesAndEightsQuote:WizardI hope you're happy, I just spent all morning refuting that article.

<snip>

The following table shows the probability of 0 to 10 other winners, how much of the share you will get if you win, and your expected share if you win. The lower right cell shows that after jackpot sharing you can expect to keep about 56% of it, and lose 44% to other winners.

Other winners Probability Jackpot share Expected share 10 0.000001 0.090909 0.000000 9 0.000008 0.100000 0.000001 8 0.000055 0.111111 0.000006 7 0.000339 0.125000 0.000042 6 0.001827 0.142857 0.000261 5 0.008431 0.166667 0.001405 4 0.032429 0.200000 0.006486 3 0.099786 0.250000 0.024946 2 0.230283 0.333333 0.076761 1 0.354295 0.500000 0.177148 0 0.272545 1.000000 0.272545 Total 1.000000 0.559602

So, after the lump sum, federal taxes, state taxes, and jackpot sharing we're left with an expected win of $103,808,379 if you do win. The following table calculates the expected value, all prizes considered. To make things easy, I'm assuming no taxes on all fixed wins.

Catch Mega Ball Pays Combinations Probability Return 5 Yes $103,808,379 1 0.0000000039 0.400974 5 No $1,000,000 14 0.0000000541 0.054077 4 Yes $5,000 350 0.0000013519 0.006760 4 No $500 4,900 0.0000189269 0.009463 3 Yes $50 24,150 0.0000932826 0.004664 3 No $5 338,100 0.0013059558 0.006530 2 Yes $5 547,400 0.0021144046 0.010572 1 Yes $2 4,584,475 0.0177081384 0.035416 0 Yes $1 12,103,014 0.0467494854 0.046749 Loser 0 $0 241,288,446 0.9320083966 0.000000 Total 0 $0 258,890,850 1.0000000000 0.575205

The lower right cell shows the player will get back 57.52 cents for every dollar bet. In other words, a house edge of 42.48%.

Sorry Business Week, but your advice was terrible. I give that an article a D-.

If anyone can dig up the actual number of tickets sold, please let me know.

Wiz, I think you're being pretty hard on that grade. They do go on to mention taxes and jackpot sharing. Sure it's toward the end and the article title is misleading. But I'd probably give them a D+ or maybe or a C :).

I would like to highly encourage you to put all that math into an article on WoO. Even better would be a graph showing the expected value correlated to the jackpot size. It would go up with jackpot size until the craze started kicking in, and then go back down due to the higher probability of sharing. Considering all relevant variables (taxes, jackpot sharing, and the cash discount being key among them), the EV should never go positive.

Also, some kudos for refraining from using the word "annuity" in these analyses (as you used to). The "annuity" option means you get the full jackpot amount, over 30 years. If you're going to use the "cash option" in your numbers, as you are, much better to use the term "cash option" or "lump sum," as it reads above. Much better.

A whole different article could be written on which is better, considering prudent investment. I've come around on that one; I used to say a smart person who can handle deferred gratification should always take the annuity for the whole jackpot amount. But given inflation and a reasonable estimation of investment returns, I think I'm in agreement that the cash option is better. If you have no self control, then the annuity probably still wins.

I succumb to the lottery craze when the "theoretical" EV goes positive, even though I know (thanks to this site) that the realistic EV never goes positive. I fell victim to a work pool for the last drawing. So a succinct page with all of them math that says "NO!" would help me.

I agree that it should be published. In ATW at a minimum....Wiz?

Is it just some underlying desire to "score a deal"? To "be smart and wise"? Or is there something else to it?

One Hundred Million Dollars. WTF is the point of maximizing your payout? Maybe others just dream bigger than me, but once I get to a certain level (which is a damn sight shorter than a hundo million), it ceases to matter. Just gimme. Whether I'm dumb and take the hundo, or play it smart and wind up with three hundo, I, my kid, my kid's kids ain't coming nowhere near spending that.

So why does it matter? When does it cease to matter?

Quote:FaceAnnuity vs lump sum...what compels people to give a rip?

Is it just some underlying desire to "score a deal"? To "be smart and wise"? Or is there something else to it?

One Hundred Million Dollars. WTF is the point of maximizing your payout? Maybe others just dream bigger than me, but once I get to a certain level (which is a damn sight shorter than a hundo million), it ceases to matter. Just gimme. Whether I'm dumb and take the hundo, or play it smart and wind up with three hundo, I, my kid, my kid's kids ain't coming nowhere near spending that.

So why does it matter? When does it cease to matter?

Right, this is why I buy lottery tickets.

I spend an amount of money that is irrelevant to me or my standard of living, for a non-zero (admittedly minute) chance of getting an amount of money that is VERY relevant to me. Plus, 30 seconds of entertainment while I check my numbers.

The problem with long-term analysis is that your life is not long-term. The numbers that Mission (I think?) posted showed a loss of around $11k, playing consistently for 120 years. That's basically 2 lifetimes of playing (if you play from 20 to 80 years old). I tend to buy tickets in bunches, but I don't buy them that often. I probably spend around $100 per year on lottery tickets. Sure, it's hugely -EV.... but who cares? It's $100 per year.

Now, if you are in a situation where that money is relevant to you and would change your life, then don't play. But if not, then why not?

Quote:CrystalMathActually, that website says that this number did not include the Megaplier sales. Also, it doesn't include sales for CT and TN. I would guess about 11-12 million in sales from those two combined.

Dang. I suppose I could make an adjustment based on population. If anybody can get a no-nonsense sum of the number of tickets in play, please let me know. Since that is pertinent to the value of a ticket, you would think there would be more demand for that information.

Also, I see Lotto Report says, "Connecticut & Tennessee are the ONLY 2 states who refuse to release their sales figures. I have to obtain them elsewhere." I interpret that to mean he got the information elsewhere, and just isn't saying where or how.

Quote:AcesAndEightsWiz, I think you're being pretty hard on that grade. They do go on to mention taxes and jackpot sharing. Sure it's toward the end and the article title is misleading. But I'd probably give them a D+ or maybe or a C :).

But that article was titled "Math Says You Should Buy A Mega Millions Ticket Right Now." It was teasing the audience to read it by that title and only mentioned there were "caveats" at the end, without any effort to quantify them. Weekly World News journalism.

Quote:I would like to highly encourage you to put all that math into an article on WoO.

I plan to make it an "ask the wizard" question in the next column.

Quote:Even better would be a graph showing the expected value correlated to the jackpot size. It would go up with jackpot size until the craze started kicking in, and then go back down due to the higher probability of sharing.

I spent a lot of time looking at that, but the data from Lotto Report looks fishy. Here is the data since the Mega Millions switched the 75-15 rules, effective with the Oct 18, 2013 drawing. Amounts are in millions:

Date | Jackpot | Jackpot Growth | Jackpot | Jackpot Growth to Sales Ratio |
---|---|---|---|---|

12/17/2013 | $636 | $236 | $636 | 70.1% |

12/13/2013 | $400 | $56 | $400 | 33.4% |

12/10/2013 | $344 | $53 | $344 | 70.3% |

12/6/2013 | $291 | $34 | $291 | 59.2% |

12/3/2013 | $257 | $27 | $257 | 55.1% |

11/29/2013 | $230 | $25 | $230 | 67.9% |

11/26/2013 | $205 | $24 | $205 | 64.3% |

11/22/2013 | $181 | $16 | $181 | 49.6% |

11/19/2013 | $165 | $16 | $165 | 57.7% |

11/15/2013 | $149 | $17 | $149 | 63.1% |

11/12/2013 | $132 | $17 | $132 | 68.0% |

11/8/2013 | $115 | $16 | $115 | 65.6% |

11/5/2013 | $99 | $12 | $99 | 57.0% |

11/1/2013 | $87 | $12 | $87 | 60.7% |

10/29/2013 | $75 | $10 | $75 | 56.9% |

10/25/2013 | $65 | $10 | $65 | 56.5% |

10/22/2013 | $55 | $18 | $55 | 113.1% |

10/18/2013 | $37 |

Look at the last three drawings. With the Dec 10 and 17 drawings the jackpot grew by about 70% of ticket sales. Yet, for the Friday the 13th drawing it went up by only 33%.

I wrote earlier that my wife made me buy tickets for the 12/13 drawing. I bought tickets at about 11:30 AM the day of the drawing, and I recall the sign at the gas station saying the jackpot was $400 million. However, that figure should have grown by sales that Friday afternoon. Or does signage reflect an estimated jackpot, based on the rate of sales? The fact that it is a round number also makes me suspicious that it is accurate.

If we remove the fishy looking 400 million jackpot for the 12/13 drawing, then we can estimate sales (as reported by Lotto Report) as 12.422 * exp(0.0052*j), where j is the jackpot size in millions.

Quote:Also, some kudos for refraining from using the word "annuity" in these analyses (as you used to).

Why do you oppose it? Is it because an annuity means payment over a period until death, or forever? If so, I would respond that such is usually the case, but doesn't have to be. The lotteries also use the term annuity.

Quote:Wizard... Or does signage reflect an estimated jackpot, based on the rate of sales? The fact that it is a round number also makes me suspicious that it is accurate.

Yes, they reflect estimated amounts base on sales trends.

Quote:DRichYes, they reflect estimated amounts base on sales trends.

Thanks. I suspect, based on my table above, that 400 million was a low estimate.

Quote:WizardWhy do you oppose it? Is it because an annuity means payment over a period until death, or forever? If so, I would respond that such is usually the case, but doesn't have to be. The lotteries also use the term annuity.

It's not the word itself, it's how you use it. In a previous analysis you said this:

Quote:WizardAt a jackpot of $550 million I find the value of a $2 ticket to be $2.11, before considering taxes and annuity. If we assume that 50% of the jackpot is lost to taxes, and another 50% to the annuity, then the value of that $2 ticket I show to be $0.80.

Getting the total jackpot amount, over 30 years = annuity.

Getting a reduced jackpot amount, right now = NOT an annuity. "Lump sum" or "cash option" or whatever. Your previous verbiage was confusing, is all. I think you got it right in your most recent post.

Quote:AcesAndEightsGetting the total jackpot amount, over 30 years = annuity.

Getting a reduced jackpot amount, right now = NOT an annuity. "Lump sum" or "cash option" or whatever. Your previous verbiage was confusing, is all. I think you got it right in your most recent post.

Point taken.

Quote:AcesAndEightsConsidering all relevant variables (taxes, jackpot sharing, and the cash discount being key among them), the EV should never go positive.

As I've written about with the PowerBall, the jackpot can get so big that value decreases, due to the exponential demand for tickets and jackpot sharing. I find the optimal jackpot size for Mega Millions is $545 million. At that size, the expected winners will be 0.816 and 32% of any jackpot will be lost to sharing with other winners. The net jackpot, after the lump sum, taxes, and sharing is $108.6 million. Expected return = 59.4%, or house edge of 30.6%.

Quote:beachbumbabsOne number out of 18. I should know better. Pathetic. Hope somebody else on here did better.

I got two numbers on the Megamillions two weeks ago when it 350 MM.

Quote:AlanCan someone explain why two of the tickets mentioned in this article are worth more than the other 18? Five numbers drawn, but no Mega number, so seems they should all be worth the same amount.

"LOS ANGELES - Two tickets with five numbers in Tuesday's multi-state Mega Millions draw, but missing the Mega number, were sold in San Diego County, and are each worth $2,621,916.

One ticket was sold at Fuller Liquor and Deli in San Diego, the other at Square Bottle Liquor in Chula Vista, the California Lottery announced.

There were 18 other tickets sold with five numbers, but missing the Mega number. They are each worth $1 million...."

Full article link:

http://www.10news.com/news/u-s-world/winning-mega-millions-numbers-for-tuesdays-636m-jackpot-unveiled-121713

edit to add that CNN has this in one of their articles, so maybe the article above is incorrect:

" Twenty ticket holders will win $1 million after matching all the numbers except the Megaball."

Full article link:

http://www.cnn.com/2013/12/18/us/mega-millions/

In California, the payments of the minor prizes are PARI-MUTUAL. Thus according to the California pool, the two tickets split the 5/5 second-prize pool.

Quote:AcesAndEightsEven better would be a graph showing the expected value correlated to the jackpot size. It would go up with jackpot size until the craze started kicking in, and then go back down due to the higher probability of sharing. Considering all relevant variables (taxes, jackpot sharing, and the cash discount being key among them), the EV should never go positive.

this is what i came up with the other day..

#players (millions)/average jp share after winning/EV*

300/.59/$1.07

400/.51/$0.94

500/.44/$0.84

600/.39/$0.76

700/.35/$0.70

800/.31/$0.64

*assuming 60% of the jackpot is the present value, $650 million jackpot

im not sure if you should count taxes, since typically returns for casino games don't take them into account, so including taxes wouldn't really be an apple to apple comparison.

http://www.philly.com/philly/news/Mega_Millions_Powerball_show_jackpot_fatigue_.html

Quote:Wizard

The following table shows the probability of 0 to 10 other winners, how much of the share you will get if you win, and your expected share if you win. The lower right cell shows that after jackpot sharing you can expect to keep about 56% of it, and lose 44% to other winners.

Other winners Probability Jackpot share Expected share 10 0.000001 0.090909 0.000000 9 0.000008 0.100000 0.000001 8 0.000055 0.111111 0.000006 7 0.000339 0.125000 0.000042 6 0.001827 0.142857 0.000261 5 0.008431 0.166667 0.001405 4 0.032429 0.200000 0.006486 3 0.099786 0.250000 0.024946 2 0.230283 0.333333 0.076761 1 0.354295 0.500000 0.177148 0 0.272545 1.000000 0.272545 Total 1.000000 0.559602

So, after the lump sum, federal taxes, state taxes, and jackpot sharing we're left with an expected win of $103,808,379 if you do win. The following table calculates the expected value, all prizes considered. To make things easy, I'm assuming no taxes on all fixed wins.

I have a question about the calculation of the expected value of a shared jackpot.

To me it seems that the table shown is the probability of total winners, not "other winners".

So I would think that the 0.272545 probability of 0 winners should be excluded from the calculation since there will be no jackpot if there are no winners. And the expected share of, for instance, 2 total winners would be 0.230283 / (1 - .272545) * .50 = 0.158280

Calculating this way I arrive at an expected win of $133,717,264 instead of $103,808,379.

Can anyone explain why it should not be calculated this way?

Thanks

Quote:AceI have a question about the calculation of the expected value of a shared jackpot.

To me it seems that the table shown is the probability of total winners, not "other winners".

So I would think that the 0.272545 probability of 0 winners should be excluded from the calculation since there will be no jackpot if there are no winners. And the expected share of, for instance, 2 total winners would be 0.230283 / (1 - .272545) * .50 = 0.158280

Calculating this way I arrive at an expected win of $133,717,264 instead of $103,808,379.

Can anyone explain why it should not be calculated this way?

The numbers for "total winners" and "other winners, assuming you bought one ticket and won" are pretty much the same (within the accuracy the Wizard used) for the 336,545,306 tickets used for the table. Your ticket has no noticeable effect on how well everybody else does, so the numbers apply to "how many tickets besides your one winning ticket were also winners."

If you take it as "total winners," then you have to take into account the fact that none of the winning tickets are yours. Remember, the numbers reflect the share if you win.

I beg my sister to quit playing every once in a while, it's so stupid.Quote:bbbbccccThere is at least some anecdotal evidence my previously stated hypothesis that there could be a jackpot fatigue may be comming true. The jackpots now fail to jump exponentially until there is a larger jackpot than before.

http://www.philly.com/philly/news/Mega_Millions_Powerball_show_jackpot_fatigue_.html

Quote:onenickelmiraclePretty damn low to have to split with tickets also winning but never claimed. That rule just is pure wrong almost to the point of tyranny. WE have to prove everything, but they just say trust us. You might never win, but if it was you, you shouldn't have to split with the phantom or the state unless it can be proven with the other tickets. Ohio took 269 million in unclaimed winnings in 10 years- enough to start a frenzy at the convenience stores.

FWIW, Florida is required to add any expired (180 days) unclaimed jackpots back in to the totals, which they do in December of every year, just to avoid the "split with the state" problem, which they see as false advertising for what they award if they didn't. Makes for some nice jackpot runups some years right at Christmas.

https://www.yahoo.com/finance/news/math-best-time-play-mega-214800829.html