Buying a Ticket?

My wife asked me if we should buy a few Mega-Millions tickets. We never do. Maybe I should run out to the local convenience store and get a few.

https://www.cnn.com/2022/07/29/us/mega-millions-lottery-jack…

I wonder why this is the second biggest jackpot ever? Are folks betting on the lottery more now?

'38Packard

I wonder why this is the second biggest jackpot ever? Are folks betting on the lottery more now?

The last time someone won the jackpot was April 15. I don’t think this one is any different. The number of tickets bought accelerates as the jackpot grows. Once over 500 million, it increases rapidly. I bought one ticket. Since the odds are 1 in 302 million, I don’t buy a second. It’s an entertainment expense.

PSU

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I bought one ticket. Since the odds are 1 in 302 million, I don’t buy a second. It’s an entertainment expense.

One ticket here, too.

Basically, so my wife and I can argue about we’ll spend the winnings. We know the arguments will end as soon as we check the numbers. Just a little game we play.

AW

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So, if the odds are 1 in 300 million and the tickets are $2 each, what would it cost to by every number combination and what would the expected value be? (and is there an app to hack and how do you move the cash into the system at that rate?)

Jeff

jeff:“So, if the odds are 1 in 300 million and the tickets are $2 each, what would it cost to by every number combination and what would the expected value be? (and is there an app to hack and how do you move the cash into the system at that rate?)”

To get the mega multiplier, they are 3 dollars each.

So if your odds are 1 in 300 million, you’d need to buy a 300 million tickets. But that doesn’t assure you of winning the 1.3 billion. Others could also win and there might be three winners dividing that 1.3 billion. or 5. But there could only be one.

So you’d spend 900 million…but maybe only win 450 million if three people got it…and of course, it’s discounted by another 50% if you take a lump sum.

There are smaller prizes…a couple of million dollar prizes…

But…with odds of 1 in 300 million, it’s like look at the population of the USA and pick out one lucky person to win… with the rest having thrown their money down a rat hole. Of course, if you buy 10 tickets…your odds go up to 10 in 300 million.

t.

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It’s cheaper than going to a movie, or going to Six Flags over Texas, or buying a book, or most other forms of entertainment.

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Maybe I should run out to the local convenience store and get a few.

'38Packard,

I had a friend pick up a ticket for me because I wasn’t able to pick it up myself. If the numbers hit, I’m giving him 10% as a commission (but he has to pay 10% of the taxes, too - LOL).

My plans are to create a charitable foundation and hope to live long enough to see it properly established to fund the kind of work I can’t do myself but would like to see carried on for as long as possible.

We all can certainly dream.

:wink:

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Notehound,

…My plans are to create a charitable foundation…

Awesome! I give back pretty much every day in my volunteering work. It makes me feel like I’m relevant and I go to bed nights knowing that I have done what I could for the greater good.

Cheers!
'38Packard

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I wonder why this is the second biggest jackpot ever? Are folks betting on the lottery more now?

How to stay poor without even trying!

The Captain

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This is a true story.

I was standing at the register at Weigel’s to buy a ticket for the Mega Millions, and the guy in front of me asked the clerk for a ticket for the Powerball.

“You mean the Mega Millions?” the cashier asked.

“No, the PowerBall,” he said. “Everybody else is playing the Mega Millions, so I figure my odds are better with the PowerBall.”

This would be funny, except, of course, I was standing in line to buy a Mega Millions ticket too, so I can’t really snark on someone for their lack of math skills.

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I wonder why this is the second biggest jackpot ever? Are folks betting on the lottery more now?

How to stay poor without even trying!

My younger brother won $270,000 in the lottery long ago. Bought himself a red sports car. A couple months later he was diagnosed with MS. Eventually he had to trade the Corvette in for a van with a lift so he could take his wheelchair along. Then they put him in a nursing home where they took his wheelchair away because he couldn’t control it and ran into things and people. Last time I visited him on a trip back from Germany he couldn’t even operate the remote for the tv so watched the same station all day.

That is the short version of a long story. He bought his girlfriend a jeep before the diagnosis, she left of course but then was in an accident with the jeep and was killed in the crash.

I haven’t bought a lottery ticket in a very long time.

Tim

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“Everybody else is playing the Mega Millions, so I figure my odds are better with the PowerBall.”

This would be funny, except, of course, I was standing in line to buy a Mega Millions ticket too, so I can’t really snark on someone for their lack of math skills.

It would be an interesting exercise to figure at what lotto jackpot value the return on a ticket maximizes. It’s not nearly so simple as larger jackpot = more return because the number of people buying tickets, and the number of tickets bought per person buying tickets both spike when it gets really high, so the odds of having to split the jackpot go up as the jackpot does.

I spent a few minutes not too long ago to calculate the expected value (EV) of a ticket, ignoring that effect of split pots, and if I did them right, I found that the cash value of the jackpot (not the headline number, which is paid out over 20 years or something, but the cash out now number) has to hit about $500 million, which is ballpark $800 million headline value, IINM, before the EV turns positive. That still ignores the effects of taxes, but I figure I’d donate the vast bulk of it to charity the first year to avoid most taxes.

Any way, I went to looking for an estimate of what effect the pot-splitting has, and the news was not good. I can’t vouch for his calculations but it looks plausible, second answer down: https://www.quora.com/What-are-the-odds-of-having-multiple-w…

He said at the time, when the lotto was spiking over $1b, the last round had produced about 450 million ticket sales and he ran his estimates as if 600 million tickets were sold as it went over $1b. “Then we get that the probability of no tickets winning is 0.135, one winning 0.271, two winning also 0.271, three winning, 0.180, four winning 0.090, and five winning 0.036.”

So if you win in this scenario, you are most likely splitting the jackpot, and you’re more likely to split with more than one other ticket than you are to win it by yourself.

This obviously craters any potential positive EV in this scenario.

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It would be an interesting exercise to figure at what lotto jackpot value the return on a ticket maximizes.

Expected outcome from statistics. Here is a simplistic calculator, it doesn’t take into account smaller prizes, i.e. 5/6 or 4/6 number matches. There are many others out there.

https://lottolibrary.com/expected-value-calculator/

JLC

Until the drawing we were all Schrodinger’s billionaires.

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Yeah - I didn’t win anything in Mega Millions - I guess I should have played PowerBall :wink:

'38Packard

Here is a simplistic calculator, it doesn’t take into account smaller prizes, i.e. 5/6 or 4/6 number matches. There are many others out there.

https://lottolibrary.com/expected-value-calculator/

Thanks, JLC. Using that calculator, $1.34 billion jackpot size, 352 million tickets sold, which I found online (not sure how reliable that figure is), and ~$.24 EV of the lower value prizes per $2 ticket that I calculated for Mega Millions, I get buying a $2 ticket sold for that drawing had an expected value of -47 cents.

It’s not nearly so simple as larger jackpot = more return because the number of people buying tickets, and the number of tickets bought per person buying tickets both spike when it gets really high, so the odds of having to split the jackpot go up as the jackpot does.

I have noticed that while it does happen, the number of times the jackpot has to be split are pretty small, at least for these “300 million to 1” games. Even with lots and tons of tickets being sold in the past few weeks, this particular jackpot still went 29 consecutive drawings without finding a perfect match.

So the “more tickets = split pot” would seem to be an outlier, making a reasonable computation of the difference in odds pretty difficult.

(I remember when the state lotteries first got going, having the pots build to $1 million caused the same kind of mania. I guess a million isn’t what it used to be.)

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I have noticed that while it does happen, the number of times the jackpot has to be split are pretty small,…

Many years ago out of curiosity, looked up to see how many times these huge jackpots were split among multiple winners. IIRC, I only looked at >$100M and it was 50/50 single winner vs multiple winners. Of those multiple winners, only one had 3 winners and the rest were 2 winners. Didn’t look into any correlation with tickets sold.

JLC

Many years ago out of curiosity, looked up to see how many times these huge jackpots were split among multiple winners. IIRC, I only looked at >$100M and it was 50/50 single winner vs multiple winners. Of those multiple winners, only one had 3 winners and the rest were 2 winners. Didn’t look into any correlation with tickets sold.

Well you are far more right than I. I just looked up the 10 biggest jackpots in history, and four of them were split winners, six were solo. Of the splits, two were 2-way, and two were 3-way.

https://www.usnews.com/news/us/articles/2021-10-05/what-are-…

Business Insider did a nice little breakdown a few years ago, when the MegaMillions was “only” a $500 million jackpot, on whether the jackpot was large enough to have a positive expected value. While obviously those values change with the larger jackpot, there’s some very useful information in there:

https://www.businessinsider.com/mega-millions-lottery-jackpo…

TL;DR - the main reasons these things are never positive EV even are because of multiple winners (as discussed above, because of taxes, and because the quoted jackpot is an annuity. Taking the $1.3 billion as a single payment reduces the payoff to “only” $750 million. How much you lose to taxes depends on your situation and your accountants’ skills, but even optimistically you’ll like drop to below $600 million in terms of money in the bank. At one-in-300 million odds on a $2 ticket, you’re barely at positive EV on $1.3 billion even if you were guaranteed to be the sole winner.

If you click the link, they provide a chart showing the probability distribution of multiple winners for the MegaMillions, based on the number of tickets sold. For an ‘ordinary’ MegaMillions, you might only have about 10-15 million tickets sold - where there’s virtually no chance of a split ticket, and indeed the most likely outcome is no winner at all.

But when you get up into the jackpot levels where the national media starts covering it, the number of tickets sold gets up into levels where there’s a non-trivial chance of splitting the jackpot. In this cycle, when the jackpot got up to $630M, the number of tickets sold for that drawing was about 85M - which, if everyone chose their tickets at random, would yield a 5% chance of a split pot. Even in the ideal number of tickets sold, you’d only have a single winner in about a third of draws. The final jackpot drawing sold 350M tickets, which was pretty close to that ideal - you’d yield a split pot around 1/3 of the time (again, assuming random tickets), no winner 1/3 of the time, and a single winner the remaining third:

https://www.lottoreport.com/mm03sales.htm

Given the above, you’re about 50/50 to split your jackpot with at least one other person if you win. Still very much negative EV.

Albaby

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