How many lottery tickets would you have to buy in order to give yourself a 95% chance of winning?

[Yavin4]

Assume :
1. Each ticket is worth a dollar
2. The odds are the same as the mega millions lottery
3. Rules of the lottery are the same as the mega-millions
4. IOW, just assume it's the mega millions lottery for $1.6 billion

Please show your work.

[at140]

1. too many to be practical

[Demovictory9]

2. it's not how many tickets, its how many possible number combinations are represented

you have to buy 95% of the number combinations for the mega millions.

google says there are 302 million number combinations. 302M X .95 = the number of tickets needed to be bought... each with a unique number.

so you need to a millionaire to buy a 95% chance!

[matt819]

3. No, you need to be a billionaire

But think about it. A multi-billionaire could game the system by spending $302 million - a $1 ticket for every possible combination - to win $1.6 billion. Or, technically, with the purchase, at least $1.9 billion. A win would cover the ticket costs and still net a profit, even after taxes.

The only obstacle, and admittedly not a small one, would be the actual purchase of the tickets.

[jberryhill]

8. Yes, there have been mass lottery ticket buying operations

I'm not going to jump into any of the really dumb discussions held here on the topic recently. Suffice it to say, there are conditions in PROGRESSIVE wagering games (i.e. where unclaimed winnings go back into the pool), which can be certain slot or lottery games, under which the EXPECTATION VALUE EXCEEDS UNITY.

The problem is that the variance is high. However, where the expectation value exceeds unity in a progressive game then, yes, it is rational to attempt to corner the market (but not in games where one splits with duplicates).



https://www.nytimes.com/1992/02/25/us/group-invests-5-million-to-hedge-bets-in-lottery.html


In Virginia this month, one investment group came tantalizingly close to cornering the market on all possible combinations of six numbers from 1 to 44. State lottery officials say that the group bought tickets for 5 million of a possible 7 million combinations, at $1 each, in a lottery with a $27 million jackpot. Only a lack of time prevented the group from buying tickets for the remaining 2 million combinations.

[California_Republic]

15. I would think to ensure a win

I would think to ensure a winYou would need to be spending more than you would win

[JI7]

22. other people could win also in which case the prize would be split

and they could end up losing far more.

[Nitram]

17. Demovictory9, Can you designate more than one number per ticket?

If not, the number of tickets is indeed the question.

[zipplewrath]

19. Other people can win too.

The problem always is that other people can pick the winning numbers too. In Florida, the person who ran the lottery said once that her worst fear was that the numbers that made a "christmas tree" on the cards would be terrible. literally hundreds of people would have had to split the jackpot.

[Demovictory9]

25. oh you are right. have to include the probability of others picking each number

[Hoyt]

4. In a couple of large past lotteries, some investors tried to raise money

to play the “expected value” aspect. Don’t think it worked.

[jberryhill]

10. Yes

The problem is coordinating an army of smurfs to buy the tickets.

[HappyBeing]

5. Why buy a 95% chance

I mean if you could afford it, leaving that 5% chance of losing is unnecessarily risky, right?

[Moostache]

6. I am doing the following:

1) Buying 1 quick pick ticket
2) Taking those exact same numbers and buying a second ticket with the same numbers

Why?

Because there is a 1 in 300,000,000 chance of getting the right numbers...in a jackpot like the one we will see tomorrow, there is a MUCH greater chance of a split prize pool. You almost never see a single winner on something generating this level of sales in a lotto...could happen of course, but a lot more likely than 1 in 300,000,000 to have multiple winning tickets!!!

Buying a second random ticket to get 2 in 300,000,000 chances is as wasteful as the first purchase (but doesn't really buy me twice the entertainment of just entering the drawing at all) so why bother with it?

But...if I do somehow get struck by lightning on a sunny day indoors, and I had to share the prize with multiple winners, I'm getting me a second bite at the apple! LOL! Now that would be entertaining to me!


(Fear not...the second share of the winnings would be funding local GOTV and Voter registration drives in Red States! Or I would be the new Soros...LOL...who wants to get paid to protest? )

[CrispyQ]

14. An interesting take.

I might follow suit. If I win, I'll PM you & share.

[WeekiWater]

7. Very unsavory risk. Not worth taking for anyone.

That is your mathematical equation.

[berni_mccoy]

9. This was actually done once

https://www.nytimes.com/1992/02/25/us/group-invests-5-million-to-hedge-bets-in-lottery.html

I was there when this happened.

The group had workers at every Lottery reseller in the state buying tickets around the clock. They could only buy 5 million out of the 7 million tickets to win $27 million dollars.

Lucky for them, they did win.

This would be absolutely impossible to physically accomplish today.

[trc]

11. the price per ticket for this mega lottery is actually $2, not $1

so the cost doubles

[Ms. Toad]

12. First,

recognize that the price of the ticket is completely irrelevant to the question you asked. "How many" is the same, regardless of whether they are $1, or $100 per ticket.

The 3rd and 4th are also irrelevant - the only thing that determines the number of tickets you would need to buy are the odds.

The only information you need is the odds - 1:302,575,350, which tells you there are 258,890,850 unique combinations.

To have a 95% chance of winning, you would need to purchase 95% of those combinations, i.e. 287,446,582.5. Since you can't buy a half of a ticket, you'd need to buy 2287,446,583 unique tickets.

[Wounded Bear]

13. A chance? Or a guarantee?

To guarantee 95% probablility of winning would require buying 95% of all tickets sold.

Still wouldn't guaratee that you win ("probability" is not "certainty" ), but mathematically, that's what you would have to do.

[MineralMan]

16. A sucker's bet. You could buy up all the possible combinations, but then

you'd run the risk of one or more other tickets also having the right combination. If that happened, you'd not break even. The problem is that multiple people can have all the matching numbers on their ticket, just by chance.

[LakeSuperiorView]

23. But then that is placing a definition on "winning" that was not stipulated.

Does "winning" mean capturing the jackpot all to oneself? Or does it mean capturing all the prizes to oneself? Or does it mean capturing any prize at all?

Without a definition of what "winning" means, there is no one answer to this problem.

[Yavin4]

20. Wow, you're a little hostile

What's wrong with you today?

[Totally Tunsie]

21. I'm so "lucky" I could have a 99.99999% chance of winning, and still lose!

[SMC22307]

24. I had $14 in my wallet so I bought seven tickets.

I'm the last of the big spenders! And I have no idea what my odds are - slim to none?

[cloudbase]

26. 50-50.

You'll either win, or you won't.

[kwassa]

29. There are 3 kinds of people in the world.

Those that are good at math, and those that aren't.

[SMC22307]

31. Ha, that's how I look at it.

And $14 is about what I spend on a Jersey Mike's sub, chips and soda, so why not?

[Yavin4]

28. 7/300,000,000

[bluedigger]

27. I don't know but I bought one for each of the big ones today.

I need to double. Got a couple bills.

[NCjack]

30. I think that

1. If I buy ten tickets, I have sufficient resources that I will never feel the loss of that cost. And, within several weeks, I will not dwell on the thought that I spent that money and lost.
2. If I win, WOW! I will think forever that of the 10, I gave away 9, and one of those nine won, then yes it matters if you buy one or buy ten tickets for yourself.

I told my wife that some very knowledgeable people stated that buying just one ticket has the same probability of winning as buying ten. She said that she agrees and suggests that I buy only one for myself and 9 for her. I'm mouse-trapped now. If I buy her only one and she loses, she will say that she lost because her winning numbers were on one of the eight that I failed to buy for her. So, I'm buying 10 and letting her select nine for herself.

[McCamy Taylor]

32. Ninety five percent of all tickets sold.

Assuming that someone will be the winner. And if the lottery is fixed as they so often are you could still lose. Your best chance to win a lottery is to be the brother-law of the neighbor the the guy who writes the software.