Lotteries are a tax on the ignorant, but ...

So I would be justified in spending $500,000 on lottery tickets then right?

@lurker 

Perhaps. That would be 250,000 tickets, all different, and would make your odds of winning equal to 250,000/302,575,350, or 0.00082624. The expected value of your winnings would be $516,648. 

That just says that a really big number multiplied by a really small number can result in a big number relative to the units employed.

To have a 50-50 chance of winning, you would have to buy 151,287,675 tickets, all different, spending (investing?) $302,575,350. The expected value of winnings would be 0.5*625,300,000 = $312,650,000.

Every dollar spent on a lottery ticket is almost certainly, but not absolutely positivelu certainly, to be a dollar thrown away. A $500,000 ticket purchase has more than a 99% chance of being thrown away. A $302 million, give or take, has a 50% chance of being thrown away.

But, sooner or later, someone is going to buy a winner and if you don't buy a ticket, it absolutely positively certainly won't be you.

$500,000? No. $2? Why not?

@mathteacher In order to achieve those odds you would have to manually select unique numbers. That's a crap-ton of old lady bubble sheets.  Lol

So I would be justified in spending $500,000 on lottery tickets then right?

If you did, and played the same numbers on all your tickets, and one other person played the same set of numbers on one ticket, and you both won the drawing, then that means you would keep the vast majority of the jackpot, and the other guy would get diddly-squat compared to you.

@thebionicman 

Sometimes there is a sure thing that requires work,but less work than we might think.

https://nypost.com/2022/06/16/jerry-and-marge-go-large-retirees-made-millions-gamin-lottery/

I wouldn't call it a sure thing, because they didn't always come out ahead. But they did find a situation with vastly better odds than the typical lottery.

Expected (average) value of a ticket is nice, but if you aren't buying all the tickets you may not get that average in a lifetime.

Good probability of a net payoff over a moderate number of plays is required for a workable schem. A key for those folks won was the large number of (smaller) payouts.

Your math is based on the jackpot being the only possible prize. I'm not a loto player, but I do believe that there are many lesser prizes. These would significantly affect the value calculations.  

@norman-oklahoma 

Indeed, those prizes enhance the value of the ticket.  But it's rare that a ticket is undervalued based on the top prize alone.

@bill93 

Yes. These folks just found a situation where the tickets were significantly underpriced. Then they bought enough tickets to improve their odds to the point where they couldn't lose.

There are other similar cases where lotteries pooled unwon money in a biased way. It pays to stay alert, but alert is not one of my characteristics.

My biggest win on the California Super Lotto was a QuickPick, a set of numbers picked by the computer ($2314).

I've always wondered why someone with cash or leverage doesn't just spend $302,575,350.00 on something like that.  Buy every combination.  Even with $625 lump sum (plus all the minor winnings) you'd still end up collecting >$375M  after taxes.  The only risk really would be splitting it with another winner, which is very low odds.

@dave-o 

I think it's the logistics. NC allows internet purchases, but you have to use a debit card to pay. There may be a dollar limit on purchases as well, but if there's not, then someone with a big bank account and an even bigger computer could conceivably pull it off.

I bought one $2 ticket for Monday's drawing and matched one number, not the magic one whatever it's called. The probability that you will match no numbers is almost 1.

But, longshots do sometimes come in ....

I play $1 every day on the California Fantasy 5 game. Been doing it so long with the same numbers I am afraid to stop. I have never hit 5 numbers, but have hit 4 quite a few times, which pays around $400 +/-. Three numbers pays about $12-15, which I have hit many, many times.

On the rare occasions where I have played when a lotto pot gets really big, I will pick a set of numbers and play them multiple times, like 5 if the buy-in is $1/ticket. Buying 5 different sets increases your odds very little, but if my numbers do come up and I have to share the top prize, I will get the majority of the total prize.

I had an uncle who used to frequent the dog tracks in New England and bet within his financial means.  On one trifecta race win he won enough to pay off his mortgage and retire. I sometimes go to casinos and wager on different games, sometimes I win decently but more often donate.  Millions wager on professional sports and college games in hopes of winning, I have won more than I've wagered in the past but don't wager on sports often and I usually bet the underdog team.  The lottery is no different, when you hit it big (not that I have ever hit more than a few hundred at a time), most times you are donating.  The moral of the story is that, you can't win if you don't play.

I'm not spending $2 of my hard earned money on some stupid lottery at 1 billion, I'm waiting until it's 2 billion. 

@flga-2-2 

Odds are that it won't get to $2 billion, but odds were that it wouldn't get to $1.5 billion either.

With random processes, there is no such thing as a strategy. Bet the month and day of your birthday, month and day of your wife's birthday (it had better be your wife's if you win), the year one of you was born and the year the other was born. Put them where you want.

Or just let the computer pick your number..It's stupid to play, but. then, it's stupid not to.

I heard the Polish lottery jackpot of $2 million pays $2 a year for a million years.

@mathteacher 

I'm pretty sure I posted this story once before I was in Elko Nevada doing some geophysical survey work for the mining companies and I'd go out and I'd play roulette just for fun and take 25 or 50 bucks depending on how much I felt like losing that night for the entertainment night.

one night I was actually up almost $600 and was tipping out the dealer is pretty heavily like 10 15 $20 every so often they kept rotating the dealers at once I lost 200 bucks I just walked away.

the whole time though when I was tipping out I was tipping out casino money cuz until you take it off the table and it's still in the casino.

not the same night but the same casino I sat there playing roulette one night with my $50 bunch and saw some guy come by for $25 down on black 35 I think it is it gets nothing.

so in the meantime he walks away some other guys come in and they spread their coins around and all those little tricks that they come up with crosses and double stacks crossing things so they can get on things and that six different directions wasting all their money.

17 comes up winner , one guy  goes nuts.  he's on 16.

cowboys are plunked down a $25 chip on 35 comes back punch another chip down spin no winner.

now for the next six pins every single time 17 comes up.

I didn't bet on it once and then in 9 spins seventeen had come up seven times.

the chance to see that in my lifetime ever again is zero.

ccowboy walks up after about another hour goes by puts $25 on 35 spins and wins. 35 to one pay out, $875

800 profit.

I'm buying a ticket.

@jitterboogie 

The best statistics professor I ever had chain smoked through every lecture and taught from both top down and bottom up so there was no way that everyone didn't understand.

He preached that, if you go to Vegas, whatever money you brought for gambling should be bet all at once on either red or black at the roulette wheel. If you win, take the cash and walk away. If you lose, enjoy the rest of your stay. His reasoning was this:

1) The odds are against you, so the longer you play the greater the chance that you will leave empty handed.

2) Roulette is the closest to being fair (probability of red = probability of black = 0.4734 on an American wheel) so that's where you place your stash. 

I wonder what ever happened to him.