Does buying a Mega Millions ticket for a chance for $1.6 billion make any logical sense?

Well, what were the odds of my first cousin winning a 90 million Powerball? In fact, what were the odds of me even being born? I say it’s worth the risk.

No; it’s not logical to me. I want to be guaranteed I’ll get something when I spend my money. Besides; that kind of windfall destroys families. And probably, marriages.

Yes, because one has a chance to win it, and it only costs $2.
When I buy lottery tickets, I always feel like I have a fifty-fifty chance; either I win it, or I don’t.

The cost/benefit opportunity is huge. Even if the chances are tiny.

So let’s say I spent $10 for tickets. Chances are I won’t win 1.6 billion. But if I do, my ROI is huge. Well worth the gamble.

1.6 billion dollars from $2 tickets means 800 million tickets to cover the cost. Did they really sell that many? If not, the odds are in your favor. Even if so, I am very risk averse and avoid lotteries.

As a gamer, I have been conditioned to expect my results to be based on skill, not mere probability. So, no, it makes no sense to me.
Really, it only makes sense to try and cheat or manipulate the game in your favour.

I’ve never thought it worth it and don’t buy lottery tickets.

My cousin had never bought a lottery ticket either. She wouldn’t have bought one that day, but the clerk suggested it and she just shrugged and said, “Why not?”

You can’t win if you don’t play.

You also can not lose, either.

$2 is nothing, but once it won my husband $30k. So that day it was worth quite a bit more to us. So yes, it’s logical that any human willing to part with $2 for the hope/ chance of winning, does so.

Your odds of finding a winning ticket on the street are almost the same as buying a winning ticket.

But for entertainment I think it’s worth $2. I buy three or four lottery tickets a year. I typically wait months to look up the results. Then for for months enjoy maybe having a winning ticket. When I look up the numbers, all the value is instantly gone.

The odds of winning is roughly 1 in 259 million. The payoff is 1.6 billion, or 2.5 times the amount if paid at fair odds.

That in itself is worth buying a ticket.

Responding to zenvelo on this: First, thanks for the response. And, you’re correct to the extent that there is no denying that the betting odds are favorable; and this is because the jackpot this time has happened to have rolled over enough times to make the betting odds favorable. However, I would have to point out that the favorable betting odds, themselves, are not all there is to logically consider in this case. Betting odds work for you if you bet many times compared to the number of possible outcomes. For example, if you knew that a crooked die were fixed such that ‘six’ side really came up, on average, once every five rolls of the die, instead of once every six rolls, then it would make sense, if someone agreed to pay you 6 to 1 if you got a ‘six’—and to keep playing with you time after time—because then you could play over and over—say 100 times if necessary—betting on ‘six’ to come up more than it normally would, and you would make money. But you can’t play play this lottery even 259 million times—let alone, the comparable (to the die roll case you might need) of 25,900.000,000 times (100×259 million) to be sure to come out a winner over time, as it would cost you $51,800,000,000 (at $2 a ticket) to be reasonably sure the favorable odds would kick in. So, in this question, I am really looking for another logical reason—perhaps some existential logical reason—why playing this time would make purely logical sense.

There is (or used to be) at least one investment group that said it was waiting for such situations and then would try to massively buy in to lotteries with positive odds rates, though I never checked to see if these were legal and actual or just scams. If legal, it could make sense in theory but would be very high risk.

It doesn’t have to make sense, logical or otherwise, it’s just a gamble.
No point in overanalysing it, you pay your money & take your chance regardless of the odds.
Oh & i’ve never placed money on any lottery but bet on sports, the trick is, of course, to spend only enough money that you can safely do without, disposable means fun.

I’m afraid, though, that that’s just an unbreakable lifetime habit of mine: analyzing everything, over and over. (It keeps me off the streets, anyway.) :)

Of course there’s no sensible excuse for buying a lottery ticket—ever!

@stanleybmanly Same with smoking and drinking alcohol, yet how much money is spent on both? At least you have a slight chance of a positive outcome with lottery.

No logic, but it’s fun. But don’t buy more than one.

Sure it does. But buying 5 tickets improves your odds, buying more than 5, not so much IMO.
Not buying a ticket gives you 0 chances! And somebody has to win sometime, so BUY THE TICKET!!!
And good luck!

From a purely logical perspective, lotteries are nothing more than a tax on people who can’t do math. But as several jellies have pointed out, there’s more to life than logic.

Even Vulcans experience pon farr.

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$2 is cheap entertainment.

Well, actually, there is “a” logical reason to buy a lottery ticket whose payout divided by odds of winning it is greater than the cost (which is the literal question asked).

But not all logical reasons are good reasons, nor do they necessarily lack logical reasons not to, as well.

Also, since many more people will try to win such a jackpot, that tends to increase the odds of having to share the jackpot, which would reduce the payoff, and I don’t think you can generally know how many people have bought tickets (though if you could, you could do the calculus to compute it, but still, it will be either hugely unlikely or require a massive investment at risk).

You’re kind of just buying the dream of being wealthy, with such lottos. When you have a chance, you can imagine how it would be to be so rich. It’s fun to fantasize about.

Plus. Someone, or more likely multiple people, will eventually win it.

Yes. I would buy a ticket to see how high the jackpot can grow. I have bought a lotto max Canadian lotto ticket that tops off at $60 million for next Friday.

@Zaku When someone asks for logical reasons, they are asking for good logical reasons. This is particularly true when they are asking if a question makes logical sense. All other interpretations are uncharitable.

I bought 5 chances. Obviously did not hit.

But it was fun going to Starbucks the next morning, sitting down with my coffee and the paper and comparing my numbers with the drawing.

I was absolutely fucking certain I had winners. Oh well…

Logical? No. Kind of fun to dream? Yes.

OP, “existential logical reason” is not a thing. What’s at issue is not logic but rationality. If your goal is to simply to maximize your money over time, then, other things being equal, it is rational to place bets when the payoff exceeds the odds, as zenvelo said. But most people’s goals are not that simple, and other things are often not equal.

How will losing $2 (or $10, or $100) change your life? How would winning $1B (or some partial payout amount) change your life? How would either winning or losing affect your pursuit of other goals? Etc.

It doesn’t matter what amount the jackpot is, the odds of getting all the numbers is the same.

With so many people playing there might be more chances of more than one person winning, so then you have to split the winnings, but it’s so big so what.

It’s a lottery, not a raffle. A raffle each person who buys a ticket put their ticket in a “hat” and so the more people who play the lower your chances of winning. In the lottery, no matter how many people play the amount of numbers to pick from for the winning number are the same. Think about it.

The question is, if someone will buy a ticket for a billion dollar lotto, why not buy it for 6 million? It’s still life changing, and basically the same odds of winning. If I won $6million I would definitely feel like I never have to worry about money again.

The only logic I see is, if you don’t buy a ticket, you are guaranteed NOT to win, if you do, you either wll win or not, 50/50.

Thanks for all the responses. All interesting! And, yes, there can be good, valid reasons for buying the upcoming $1.6 billion Mega Millions ticket other than a purely logical one. But in this case I wanted to know if there were at least one reason that could be considered “purely logical”. So, ultimately, I did manage to come up with what I think would be a purely logical reason for buying a ticket. It is one, however, that would pertain only under very rare circumstances (but circumstances which I think could validly be termed “existential”—at least in one valid dictionary sense of the word). With the odds of winning all or much of today’s jackpot so incredibly remote that one would be far more likely to die today than to match all of the numbers (and even share the jackpot), the only “purely logical reason” I could come up with for risking even two dollars, would be if the circumstances were truly desperate! And the only such circumstance I could think of off hand was if for some reason one happened to need, almost right away, several hundreds of millions of dollars, just in order just to stay alive—or in order to save the life of someone else one cared about. For example, say there were a brand new medical procedure that could likely save your life, but one that was only just developed, not yet approved or on the market, and for which one would need that much money for the enormous costs and to get the developers to try it on oneself or on ones loved one. Since one is otherwise going to die anyway, then in that case bothering to bet against such incredibly high odds would be perfectly logical, as there would simply be no other chance of survival. (Just as an anecdote, I recall that Mr. Spock once replied, at the end of an episode of the original Star Trek series, that there having being almost no chance of their survival, his only logical recourse had been an act of desperation. Therefore, he asserted, he had been perfectly “logical” in acting in what others had claimed was an, uncharacteristically for him, illogical manner. And, it being Star Trek, this desperate act on his part had, against all the incredible odds, succeeded and saved the day!)

@YARNLADY And that’s why people say that lotteries are a tax on people who can’t do math. Just because there are only two possibilities doesn’t mean that the odds are 50/50.

@noitall The scenario you bring up is interesting, but I’m not sure it fits into the parameters of your own question. For one, it involves emotional value (we don’t continue living for purely logical reasons, after all). For another, it is no longer a case where the size of the potential payout is itself sufficient to make buying a ticket logical (as per the penultimate sentence of the OP). One might also think, however, that your scenario is no longer a genuine lottery situation. For all intents and purposes, the money is already lost (since you can’t take it with you if you die). So now the scenario has transformed into “is it rational to spend this money that you won’t be able to spend on anything else on something that may or may not extend your life?” That is clearly a much different question.

@SavoirFaire It seems you me it’s also uncharitable to let people persist in their phrasing of “is there a logical reason”, because I find that it often indicates people are thinking in a limited and inaccurate way, waiting for one logical reason and mistaking it for a good idea, and/or the other very common fallacy of stopping thinking about a question once one good-seeming perspective is found. It’s particularly true of probability questions, which this is a form of.

I’m often reminded of the smart, educated young colleague of mine who was waiting late for a ride, and I offered that he could get a ride home with us, and he responded that no, he was certain he could get a ride, because he remembered his probability math, and he had two others who might give him a ride, and 50% plus 50% equals and 100% chance he would get a ride…… and he wasn’t joking, and couldn’t be talked out of the idea. Fortunately, he was also only about a mile from home, so he could also walk.

In the case of this question, I wasn’t just meaning that there is a logical reason but it’s invalidated by other thinking. In this case, I do think it depends on your perspective and circumstances whether it makes sense for someone to buy one of those tickets or not.

Logically speaking…NO it doesn’t!!! Realistically speaking…it’s a great way to spend my day!!! It’s cheaper than a meal & gives me a few days of pleasant thoughts until reality smacks me in the face once again when I don’t win!!!

Every time my brother pisses off his wife, he buys her a lottery ticket & picks up a FREE real estate guide. She spends the next several hours looking at the mansions available in their area & dreams about how she can afford her preferred home when she wins the lottery. Bro gets some peace & quiet as long as she’s dreaming & the fight is over!!!

My Mom always told me that I had a snowball’s chance in hell of winning IF I bought a ticket to which I replied I have NO chance in hell of winning IF I don’t buy a ticket. I DON’T abuse the system & ted to play very responsibly!!!

I think the chances of winning any lottery is pretty astronomical….something like 1 in 259,000,000. Yet someone will win it. Or some ones. If you go at buying a ticket as a way to make your way through life, no it makes no sense. If you want to buy one on the off chance you will win, have at it. We are humans. Not everything we do makes sense. And we are certainly not a logical breed. I bought a couple tickets. Why? I guess my answer is…why not?

“Someone will win it!”

And someone did. In South Carolina.

shit.

^ times 2!!!

So the “Real” odds are your one chance in winning vs every other buyers chance of losing?

@Zaku “It seems you me it’s also uncharitable to let people persist in their phrasing of ‘is there a logical reason,’ because I find that it often indicates people are thinking in a limited and inaccurate way.”

The principle of charity has to do with how we interpret others. So while it is certainly legitimate to discourage limited ways of thinking, I don’t think that doing so falls under the purview of the principle of charity. I also don’t think it is helpful to fight bad rhetoric with more bad rhetoric (and uncharitable responses constitute bad rhetoric). Nevertheless, I take your point.

@YARNLADY “So the “Real” odds are your one chance in winning vs every other buyers chance of losing?”

Not quite. Your odds of winning are a ratio of favorable outcomes to unfavorable outcomes. So let’s say you are rolling a six-sided die and need a six to win. There is exactly one favorable outcome (you roll a six) and five unfavorable outcomes (you roll a one, a two, a three, a four, or a five). With one way to win and five ways to lose, your odds of winning are 1 to 5 (usually expressed as 1:5).

Now let’s look at the Mega Millions lottery. Assuming you only have one ticket, there is again exactly one favorable outcome. But there are 302,575,350 possible number combinations, 302,575,349 of which do not match your ticket. With one way to win and 302,575,349 ways to lose, your odds of winning are 1 to 302,575,349 (that is, 1:302,575,349).

Note that the odds of winning are closely related to, but not the same as, the chances of winning or the probability of winning. Unfortunately, these words are often used interchangeably despite meaning slightly different things. In the case of a six-sided die, for example, you have a 1 in 6 chance of rolling any particular number (for a probability of 16.67%). In the case of the Mega Millions lottery, any given ticket has a 1 in 302,575,350 chance of winning (for a probability of 0.000000003%).

^^^thank you, now I get it.

I did buy a powerball ticket and hit the first two numbers. I’ll admit to getting a little tickle in my stomach and a somewhat elevated heart rate. Worth $2 to break the monotony.