With the Mega Millions jackpot drawing lots of attention, I have to ask, do you play it? I love gambling and trying to beat the odds, but I draw the line at the lottery. So much is raked off, and the rest is put into the big money payoff, its a hideous bet. If you get three numbers right for e.g. you win $5, but your chances of doing that are 766-1. That's obscene.

Anyway, the topic came up at the poker table today, and I sensed that most of the players were gonna plunk down $2 or $20 or whatever on the Mega Millions. The odds of winning the big jackpot are roughly 259 million to one. I said you could reduce your odds to a million to one by buying 259 tickets. Only one guy at the table agreed....the rest either insisted your odds don't change, or they just kept staring blankly into space. I'm no math whiz, but that seems pretty basic to me. I think I've been giving my fellow players way too much credit.

I'm not going to explain expected value (EV) to you, but at a certain point, a jackpot-based game like Mega Millions can become a good bet. (Hell, even a progressive slot machine can become a good bet.) It has certainly passed that point with the jackpot where it is, even considering the cost of taxes and of taking the cash option.

The downside to playing isn't that "So much is raked off" or that the odds against such-and-such are "obscene." It's that, unless you're buying an unrealistic number of tickets, it's an exercise in extreme variance, even if the jackpot amount makes it a +EV bet. The lesser prizes are –EV on their own. Hitting the jackpot, which is the payout that tilts it to +EV, is such a longshot that there is no "long run" in the lifetime of any human player.

To minimize the amount I lose, I generally only play when the jackpots are $200 million and higher.

If I win Mega Millions, I am going to see about renting a few Congressmen.

I'm not certain that it has passed that point when you consider that big jackpots draw a lot of players and this increases the chances of a shared jackpot.

In any event I put some money in with my parents to buy tickets whenever the jackpot gets insanely huge ..... It doesn't matter that its negative EV. The $10 I spend will make no difference in my life so I don't feel the pain of any loss. But if we win a huge jackpot it would be a life changing event.

(BTW I tell people if I win I won't quit my job, but I'll definitely have a different attitude at work)

I did the math on Powerball a while back, and you'd be surprised at what point the jackpot exceeds the profitability threshold when you account for the lesser prizes. Mega Millions has a similar prize structure to Powerball, and right now the jackpot alone is more than twice the odds against. I'm not up for doing the math at the moment, but even considering the possibility of a split jackpot, I'd contend that it's +EV. Marginally so after expenses, and with extreme variance compared to the EV per bet, but still +EV.

If I were to win, I'd wrap up my current project, but then I'd absolutely quit my job. I work from home, so it would hardly make a difference as appearances are concerned. And I would go out of my way to keep people from knowing that I won the lottery.

it may be more than twice the odds against, but shouldn't we be considering taxes at the minimum? well in this case i think it's worth it anyway since the jackpot is f'ing huuuuge.

I'm considering taxes and taking the cash option—$341M at the moment—rather than the annuity option. (I'd never take the annuity, but more importantly, inflation, future tax rates, and the possibility of dying prematurely make it impossible to realistically calculate EV for the annuity.)

Assuming a 30% tax rate, that's $341M(0.7) = $238.7M net. Someone please correct me if that tax rate is off of the true federal rate. I live in a state with no local gambling or income taxes, so that wouldn't apply in my case.

That makes a jackpot-only bet about –$0.078 on its own. There's no way that the lesser prizes don't bump it more than that tiny margin into +EV territory.

Personally, I'd prefer an equal EV bet against a smaller jackpot with shorter odds. The absolute size of the jackpot stops mattering much after it passes the point of making me obscenely rich, say the tens of millions.

EV is irrelevant because of two reasons:

1. You will never play the lottery enough so that your results will approach EV.

2. EV assumes all dollars are created equal - they are not. You want EU, expected utility. Utility takes a big jump above amounts you can reasonably earn at a job. If you make $1,000,000 a year with a potential $5,000,000 bonus, the prospect of spending $1 for a shot at $10,000,000 is silly. But if you're making $10,000 a year, the lottery is the only way you'd ever have more than six figures.

I lean that way as well. I do the EV calculations on big jackpots all the time and they are occasionally +EV if you assume only one winner. The issue is you will probably never play enough tickets to realize this value. Take out the single winner assumption and I think its reasonable that none of the MM or PB jackpots have ever been +EV. People have done calculations on the increased chances of multiple winners, but I haven't gotten into that.

Taxes are an interesting issue. I argue that they shouldn't be included since you can deduct losses from your winnings. Imagine you bought all ~259M combinations for ~$259M. You win ~$341M and can deduct ~$259M and pay taxes on the rest. This is for argument only as I believe there are rules against buying a large number of tickets.

Assuming one winner and $341.2M jackpot, I get an EV of $1.49 per ticket.

Another thing to consider is that even if it is a bad bet, the money spent on lottery tickets is usually small, but a jackpot could change your (short) life. You also get some entertainment value out of it.

Sure, that's why it's not worth bothering about. If you do play, know that it's a super-longshot and that you may as well go out bounty-hunting for hen's teeth.

I haven't put much time or energy into expected utility. However, your example is leaving something to be desired. It feels like you're justifying a poor person wasting a much larger portion of his income to win a nearly unattainable prize. I get that the prize is life-changing for the $10K guy, but the dollar he's risking is much more meaningful than it is for the millionaire as well. The meaningfulness of the risk and the prize are still in the same proportions. Am I making sense?

Are people really entertained by the lottery? I rarely play, but when I do, it's about as entertaining as cross-checking numbers in a spreadsheet.

With a jackpot this big, you can make a +EV argument if you like. But really my point is that lotteries in general are such a scam. The marketing is particularly effective with the poor and the stupid, the folks who are least able to afford it. It sells the lottery dream to them, and they fall for it, over and over...never beginning to understand what a horrible bet it is. Its kind of tragic.

That said, I see no harm for those who can afford it, to buy lottery tickets. But I hope they do so, knowing that its an incredibly bad bet, and if they're going to gamble, they'd have a much better chance of winning with poker, black jack or virtually any other game other than the lottery.

That's a side effect of the fact that marketing of any kind is particularly effective with the poor and the stupid.

If your goal is to turn $1 onto $600,000,000 I think the lottery is your best bet.

Good point. Like if you owe a certain Russian gangster exactly $150,000,000, but your law professor can only give you $100,000,000, definitely dump that $100,000,000 on Mega Millions tickets.

Then, when you win the jackpot, put the $100,000,000 for your law professor in an envelope and hand it to your bitter ex-girlfriend, with no witnesses.

Good point. Like if you owe a certain Russian gangster exactly $150,000,000, but your law professor can only give you $100,000,000, definitely dump that $100,000,000 on Mega Millions tickets.

Then, when you win the jackpot, put the $100,000,000 to pay back your law professor in an envelope and hand it to your bitter ex-girlfriend.

Winner.

I see what you did there.

My parents are comfortable and very financially stable but my dad has played the lottery fairly regularly my whole life. When I was you like 7 I would check the numbers online for him. Anyways the other day he said he works too hard to gamble it away at a casino. And all I thought about was the lottery he's spent countless dollars on over the years. Atleast I get entertainment out of a casino. To each their own
Sent from my SAMSUNG-SGH-I747 using 2+2 Forums

The mitigating factor in a draw lottery is that it only gets drawn a couple times a week (or once or twice daily for some smaller-scale lotteries). It's a waste of money, to be sure, but it doesn't have the same potential for rapid-fire abuse as a casino. An addicted gambler who is only tempted to buy a Mega Millions ticket for each drawing could easily blow decades worth of lottery plays in a single sitting at a casino.

It's still kinda silly pseudo-logic, but it does keep him out of trouble. Sometimes that's the most you can reasonably expect.

I throw $20 at it every once in a while. I won't even notice the money gone and if I ever win anything big, yay for me, if not its only $20, I've done waaaaaaay dumber things with $20. Looking at the lottery in terms of EV is crazy IMO.

"Entertainment" in this context is not literally purchasing the ticket or watching the numbers roll out — it's the fantasy of winning. It is a large part of the value for me and many others. We're not bothered to crunch EV and utility over such a long shot.

I suppose I do get some enjoyment out of calculating the EV, now that you mention it. And musing with people about "What would you do with $500 million?" can be kinda fun.

Okay, I guess you got me there.

That wasn't a dig on you. I was explaining how the entertainment portion trumps all other relative values (by downplaying the significance of those values).

Right right, but my original post along these lines had the subtext that there's no way people really enjoy it, and that they're just gambling as a sort of compulsion. That's all I meant by "you got me."

(Not that the compulsion angle isn't true for untold numbers of people, of course.)

39.6%