The Case for Buying a Powerball Ticket | Hacker News Reader

The Case for Buying a Powerball Ticket

nytimes.com

13 pointskhc27 comments

I hate the argument that, on the grounds that the aggregate money spent on lottery tickets is typically larger than the aggregate money paid out on lottery tickets, purchasing a lottery ticket is inherently irrational.

The same is true of insurance, yet few people consider the purchase of insurance to be intrinsically irrational by the same argument.

People are free to have whatever preferences they want. Some people prefer a life with a slim possibility of a tremendous windfall (and but a negligible loss in the more likely alternative) to a life of certain continuation with the status quo grind. More power to them.

> The same is true of insurance, yet few people consider the purchase of insurance to be intrinsically irrational by the same argument.

The offsetting argument for insurance is that it provides risk management against unaffordable, catastrophic expenditures -- it is a trade-off of a certain expenses, against the risk of a much larger uncertain expense, with an expected net cost in financial terms, but that it is rational in some cases given the decreasing marginal utility of net income (which, conversely, means that there is an increasing marginal cost of high expenses.)

Of course, the trade-off in the lottery is you are paying a certain, low cost for a chance at unlikely larger payoff -- this has not only a negative expected financial value, but -- given the declining marginal utility of income -- an even larger expected negative utility in most cases, considering utility of money on its own.

Of course, it may be rational if the utility provided to a particular player by "playing the lottery" (the entertainment value, etc.) exceeds the expected net disutility associated with financial expectations.

If some people do, in fact, prefer situations in which there is a slim chance of tremendous windfall and large chance of small loss to guaranteed status quo, who is the economist to tell them "No, no, this is incompatible with the theory of diminishing marginal vNM-utility. Your preferences are misguided!".

Utility is just a construct for describing people's preferences; to turn around and demand that people's preferences ought change to match some textbook model of utility is to put the cart before the horse.

People can reasonably have all kinds of different personal preferences, right? If your theory doesn't account for that, that may not be an example of muddled thinking on your subjects' part; it could just as well be a problem with your theory. I mean, what is actually factually misinformed about preferring the risk profile afforded by a lottery ticket to the alternative?

Because it's hard to imagine that anyone actually has a increasing marginal utility of money. If they did, over wide enough of a range, they'd bet their entire life savings on the Powerball.

What's much more likely is that they're getting some entertainment out of playing the lottery, or they're poor calculators of risk and reward.

I don't have to imagine that anyone prefers occasionally playing the lottery to never playing the lottery. I can see it in action any time I please, and while some of the people doing so may be laboring under delusions as to the quantities involved, I see no reason to conclude that all are. (I will proffer myself as an example.)

A person might well prefer the risk profile resulting from occasionally playing the lottery (small chance of tremendous gain, large chance of minor loss) to both the risk profile resulting from never playing the lottery (guarantee of no gain or loss) and the risk profile resulting from betting their entire life savings on Powerball (large chance of catastrophic loss, small chance of tremendous gain); these are all different risk profiles, so they can all perfectly well be valued arbitrarily differently.

[And I do mean arbitrarily differently. What rule of rationality demands that anyone who might want to play the lottery from time to time for the risk profile it produces ought further prefer to bet their entire life savings on the lottery? Whoever claims that to be a rule of rationality, I say they're the irrational one.]

Whether you would describe someone with such preferences as having "increasing utility of money" or not is up to you. But I see nothing problematic in having and acting on such preferences.

The same logic can't really apply to insurance - one is an investment with expected return, the other is risk mitigation.

You are happy with insurance because you see it as reasonable to prefer the risk profile it offers over that of forgoing it. But one might just as well also prefer the risk profile offered by a lottery ticket over that of forgoing it. Why not prefer a slim chance of a tremendous windfall and large chance of negligible loss to a guaranteed status quo? People can prefer whatever they want.

There is a fundamental rationality to insurance that is not present with the lottery if you accept the marginal utility of money to an individual. Your top dollar is worth less to your than your bottom one. So it is worth sacrificing the first to safeguard the second.

> Yet few people consider the purchase of insurance to be intrinsically irrational by the same argument.

I don't really know to many people who think this?

Skipping some small attempts at loopholes for insurance ($300,000 of medical might return infinite benefit to oneself), yes it's stupid. Most intelligent people know this.

Your argument goes all the way, want to spend 'all' your money on gambling (or insurance), more power to them? People can do as they wish, but I'm not big on perpetuating bad memes.

The opposing argument is pretty simple, by not creating a false happiness through gambling people might create real happiness.

By not waiting on that big win, people might work towards their happiness. IE save for that big trip and get something of long term value imagination could never give.

This article is trash. First he makes a dumb argument that comes down to, what's $2 in exchange for the warm fuzzies of imagining where you'll move with that money.

And then goes on to explain why now's the best time to waste your money if you like wasting your money because of the ridiculously obvious point that the jackpot is larger now.

This is abysmal garbage and the author should feel bad and so should everyone who upvoted this. I rarely ever get mad but the lottery is one of my biggest pet peeves, and this brings no insight or elaboration on the issue besides, "gee wouldn't it be great to instantly have millions of dollars."

There are a number of things you can spend a small amount of money on with ultimately nothing to show for it but some brief enjoyment. It seems the author is encouraging his (non-addict, non-destitute) audience to reframe their thinking about what the lottery provides as entertainment value rather than simply being 'a tax on people who are bad at math' - even if you don't ultimately play, you don't have to view those who do in a negative light.

That's certainly how I used to feel, but once I started thinking of it as a lark rather than a blight, it just didn't seem like that big of a deal.

Hasn't it been shown time and again that the act of thinking positively about your future often carries over in to your real life, making you happier in the present?

Besides, I could drop $100 on Blackjack in AC once a year or $2 every time the jackpot climbs above $500m. My (minuscule) appetite for gambling is satisfied in both situations, and I save $98/year :)

Buying one ticket is a much bigger benefit over buying none than buying two is over buying one.

Buying one ticket does seem reasonable to me (even with excellent math skills). Buying two is just silly.

"It’s actually more complicated than that, because that calculation doesn’t account for the fact that there could be multiple jackpot winners who must split the pot."

In other articles, it's been said that when the jackpot is high, the expected value actually goes down due to the increased chances of multiple winners.

I don't think there's anything wrong with buying a lottery ticket if its cost is a trifle for you.

Buying one when the expected value is positive is not a sound gamble however. Suppose there is a jackpot of $300M and you have a 1 in 150 million chance to win. It's obvious that you have an edge, so you calculate how large part of your bankroll you should bet with the Kelly criterion[1] and get: f=3.33e-9

Oh well, if you are a centimillionare you can buy a ticket and be rational.

[1]http://en.wikipedia.org/wiki/Kelly_criterion

You need to factor in ticket price, odds of winning, cash payout, taxes. Powerball is $2 a ticket. The cash payout is around $338 million. The odds of winning with a ticket is about 1 in 175. Assume taxes will take half. You shouldn't buy a powerball ticket using reason unless the cash payout is at least $700 million. Problem then is so many people are playing there's likely more than one winning ticket which would mean the numbers don't work.

Edit: the payout tonight is $338m

I assumed a $1 ticket in the example. The point is that even if the expected value is high, buying a ticket means that you are likely overbetting by several orders of magnitude.

Yes. And even if you get to pot odds or better after taxes and decide to spend $20 (10 tickets), $200 (100 tix), or even $2000 (1000 tix) because you're at pot odds... 1 in 17.5 mil, 1 in 1.75 mil, even 1 in 175,000 are still very long odds. So, you can't win and dream if you don't play but if you play buy just one ticket. Buy it more for the fantasy you get to play in your dreams at night in your head, because that's most likely the greatest payout you'll get. $1 or $2 for a bottled drink or for some sweet dreams... Your choice, both are okay choices in my mind.

Edit: typos.

Chinjut's multiple posts here have argued much more eloquently than I can about "utility" or what is "rational" to different people. Here's my simple way of explaining why I will buy a ticket tomorrow if the prize isn't won tonight:

If, for a $1 bet, you offer people a 1/2 chance of winning $2, most people won't bother. However, if you offer those same people a 1/1000000 chance of winning $1000000, many more people would become interested.

Winning $2 isn't meaningful to most people. But a chance of winning a sufficiently large amount of money that they could significantly change their lifestyle is a much more "rational" decision for them to make. And that, in a nutshell, is why lotteries exist at all.

I do love the idea of the Kelly criterion, and I do try to keep it in mind when investing. Unfortunately my "edge" in most investment situations so small that I shouldn't be betting, err I mean "investing" anything!

The Kelly criterion is a way of choosing a number to bet from the set of rational numbers between 0 and your bankroll (inclusive). However, this isn't the set you're choosing from when playing the Powerball. You're rightly accounting for this. However, you're accounting for this incorrectly by adjusting the size of the bankroll ("Oh well, if you are a centimillionare you can buy a ticket and be rational."). Your bankroll is fixed. The correct adjustment is to change the set of values from which the fraction of the bankroll can be chosen.

The optimal bet for a +EV bet is always positive when the set of possible bets includes positive numbers, because a zero bet has effectively a zero EV. My intuition is that you want the number in the set of possible bets that is closest to the Kelly Criterion number when weighted along some curve (I'm too lazy to calculate which curve on my mobile device). If this is correct (I haven't proved my "closest on a curve" idea) then the optimal bet is to buy a $2 Powerball ticket (the smallest positive bet).

That said both these ideas assume an infinite number of future bets following the same strategy, with no other games to play. If you play the Powerball every time the EV is positive, this is like an investment that will yield a return, on average, long after you are dead. And there are alternate games (the stock market, education, job searching) which yield more consistently and possibly with a higher EV.

Finally, the goal isn't to maximize your bankroll. I just spent the cost of a Powerball ticket on a coffee, which has a -EV, and I couldn't be happier with my decision.

We all know that there are negatives to winning the lottery or getting rich. One big drawback would be never being able to make new ("poor") friends without knowing if they were true friends or only friends because of your wealth.

I can certainly see "rolling the dice" on a life changing outcome if you had nothing to lose because you were miserable. I think it make less sense if you are happy. Am I the only one who is so happy that I wouldn't take a chance on wrecking my life?

The lottery is a tax on people with bad math skills.

You don't have to have bad math skills to play the lottery. For example, I am a mathematician who has on occasion chosen to purchase lottery tickets. And I see nothing at all irrational about this.

I used to buy one powerball ticket a week. About ten guys at work would pool together and buy ten tickets on the pretense of splitting it if we won.

We saw it pretty much exactly the way the article described. There'd almost always be an hour or two talking about what would be an interesting use of that much money, or talking about how stupid we were for playing the lottery, and it'd come back up over the work day.

We were paying for group amusement, and I still remember having a lot of fun with those conversations. I don't regret it any more than I regret spending money on a soda here or there during the same time period (long term health wise I regret the soda way more :) ).

Oh, I'm not above buying the occasional ticket, either -- for that matter, I like playing Blackjack and view any losses incurred as entertainment.

However, people at the lower end of the income spend a lot more of their money (proportionally) on lottery tickets. [1]

And states are increasingly dependent on those revenues [2], which means in effect we've got a system where our schools become dependent on our lowest income population wasting money on what is essentially a pipe dream.

Note: I'm not saying "we've got to stop lotteries!" As I said: I play myself. Just noting that we are funding our government on the backs of people who are making what is arguably a terrible investment.

In other words: lotteries are a tax on people with bad math skills.

[1] Lots of studies back that up; there's a pretty good list here: http://stoppredatorygambling.org/blog/category/research-cent...

[2] http://taxfoundation.org/article/gambling-tax-policy-states-...

Former Math Professor wins lottery 4 times

http://www.forbes.com/sites/kiriblakeley/2011/07/21/meet-the...

That is a fascinating story. I hope she writes a memoir some day.

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