lottery-ticket buying: a rational purchase of fantasy
http://www.overcomingbias.com/2007/04/lo…
The classic criticism of the lottery is that the people who play are the ones who can least afford to lose; that the lottery is a sink of money, draining wealth from those who most need it. Some lottery advocates, and even some commentors on this blog, have tried to defend lottery-ticket buying as a rational purchase of fantasy – paying a dollar for a day’s worth of pleasant anticipation, imagining yourself as a millionaire.
But consider exactly what this implies. It would mean that you’re occupying your valuable brain with a fantasy whose real probability is nearly zero – a tiny line of likelihood which you, yourself, can do nothing to realize…
Seriously, why can’t we just say that buying lottery tickets is stupid? Human beings are stupid, from time to time – it shouldn’t be so surprising a hypothesis.
Unsurprisingly, the human brain doesn’t do 64-bit floating-point arithmetic
This seems sufficient to explain the popularity of lotteries. Why do so many arguers feel impelled to defend this classic form of self-destruction?
(a) I think that lottery ticket purchasing is stupid.
(b) I can defend it.
I think it’s stupid because, to my utility function, the cost far outweighs the benefit. I do not get any enjoyable fantasy about thinking that I might win a million dollars. I’d enjoy a million dollars falling from the sky, sure, but I take greater enjoyment from knowing that I’ve earned everything I have since college (my folks paid for half of that, I covered the rest). Heck, I’m scrupulous to the point that I’m still debating whether I should give my dad $2k for the beat up pickup truck with 97,000 that he gave me when I bought my house 11 years ago.
…but not everyone has my utility function, just as not everyone has my religion or my politics.
So: taken as given that some people have different utility functions, can the lottery make sense?
Obviously.
Most folks don’t consider the decision to watch TV an hour or two a day stupid. Cable costs about $1/day, and folks get some middlin’ amount of pleasure out of it. A lottery ticket can, I believe, cost about the same. Do people get more or less pleasure from a lottery ticket than from a marginal hour of TV? The principle of revealed preference suggests that they get more.
If you’ve got something that costs $1/day and takes 5 minutes of work to deliver more joy to the average person than a lottery ticket, go off and sell it. If you actually sell it, then you’re right.
If you either can’t come up with such a product, or can’t succeed in selling it, then you’re wrong, and your product is less pleasing.
Either way, don’t call the consumer stupid. His job is just to like what he likes.
Call yourself stupid. You’re the one who simultaneously insists that the current mousetrap is obviously defective, and yet you can’t build a better one.
April 13th, 2007 at 1:20 pm
Agreed. All the same, we can also agree that one’s odds of winning the lottery aren’t much improved by buying a ticket!
April 14th, 2007 at 2:23 am
Oh, I disagree – they’re improved a great deal by buying one ticket, as opposed to none.
What doesn’t improve your chances significantly is buying more than one.
I look at buying a lottery ticket as an investment. Extremely low cost, very very small chance of an extremely large return. Sure, for a buck or two I’ll play those odds now and then (when it’s $100M+, usually).
What do I dream about doing with it, if I win it? Oh, sure, I can shop for all I want then, but that’s just details – what I dream about is hiring a really good accountant and tax attorney…
April 22nd, 2007 at 3:21 am
Here’s a point I keep having to make when talking to people about the Lotto: the (California, at least) lottery isn’t necessarily a sucker bet. The jackpot increases every time there’s a draw without a winner; eventually, the payout crosses over the odds, and the lottery becomes a positive-expectation wager.
It’s still a wager with very, very long odds, so you shouldn’t bet your mortgage payment – but there’s a reason there’s case law documenting that the only way to play every possible combination of lottery numbers is to buy all those tickets one at a time; you can’t give them a check for ~$15 million dollars and receive in exchange an “every combination” ticket.
When computing the crossover point, make sure your calculation includes (a) the flattening of the 20 year payment plan into a single payment, and (b) how much will be left of that after taxes. I haven’t sought the advice of professionals, but newspaper accounts of winners consistently report that a nominal jackpot of $X becomes roughly $X/3 as a post-tax lump sum payout.
Also, don’t play any numbers under 31, and absolutely no numbers under 13. There’s no bias in the distribution of numbers as drawn, but there’s very much a bias in the distribution of numbers on winning *tickets* – people play dates. Thus, using only numbers > 31 reduces your odds of having to share the jackpot with another winner, without damaging your odds of winning.
July 19th, 2007 at 8:24 pm
listen, imagine u d buy every possible combination out there when the jackpot reaches 100 millions plus: every bet costs u 1 buck, so in total that d make 26 billions just to win 100 millions (-taxes)
so really, there s never gonna be a crossover of odds.
my advice: go ahead and waste ur cash on a dream, there s worse out there to spend money on (cigarettes shorten ur life, drugs make it less enjoyable, prostitutes in the long run miserable, food gets u fat, stocks reward only ceos, cool cars crash, and so on and on and on) but know one thing. to really win takes more randomness ur brain can imagine
July 19th, 2007 at 11:04 pm
Where to start?
First, in addition to randomness, my brain can handle capital letters and correctly-spelled words.
Second, what lottery are you playing where you’d have to spend 26 billion dollars to purchase every possible ticket? The California Super Lotto draws 5 numbers from the set (1-47) plus a “mega” number from the set (1-27), which allows for 41,416,353 possible combinations.
Admittedly, 41.4M isn’t the 15M figure I threw out in the earlier message; $15M was my mistaken recollection how much it would have cost to buy every possible California Super Lotto ticket between 1990 and 2000, a period during which the game was C(51,6), and the customer had a much better shot at the jackpot. But it’s a lot closer to 41M than to 26B.
July 19th, 2007 at 11:16 pm
[quote comment="68220"]listen, imagine u d buy… [/quote]
If you post this again, in English, I may deign to respond.
July 20th, 2007 at 12:09 am
I can parse most of that…except that ‘d’.
What the hell is that?
February 24th, 2008 at 9:37 pm
Rationally speaking the lottery is a bad investment.
Okay the odds do get better as the jackpot goes up, but not by much. If you discount the cash flows and the divide by the average number of winners, the best case scenario is you come out losing an average $0.20 per $1 ticket (depending on the size of the jackpot.)
Take for example the Florida Lottery C(6,53):
E(P) E(W) E(P)[adj] Lump TVM Lump Sum TVM
$105.7 5.0 $21.1 $7.0 $0.92 ($0.69) ($0.96)
$84.7 3.9 $21.8 $7.3 $0.95 ($0.68) ($0.96)
$67.6 2.8 $24.1 $8.0 $1.05 ($0.65) ($0.95)
$53.6 1.9 $28.4 $9.5 $1.24 ($0.59) ($0.95)
$43.0 1.9 $22.4 $7.5 $0.98 ($0.68) ($0.96)
$33.2 1.6 $21.3 $7.1 $0.93 ($0.69) ($0.96)
$23.9 1.5 $15.5 $5.2 $0.68 ($0.77) ($0.97)
$19.5 3.3 $6.0 $2.0 $0.26 ($0.91) ($0.99)
$18.2 1.8 $9.9 $3.3 $0.43 ($0.86) ($0.98)
The first column E(P) is the jackpot (millions) the second column E(W) is the expected number of winners, (extrapolated from historical data. E(P)[adj] is the E(P)/E(W) giving the expected payout per player. Now we break this down further into taking the lump sum (after taxes) and the annuity discounted 30 years at 6% inflation and a treasury rate of 5% (no taxes.) Obviously your better off taking the lump sum, but as you can see the house still wins. As you can see your best odds are probably around $50 million or so, because as the jackpot gets higher and amount of players grows exponentially.
Bottom line, the Florida Lottery is a waste of money.
May 28th, 2009 at 6:48 pm
Actually, with the Florida Lottery, there are only 64 numbers used, meaning you could buy every possible ticket combination for around $2.1 million (since numbers aren’t repeated). Assuming no one else wins, this will lead to a profit with jackpots as small as $10 million or so. With higher jackpots come more profits, especially if you’re the only winner. You could theoretically take out a loan for around $2.1 million, play every number when the jackpot goes over $20 million, pay off your loan, play all the numbers again, and still have nearly $3 million left after taxes; you could repeat the process for years and make millions, even billions, if you sometimes waited a bit to allow the jackpot to increase.