Econ Tricks

Why Do People Play Cards More Aggressively Online?

2011-08-12T14:31:00.000-04:00

I am a big fan of two rather different card games. Spades is a partner game that involves bidding, trumping, and taking tricks, while Texas hold 'em is a game of betting and shared board cards. Yet they have something in common: people play both a lot more aggressively online than they do in person.

In live tournament poker, it's usually two players to the flop and only rarely three. Many pots go to the lone raiser before the flop uncontested. Online players are much looser, and pots involving four players are more common. Online poker is also home to more "calling stations," or players who can't be bluffed off a marginal hand.

In spades, each player begins with 13 cards, so there are 13 tricks to be had in each hand. Online play is full of 12 and 13 bids, which can net players the most points but also put them in the most danger of being set. Live play, in contrast, has a greater share of 9 and 10 bids, where making the bid is safer and the game becomes an art form of avoiding bags.

The tendencies of online players are generally losing propositions. Conservative poker players rarely play more than 10 to 15% of their starting hands; play many more than this without an extremely solid post-flop strategy is asking for trouble. And players who routinely stretch their bids can be goaded into getting set if the other team underbids.

Perhaps online players aren't as skilled or aren't paying as close attention as live players. In poker, there's often much less on the line: players can enter online tournaments for a few dollars, while the buy-in for a live event is often around $100. So reckless play doesn't quite cost as much.

However, I would argue that to some extent, we all play more impulsively online, because of the web's anonymity.

In poker, there are certain situations where the pot odds dictate that you should call a bet on the river with just an ace high. This is much easier to do if you can hide behind a screen name than if you have to sit at a table full of people laughing at you after the hand and saying, "You called with ... what?!?"

In spades, I'll attempt a more borderline nil when paired with an anonymous stranger than I would with a friend I play with regularly. If it doesn't work out online, I can just leave the table in disgust with no real consequences, but in person, I might have to deal with a frustrated partner for the rest of the game.

A Fun Spades Endgame

2011-08-12T13:49:00.000-04:00

This example is based off a play that one of my opponents made at a recent match. Suppose that your team is winning 499-341. You are one point away from winning, but also one bag away from going back 100 points.

The bids are:

Your partner: Nil
Opponent to your left: 5
You: ??
Opponent to your right: ??

Regardless of what cards you have, you should bid ... 9! You're almost certain to be set, of course, but with a successful nil your team will net 10 points for the hand and win without the risk of getting any bags. If you have a competent partner, she would only nil in this situation if it was pretty safe, given that she's first to act and that your team is well ahead. You can now focus on covering the nil without having to worry about how many tricks you take.

But J.K. Rowling DOES Have a Price ...

2011-07-12T13:55:00.000-04:00

She wouldn't allow someone to pay her to have their child's name in her Harry Potter series, according to the Financial Times.

I would argue that she does have a price, but none of us has enough money. But imagine if Bill Gates wanted the above transaction and offered Rowling a cool $1 billion. Even if more money has no marginal value for her personally given her vast wealth, a billion dollars could do an immense amount of good for the charities of her choice. It would be impossible to deny the world so much good for something so trivial.

But she, like anyone else, probably wouldn't be able to tell you her price ahead of time, until the money is actually on the table.

Distinctions

2011-07-12T00:32:00.001-04:00

I came across two things today that have challenged my mental shortcuts and made me think about what people are really saying.

At work, a vice president gave a presentation about listening to other people's perspectives. He gave the example of someone arguing that a given model won't work. This could mean that they don't think our systems can handle the amount of data, bandwidth, and storage required to the run model. Or it could mean that while the model would be technically feasible, it would be statistically invalid or misleading. Or it could mean something else entirely. Finding out what this person is really saying will help you convince them of your point of view, or convince yourself of theirs.

Just now, the heralded literature that is "South Park and Philosophy" pointed out to me that there's two ways to interpret the phrase "child abduction is not funny." One could be that it "fails as humor," in the same way that Cartman believes Family Guy's endless cutaways do. Another is that it's morally apprehensible to laugh at the subject.

Prediction Markets in the World Ending

2011-05-06T11:44:00.000-04:00

I loved this quote from the Post story about the nuts who think the world is ending May 21. (Wasn't it supposed to be 2012?)

Another man was so perturbed by the May 21 message that he brought over a woman he found on the street who needed money. He asked whether the Camping followers would give her some cash, because there was no need for them to keep money with the world ending. They did not.

If you want me to take your doomsday prediction seriously, you should be willing to put money behind it.

I'm reminded of GMU professor Alex Tabbarok's paper about Pascal's wager, which boils down to there being a small-but-nonzero chance that your getting into heaven depends on giving all of your money to Tabbarok, which, he argues, you should do just in case.

The Economics of "Snakes on a Plane"

2011-05-05T20:48:00.000-04:00

I really hope someone Googles that some day and I'm the first hit. Take that, Demand Media!

I just read 50 or so painstaking pages of Bryan Caplan's new book Selfish Reason to Have More Kids, where he goes over seemingly every twins-separated-at-birth study ever conducted and argues rather exhaustively yet convincingly that nature matters a lot more than nurture in terms of how a child develops.

I am five minutes into watching "Snakes on a Plane." In this scene, the dude in the picture above has just said the following to another guy who's tied up in front of him:

I'll make sure to tell your son
all about it.
The reason he gets to grow up without a father
is because of how goddamn noble he was.
Then again, I was raised by a single mom and... (he takes a swing at the guy with a baseball bat, spewing blood everywhere)
I didn't turn out so bad, huh? Whoo!

And my first reaction was: "That probably had a small or zero statistical effect on your upbringing! It's all genetic!"

Yes, the master's degree in econ was totally worth it.

Where Are Today's Aladdins and Lion Kings?

2011-04-30T11:49:00.000-04:00

Movies in the Disney vault are only available for sale on DVD at limited times. For instance, if you want a copy of Lion King or Aladdin, you'll have to buy a second-hand copy or one at a huge premium (list price of $50 on Amazon).

No new films have entered the vault since Lion King, in 1994. Why? Some theories:

1) Today's movies are just as good. The Princess and the Frog and Mulan are just as awesome as Cinderella or Beauty and the Beast, but today's entertainment market is so saturated that these movies don't have the network effects of movies in decades past and thus aren't considered classics.

2) Today's movies are worse. You could blame this again on market saturation: Disney nows that a Lion King-esque movie released today wouldn't make much money, so they don't bother creating it. Or maybe there's a greater emphasis now on animation instead of music and overall quality.

3) All the good new Disney movies are Pixar projects (Toy Story, Up), and thus perhaps aren't subject to the vault? The existence of these movies probably refutes my second theory.

4) My view is skewed by being someone of my generation, who will always hold a higher opinion of movies I was exposed when I was young (I notice that I also tend to deify Padres players of my childhood, who by any objective standard were average or worse). Maybe Disney's decision-makers fall victim to the same fallacy, and The Princess and the Frog will become vault material once today's children rise up in the ranks.

Is the NFL the New NASCAR?

2011-02-18T11:07:00.002-05:00

USA Today ran a front-page story today about how NASCAR's ratings and popularity have plummeted since Dale Earnhardt's death 10 years ago. No drivers have died since, and the article speculates that NASCAR has overemphasized its safety improvements, to the point that fans feel that the sport has lost its exciting edge.

I see some parallels with the NFL's recent crackdown on helmet-to-helmet hits this year. This is not to mention the longer-term increase of protections on receivers and quarterbacks via strict roughing the passer and pass interference penalties. All the while, the defense becomes increasingly marginalized.

It's sort of uncomfortable to speculate on where we stand on the trade-off between death and entertainment. The NFL has had an easier time favoring the latter, because, as Robin Hanson points out, the adverse health effects are often delayed beyond the player's retirement and thus less in the public view. I've always loved how he's framed the devastation:

Surely we can see football hurts players – we often see them carried off in on stretchers. But I wonder: would we accept this harm nearly as much if we saw it all up close? Players would suffer the same average loss if each season one out of ten players just dropped dead on the playing field! (A dead 25 year old player loses 55-25 = 30 years, which is ten times the three years life lost per player per season.)

Watson's Unfair Buzzing Advantage on Jeopardy

2011-02-16T10:12:00.000-05:00

By now you've probably heard about the exhibition Jeopardy! match between the IBM-designed machine Watson and the two most heralded players of the show's history.

After watching the constant frustration on Ken Jennings' face, I was confident that all the players knew most of the answers. It was just a matter of who buzzed in first, with Watson doing so most of the time.

Check out this description of the Jeopardy! buzzer, from Jennings' Web site:

If you watch Jeopardy! casually, it's easy to assume that the player doing most of the answering is the one who knew the most answers, but that's not necessarily true. All three contestants, after all, passed the same very hard test to be there. Most of the contestants can answer most of the questions. But Jeopardy! victory goes not to the biggest brain—it goes to the smoothest thumb. Timing on the tricky Jeopardy! buzzer is often what separates the winner from the, well, non-winners, and the Jeopardy! buzzer is a cruel mistress.

Here's how it works: the buzzers don't get activated until Alex is finished reading each question. If you buzz in too early, the system actually locks you out for a fifth of a second or so. But if you're too late, the player next to you is going to get in first. Somewhere between too early and too late is a very narrow sweet spot, like swinging a tennis racket or a baseball bat. No, that's not right. The Jeopardy! buzzer, she is like a woman. No, that's not it either. All I know is, the more I thought about the timing, the less I could nail it. When I could somehow just Zen out and not think about what I was doing, I would do okay.

Watson won primarily because it had first dibs on every question it pleased. I'm much less impressed by this victory because it involved a machine "hitting a button" much more precisely than any human ever could.

Yes, it's still impressive that the machine can perform so well on Jeopardy!-style questions, but the lopsided final score shouldn't imply that Watson is vastly superior to its human counterparts.

Ruralites Are People, Too

2011-01-25T19:28:00.001-05:00

A job candidate at work presented his paper, which details a government program that attempted to revitalize rural areas in the '90s. Some tactics included improving transportation, offering tax incentives for firms to open factories in rural areas, and so forth.

Such programs give me pause to beginning with, but my feelings were cemented once the speaker mentioned that they generally discourage job training. This is because job training helps people build skills and human capital, thus empowering them to move elsewhere for better prospects elsewhere, leaving the area even more impoverished.

Rural areas have no inherent right to exist, and discouraging their residents from improving themselves seems absurd. We don't want to help rural areas for their own sake; we want to help them because of the impoverished people who live there. And if these people feel that they are making themselves better off by choosing to move somewhere else, more power to them.

In Defense of Adjustable Rate Mortgages

2011-01-23T11:12:00.000-05:00

"No!!! We are not getting an ARM! If you want to get an ARM, I am done looking at condos with you!"

"Haven't you read about those people in the newspaper? It's worth it for peace of mind!"

"If you want to get an ARM, I'm not giving you any of the blanket!"

Normal people, like my fiancee, tend to say that they don't want X, no matter what. Economists, in contrast, tend to say that they might want X, if the price was Y.

To see if an adjustable rate mortgage would be right for us, we have to estimate a few parameters. For instance, consider a 5-1 adjustable rate mortgage, where the interest rate is fixed for the first five years. If an ARM offers a rate that's 1 percentage point lower than a fixed-rate loan, that's quite a bit of money: for instance, 1% of $300,000 is $3,000--per year.

If there's a 100% chance (or something close to it) that interest rates won't rise during the duration of our loan, then an ARM is a great deal. But it's very hard to make this assumption. More realistically, if there's a 100% chance (or something close to it) that we'll move to another house within the first five years, then an ARM is a great deal. Neither of these conditions is necessarily true, but we should at least consider if they might be.

But one meta parameter trumps everything else: my spouse's happiness is worth more than potentially saving some money by "gambling" on the mortgage.

Is Weird Stuff Smaller at Costco?

2011-01-22T13:03:00.001-05:00

As an economist, it's hard for me to shop at Costco. Everything in life is subject to diminishing returns, so while the first pack of trail mix might be great, I'll probably be sick of it by the time I get to pack 18.

I often find myself thinking: Even if half of this item goes bad, it would still be a good deal. Plus, as someone who lives in a relatively small apartment, it's sometimes difficult to make the size-price tradeoff.

Above is 5 pounds of butter and 16 ounces of lobster spread, the only size available for either product. At a normal supermarket, these products would be about the same size. Yet Costco's lobster spread container doesn't even seem to be comically bigger than its mainstream counterpart, as most items at Costco do.

Costco can get away with selling staple items like paper towels in huge portions, because people figure they will use them all eventually. However, this is less true for more specialized items. We picked up the lobster spread after trying a free sample; if it had only come in a 5-lb. container, we probably would have seen that as too big of a commitment.

Carrot and Stick of Parenting

2011-01-19T23:35:00.000-05:00

I've recently been exposed to two theories about parenting, and I find the contrast between the two rather amusing.

We just watched the Freakonomics movie, which describes among other things how co-author Steven Levitt tried to motivate his three-year-old daughter to learn how to be potty trained. As an economist, he surmised an incentive scheme: he would give her candy every time she used the toilet successfully. Before long, though, the daughter began gaming the system, increasing her frequency of bathroom trips by peeing just a little each time in order to pad her candy haul.

Contrast this with the recent excerpt in the Wall Street Journal from Amy Chau's book in an article titled "Why Chinese Mothers Are Superior" (you really have to read the whole thing to get the full effect):

I rolled up my sleeves and went back to Lulu. I used every weapon and tactic I could think of. We worked right through dinner into the night, and I wouldn't let Lulu get up, not for water, not even to go to the bathroom. The house became a war zone, and I lost my voice yelling, but still there seemed to be only negative progress, and even I began to have doubts.

It shouldn't be surprising to anyone that you get better results (at least from the parents' perspective) by brandishing a hefty stick than you do by offering a carrot of trivial value.

The Jolly Roger

2010-12-30T08:52:00.000-05:00

The following passage in Pete Leeson's book on pirates reminded me of my earlier post about why rapists shouldn't be treated as harshly as rapists who are also murders (emphasis added):

The presence of these other belligerent marine vessels provides a clue why pirates went through the trouble of using the Jolly Roger when they attacked their prey: Pirates wanted to distinguish themselves from the other assaulting vessels merchant ships might encounter. Britain criticized the Spanish Guarda Costa for inhumanely treating some British prisoners it captured. Nevertheless, at least in principle, the viciousness coast guard vessels could show toward merchant crews they assaulted was limited because they were government-sanctioned cruisers. They weren't permitted to wantonly slaughter merchant crews that resisted them after these crews cried out for quarter, for instance. In contrast, pirates weren't even theoretically constrained in how they treated those they overcame. Pirates were outlaws and would be hanged if authorities captured them whether they massacred merchant crews they attacked or not. In this sense, for pirates, massacring resistors was essentially costless.

Thus, the skull-and-crossbones Jolly Roger served as a credible signal to merchant ships that they should surrender instead of face probable death.

Evolutionary Impulses

2010-12-29T13:11:00.000-05:00

Imagine that, all of a sudden, humans no longer found food to be delicious or sex to be enjoyable.

Would we go on eating, procreating, and surviving with the big picture in mind, or would the human race die off after a few decades because we'd all be too short-sighted? In other words, how important are our evolutionary impulses today, now that we have an established society?

Tom Sawyer: Economist

2010-12-17T09:32:00.000-05:00

Economists since Adam Smith have demonstrated that the way to riches is trading. Through comparative advantage, we can trade for things that are cheaper for others to produce than they would be for us to produce ourselves--leaving both parties better off. Happily, this often takes the form of the buyer thinking "I can't believe this product is so cheap" while the seller is thinking "I can't believe people are paying me so much to produce this."

In light of this, I found the following passage from Mark Twain's "The Adventures of Tom Sawyer" rather amusing:

"Nothing but a tick."

"Where'd you get him?"

"Out in the woods."

"What'll you take for him?"

"I don't know. I don't want to sell him."

"All right. It's a mighty small tick, anyway."

"Oh, anybody can run a tick down that don't belong to them. I'm satisfied with it. It's a good enough tick for me."

"Sho, there's ticks a plenty. I could have a thousand of 'em if I wanted to."

"Well, why don't you? Becuz you know mighty well you can't. This is a pretty early tick, I reckon. It's the first one I've seen this year."

"Say, Huck— I'll give you my tooth for him."

"Less see it."

Tom got out a bit of paper and carefully unrolled it. Huckleberry viewed it wistfully. The temptation was very strong. At last he said:

"Is it genuwyne?"

Tom lifted his lip and showed the vacancy.

"Well, all right," said Huckleberry, "it's a trade."

Tom enclosed the tick in the percussion-cap box that had lately been the pinchbug's prison, and the boys separated, each feeling wealthier than before.

My 16-Year-Old Self and the $89,000 Check

2010-11-12T11:37:00.000-05:00

In high school, I had a job working at a very small tax office: just my boss and me. She was going out of the country for a while, so she asked me to monitor the mail while she was gone for a certain check and to deposit it at the bank.

When the check arrived, I was floored to see that it was for $89,000. I felt nervous handling it, driving it to the bank, and handing it over to the teller. My mom even accompanied me into the bank to make sure that everything went OK.

Of course, the teller accepted the check without batting an eye or calling over a senior manager.

Maybe I was destined to become an economist someday, because I imagined what would happen had I tried to sign the check over to myself. Perhaps it would have been technically impossible to take the money myself, but that didn't stop me from daydreaming about my ill-gotten sportscar and big-screen TV.

But I quickly realized that I couldn't live forever on $89,000, and that I'd have to sacrifice my job, my family (my boss was a good friend of my aunt), and probably all of my future academic and professional opportunities for this one-time score. Not to mention the constant need to look over my shoulder for law enforcement. It simply wasn't worth it.

Why do armored car drivers almost never take the cash for themselves (despite the recent movie)? Why do the millions of cashiers around the world rarely skim off the top? Why could merchants as early as the 11th century trust hired agents with boatloads of valuable goods (as described in Avner Greif's classic paper)?

Economists generally give two explanations:

(1) Workers are paid an efficiency wage. If the market value for carpenters is $20 an hour and I pay someone $35 an hour, that will give my employee a huge incentive to keep that job by not only working hard but also by not jeopardizing his employment by trying to steal from me.

(2) As described in Greif's paper, reputation is crucial. If you screw over one employer, your chances at future employment are vastly undermined. That's why references for job applicants are so important, and why eBay feedback can quickly sort out the good sellers from the bad.

A Farewell to AdSense

2010-11-08T17:48:00.001-05:00

I'm sure there's an economic point in here somewhere, but as of today, I'm removing AdSense from this blog.

This is mainly in response to AdSense's payout scheme: if your account is active, you need to reach $100 before getting a payout, while you can cancel your account and get paid if your balance is $10 or higher. I've been stuck in the middle of that range for months; I made a little money after my post about the Nationals ticketing office attracted a few thousand hits, but now I get about 15 hits a day. I'm sure my almost complete absence of new posts has something to do with that, but at this rate it would take decades to reach the $100 threshold.

So, there you have it: Econ Tricks, with a little less clutter. There are more than a few cautionary tales online about people getting screwed out of AdSense payouts, so wish me luck.

Thoughts on Online Voting

2010-11-02T12:45:00.000-04:00

I can apply for loans, communicate with doctors, and do any number of other sensitive things online, but to vote I must go somewhere (which may be close to where I live but far from where I work) and wait in line, or send a bunch of stuff through the mail. These transactions costs are just as real as any other costs, so theoretically their elimination would be an unambiguous win for society.

The cynic might say that the nonexistence of online voting is deliberate. If online voting is allowed, the demographics of the turnout would be much different (i.e., more busy young people), which might be to the disadvantage of those in power. It's easy to see that the most passionately political people and those with the most spare time or the shortest commutes are overrepresented in the final tally. Whether this is good or bad is an open question.

Netflix Pricing Paradox

2010-10-29T15:11:00.000-04:00

I'm sure I'm not the first to recognize this (and I'm too lazy to use Google to find out), but Netflix's pricing policy seems a bit odd.

Having one DVD out at a time costs $8.99 a month. The marginal cost of the second DVD is $5 ($13.99 - $8.99). In order, additional DVDs after that cost you an extra $3, $7, $6, $6, $6, and $6.

Usually, businesses give you discounts when you buy in bulk, because their costs are lower. This is reflected in lower-end Netflix plans (i.e., getting 2 DVDs a month costs less than twice as much as getting 1), but why is that fourth DVD (and thereafter) so much more expensive than the third?

Maybe Netflix figures that subscribers with 3 DVDs and below are people like me and Sharon, who have busy lives and often let a Netflix DVD sit unwatched on our coffee table for a week or longer. We are highly profitable customers, so Netflix will let us have yet another DVD lying around for fairly cheap.

Conversely, it's hard to imagine anyone signing up for 4 or more DVDs at a time unless they fully intend on watching them. These people are signaling to Netflix that they'll be mailing DVDs back and forth with great frequency, so Netflix is anticipating a higher per-monthly-DVD cost and thus charging accordingly.

On a related note: we've had the 2-at-a-time plan before but switched to 1 at a time several months ago. Now that baseball is almost over, we might switch back, but it's interesting how much being able to watch an unlimited amount of Netflix's hodge-podge assortment of "instant" movies makes you reluctant to pay for more DVDs.

Will Telecommuting Upend Housing Prices?

2010-10-20T20:33:00.000-04:00

I was just watching "House Hunters" with my fiancee, and we saw an enormous, gorgeous house in east Bradenton, Fla., for $450,000. "That would get you a one-bedroom condo in D.C., if you're lucky," she commented.

Which got me to thinking: If full-time telecommuting became a substantial percentage of the workforce, it would probably result in plummeting real estate prices in places like D.C.--where many who aren't in love with the city itself move for jobs--and soaring prices in places like Florida and California--where many people would love to live but can't afford to do so because of a lack of local employment opportunities. It would also have an enormous effect on locality pay.

Not that I think mass telecommuting will happen anytime soon. Social capital, such as in-person training and rapport with co-workers, is likely more important than most people realize.

Rethinking Pythagorean Winning Percentage

2010-09-27T12:36:00.000-04:00

Baseball-reference.com describes Pythagorean winning percentage as "an estimate of a team's winning percentage given their runs scored and runs allowed. Developed by Bill James, it can tell you when teams were a bit lucky or unlucky." Click through for the formula.

An example is the 2009 Washington Nationals. The team finished 59-103. However, the Nationals scored 710 runs while allowing 874 runs, so their Pythagorean W-L is 66-96. The Baseball Reference folks would thus argue that bad luck cost the Nats 7 wins, which is a substantial number in comparison to their actual number of wins.

However, while winning is a function of runs scored and runs allowed, runs in the late innings are also partially a function of runs in earlier innings. Your team's run expectations in a given inning are highly sensitive to what's happened earler in the game.

Consider a game where your team is tied in the top of the seventh. And another where you're losing (or winning) by 10 runs. On average, you'll score more runs in the latter scenario, because both teams will insert inferior relief pitchers, saving their star bullpen guys for another day. Hell, they might even have a position player pitch. Losing by 15 or 5 is just as bad as losing by 10, so it makes sense to conserve baseball resources, even at the expense of the final score in a hopeless game. Any cheap runs you score in such situations won't do much to improve your winning percentage, but Pythagorean winning percentage has no way to account for this.

On the other hand, in a tied game, the other team will do everything possible to prevent you from scoring, because a run or two could mean the ballgame.

Of course, teams also conserve offensive resources in blowouts. Pinch runners and defensive replacements often swap in for the likes of Adam Dunn or Barry Bonds. I suppose it's possible a weaker offense could offset the effect of inferior pitching, or even trump it.

Additionally, batters could be trying less hard in blowouts, just wanting to get the game over with, but I don't think there's any evidence to support this (why not pad your batting average against bad pitchers?).

Proof that Washington Nationals Tickets Are Overpriced

2010-09-23T15:52:00.001-04:00

Around the time that they set another record for lowest attendance, the Washington Nationals announced a "Buy 2 Get 2" promotion (see screen grab above once this link becomes obsolete) in which fans can get two full-season tickets free when they buy two in select sections (read: near or behind the foul poles).

At first, this seems like an arbitrage opportunity, or opportunity to make a profit with no risk. There are some time and money costs to reselling tickets, such as researching prices on StubHub or haggling with scalpers, but someone could theoretically make easy money just by selling each ticket for half of its face value. They just need to buy four tickets (two at face value and two free) from the Nationals for $60 and sell each ticket for a little more than $15.

The fact that someone couldn't expect to sell all these $30 Nats tickets for as little as $15 each, and thus make a profit, says a lot about the lack of demand and the sorry state of the franchise.

The Gift Card Paradox

2010-09-23T15:24:00.000-04:00

Imagine a retailer with many outlets nationwide. Two stores in particular have $1,000 in monthly fixed costs, which are not impacted by the amount of products sold (rent, payroll, utilities, etc.). The products have an insignificant marginal cost, which we can round down to zero.

Suppose that each store only makes an $800 monthly profit in cash for sold merchandise. However, Store A also sells $300 in gift cards each month, but no customers redeem gift cards there. Meanwhile, customers redeem $300 worth of gift cards each month at Store B, but no one buys gift cards there.

If these are the company's only two stores, it will quickly go bankrupt. It's only taking in $1,900 a month while spending $2,000. Assuming that nothing can be done to stimulate business or cut costs, the best option is to shut down.

If instead the company has thousands of stores, does it make sense to shut down either or both of the stores detailed above? This answer is much more difficult.

One crucial factor is how the demand for gift cards would change. Perhaps the closure of Store B would have little or no effect on gift card sales at the other stores. This is a reasonable assumption for a company like Starbucks, which has a store seemingly every few blocks. The recipients will likely be able to find another Starbucks near Store B anyway, so it makes sense to close that store. (Indeed, Starbucks closed 300 stores last year.) Here, the firm's existing stores make a decent substitute for any stores to be closed.

Whether to close Store A depends on how receiving a gift card affects customers' spending. If the typical customer increase his spending by the amount of the gift card, Store A should stay open. If instead he keeps his spending constant, except now he's paying partly in cash and partly in gift cards, Store A should be closed.

Another scenario: perhaps the closure of Store B reduces the chain's gift card sales by the full $300 a month that was redeemed there. This could be plausible for a store like IKEA, which typically only has one outlet per metropolitan area. If IKEA closes Store B in a college town, it's easy to imagine many grandparents spending less on IKEA gift cards (not just at Store A, but at many stores nationwide), because their college-aged grandchildren no longer have a local store at which to redeem them. Here, consumers will likely substitute not to other stores within the same chain, but to stores of its competitors. That does not necessarily mean that both stores should remain open; I think the decision is unclear under this scenario.

Abstract Thoughts on the Chance of Rain

2010-09-23T14:18:00.002-04:00

I have a day in mind, but I'm not telling you. My question is: what is the chance that it rained that day in Washington DC?

You have no knowledge of the cloud formations, temperatures, or time of year. However, suppose that over the last four decades, it rained 15% of the time in DC. So your best guess is 15%, but you're not very confident.

Suppose that I told you that my mystery day was in September. You could look at historical September predictions and adjust your guess accordingly, now with slightly more confidence.

Yet when we look at the 10-day forecast, we routinely see that the chance of rain is around 50%. This could mean that, historically, it has rained about 50% of the time during this time of year. More likely, it means that historical patterns mean very little when we want to know if it will rain any particular day; instead, the forecast is primarily influenced by the latest meteorological readings.

If it's for sure not going to rain tomorrow, the chance is 0%. If it's for sure going to rain, the chance is 100%. It's amazing to me that, given modern technology, we so often see chance of rain predictions for the very near future around 50%, essentially a coin flip.