An Experiment in Adverse Selection

An article in Friday's Wall Street Journal, written by Chad Terhune, describes new health insurance policies being offered by some insurance companies. I can't give a reference to the WSJ piece, but another paper reports on it here. The ones offered by American Community Mutual Insurance are particularly interesting. They are targeted at the "healthy young" and offer low annual premiums, around $1000 per year. That doesn't get you much, however, as there is a rather small maximum benefit and a large deductible. What it does get you is the option to buy a much larger benefits cap -- up to $5 million -- if you do get sick and want to initiate the higher coverage. "Coverage on Demand," the company says. Of course, that additional coverage is expensive. It HAS to be, because only the ones who buy it will need it! So given the adverse selection that has to happen, is there a price that will allow the company to break even at least, and that will attract some customers into the program? Or at any price, will the only customers who sign up be so costly that the company will have to lose money? The higher the price of the "coverage on demand," the sicker and more costly will be the individuals who sign on. Or, maybe, the individuals who get sick will have enough uncertainty and be so risk-averse that they will buy expensive coverage even when their medical bills will not be all that large.

There is a large market of rational individuals who find medical insurance too expensive and therefore go uncovered, so I can understand the experiments at attracting them. And there are a lot of new plans coming out, especially as some states like Massachusetts require insurance. The fine print is going to lead to a lot of litigation, I predict: what maximum benefits really are, whether they were disclosed, non- covered conditions, etc.

Great case to cover in a class on the classic information economics problems of adverse selection and moral hazard.

General Petraeus and Ambassador Crocker

A few observations on the testimony today of General Petraeus and Ambassador Crocker. I listened to some, watched a bit on TV, and based on what I saw:

1. If the White House communicated as well as these two fellows (heck, half as well), these hearings would not be happening – because the Democrats would not be in charge of Congress.

2. The moveon.org ad in the NYT brings rational discussion to a new low. To refer to General Petraeus as General Betray Us not only gratuitously insults someone who appears to really care for our country, and obviously works hard at his job, but it demeans the debate over the war. Shame on them.

3. The Democrats are really scared, because they see that if they do indeed win the White House next election and keep control of Congress, any pullout from Iraq will be their decision – and they could well be in a position of explaining to their supporters why we have to stay in even longer. Political posturing is cheap for them now, but they realize that if they were actually in control, they would be making the same decisions.

4. I never understood why “exit” is valued so highly, even if we succeed in stabilizing the situation. I see tremendous value in having, say, a US military base on the Iran/Iraq border – something widely reported today. What, strategically, is bad about having 100,000 well-trained and well-equipped troops on the borders of Iran, Syria, Kuwait, and Saudi Arabia?

Apple’s iPhone Price Cut

So no sooner did I write my post below about how Apple rarely has sales, and they promptly cut the price of the iPhone by $200. I did not mean by “sales” the (anticipated) cutting of price after an initial product launch, but instead the kind of sales like “back to school” or “holiday” or “Labor Day.” Cutting of price after an initial launch can often be wise, and I like to refer to it as “temporal versioning.”

Versioning is generally the idea of offering different versions of the same basic product at different prices. If you offer a deluxe version at a high price and a basic version at a lower price, you can effectively price discriminate, with some folks buying the high-priced version and the more price-sensitive folks going for the cheap version.

Critical to this strategy is separation: the two versions have to be kept distinct enough so that the folks who like the deluxe version won’t see the cheap version as almost as good, and at the lower price, a better deal overall.

With temporal versioning, separation is also temporal -- the time between the high price period and the low price period has to be long enough to keep everyone from seeing the sense in waiting for prices to fall.

Apple seems to have not temporally separated its versions well enough. Nice strategy, but off a bit on the implementation. The consumer outcry is pretty good evidence of the error. Interesting, often when discussing price discrimination students will mention the anger when some consumers discover that others are paying a lower price (economists like to walk down an airplane’s aisle asking people what they paid for their seat). My response to this is often: who cares if the consumers are mad? With Apple, and the importance of repeat purchases, consumer anger could translate quite powerfully into lower sales.

The Irrational Allure of Liberal Songwriter/Singers

So Pete Seeger has written a new song, "Big Joe Blues" that recognizes Seeger's earlier errors in overlooking the evil of the Stalin/Soviet empire:

He ruled with an iron hand
He put an end to the dreams
Of so many in every land
He had a chance to make
A brand new start for the human race
Instead he set it back
Right in the same nasty place

I admit to a certain attraction to songwriter/singers like Seeger, Lennon and Dylan. I think it is the pureness of their idealism, no matter how wrongheaded it might be, I just have to admire it. "Imagine there no possessions." Well, I can imagine that, and it is not pretty, but I can understand what Lennon was trying to accomplish.

Steinbeck' stories are similar. A very socialistic message, but one that hits you very hard and that cannot be ignored.

Apple and NBC Disagree on Pricing

The New York Times reports that Apple and NBC disagree over pricing of NBC’s video content on the iTunes site. Apple prices all TV shows at the flat rate of $1.99; NBC wants more popular shows to sell for more and to be able to offer promotional prices.

Such disagreements are not surprising. Both firms have monopoly power, so both want to make a monopoly profit. Of course, from one firm’s perspective, a monopoly profit by the other firm is equivalent to a tax that reduces sales and revenues.

Right now, there is a standoff, with Apple not offering any new shows from NBC. Negotiations are supposedly continuing. Who wins will suggest to me just how important the iTunes site is to the content providers.

The other interesting observation is how little Apple uses promotional pricing. I am thinking of buying a new Mac, and there is really little reason to hope for a “back to school” sale – well, I guess they offered an iPod to college kids this year, but generally you might as well not look forward to any big sales by Apple. Interesting pricing strategy -- and of course there is also the uniform 99 cent per-song price that has also been criticized by some copyright owners. Why not adjust price on the basis of demand for a song? Thoughts, anyone?

The Great Quiet

Anyone notice the lack of stories in the press about deaths in Iraq? Or how the decision by Muqtada al-Sadr to have his army take a six month break has hardly been discussed at all?

These are the best signs that "the surge" is working. Those who want to pull out, and those who want to make the Bush war policy look bad, are running scared.

Pessimism Runs Rampant

Who can't help but marvel at the obvious attempts by the liberal MSM to cast a negative pall on anything that could be even remotely linked to the Bush administration.

Yesterday in the Valley News there was a lead above-the-fold article with a Washington Post by-line (authors Christopher Lee and N.C. Aizenman). Headline: US Poverty Rate Down .3% in 2006. The second headline: But More Americans Lacked Health Insurance.

The article goes on to offset any positive aspect with a negative counter. For instance: "While median household income rose for the second consecutive year in 2006, the increase appeared to be driven by a jump in the number of people in each household taking on full-time jobs, rather than a rise in wages."

In fact this is the first time this decade the poverty rate has declined, and it was accompanied with an increase in median household income of .7%.

Record Low Temps Again?

The record low temperature for Lebanon, NH on August 18 is 41 degrees, recorded in 1957, the year I was born.

The National Weather Service forecast for tonight is a low of....41 degrees.

I think I have to build a fire.

Apple turns the corner

One of the top electronic game makers, EA, has shipped two new Mac games and will soon be shipping two other popular titles written for the Mac (well, maybe not really written for the Mac, but deciphered from the Windows version).

While still not quite matching the release dates of the Windows version of the games, EA's step into Mac-dom is welcome.

One of Apple's weaknesses has always been the lack of certain software, especially in the gaming arena.

With a few more hits like this, the only remaining reasons for not switching to a Mac would be.........ummmmmmhhhh...

Bill, can you help me here?

Hanover High Cheating Scandal

At the local high school, Hanover High, nine 17-year old students (all males) have been charged with misdemeanor counts of criminal trespass and/or criminal liability for the conduct of others, in connection with the theft of final exams in math and chemistry courses. It sounds as if the kids hatched – and implemented – a plot to steal exams before test day, so as to be better prepared. I believe they also gave other students the exams as a gift, which causes one to further question the kids’ common sense (unless they sold the exams, which raises the old economics question of whether you can profit more from information by using it yourself or selling it).

I am sorry for the kids, but it certainly was not a very bright thing to do. And I would have to say that in my ranking of crimes, this is one notch worse than, say, colluding with another student to share answers. These guys not only (allegedly) violated academic integrity by cheating, but they also allegedly criminally invaded school property and stole something. Not good.

But, the most interesting part of this is that, naturally, some of the kids are children of folks we know. I will resist any urge to engage in schadenfreude, for the usual “there but for the grace of God…” reason. However…one of the poor kids is the son of Jim Kenyon, a notorious columnist for the Valley News. This is the guy who never misses a chance to tear into Dartmouth and generally side with the forces of bleeding hearts and evil. His column is one I never miss, and much like Paul Krugman’s, it never ceases to raise my ire. The last one he wrote got me upset because he criticized our local food co-op for having a 60-year old woman arrested for shoplifting (she was later acquitted by the judge). The co-op should have shown mercy on a nice old lady, Kenyon said; my reading was that he has one kind of justice for people he knows and likes and another kind of justice for outsiders and “ne-er do wells”. Nothing like a little discrimination, eh?

Perhaps Mr. Kenyon knew when he wrote that column that his son was being investigated for his own form of shoplifting?

The Valley News had some quotes from Jim Kenyon regarding the incident and his son:

He said Hanover High School’s “high pressured academic culture” leads to widespread cheating.

“The entire community must be willing to take a hard look at how it might have unwittingly contributed to this problem and work together to find solutions.”

Kenyon said the school’s cheating problems “do not begin or end with the final exams now in question.”

Give me a break, please! So we are to sacrifice our academic ambitions because nine kids can’t resist the pressure to steal exams? And this is not mainly the problem of the kids and their families, but of the entire community? Yes, society is to blame, competition is evil, we are not responsible for our own actions, we all have to work together…blah blah blah.

The Fed to the Rescue

The Federal Reserve today singlehandedly created a 2% rally in the stock market and put to rest at least some fears of a credit crunch. I applaud Ben Bernanke and his colleagues’ move.

The critical distinction here is between bailing out investors who made bad decisions versus preventing a classic financial panic, of the “run on the bank” variety. I give my vote to the idea that there was indeed risk of a credit crunch, with a cascade of negative opinion creating feedback that was preventing capital from flowing to positive net present value projects.

The classic bank run occurs when depositors come en masse to a bank, demanding their deposits. These deposits are not, of course, in a vault at the bank but instead have been lent out to borrowers, with only some small percentage kept close at hand. If too many depositors demand their account balances, the bank must begin calling its loans, and therein lies the contagion effect.

In today’s market, the problem is not so much with traditional banks. But consider an investment bank like Bear Stearns. Bear Stearns discloses that one of its in-house investment funds held mortgage-backed securities that has declined in value so much that the fund is worthless – presumably the fund managers had leveraged their investments, so a relatively small decline in value could wipe out the net assets of the fund. Once disclosed, and given the overall worries about mortgage-backed securities, negative sentiment about Bear Stearns increases. In the normal course of business, an investment bank needs to borrow large sums of money to finance its activities. But given the concerns, and lack of knowledge of how bad the problems really are, who will want to throw money into a pot that might turn out to be rather empty? Afraid of being the claimant of lowest priority, nobody wants to lend money to such an institution under almost any conditions. This causes the investment bank to reduce its activity in a whole host of areas, and to sell assets it otherwise would hold, in order to raise funds. The vicious cycle begins, with lower prices in asset markets putting other institutions at risk…

I have been hearing from friends on Wall Street since at least June of the funny conditions in the credit markets. Credit was drying up, in the sense that lenders were just saying no, rather than just increasing prices by a reasonable amount to cover new risks.

It is funny how long it took for those fairly wide-spread debt market fears took to spread to the equity markets. One of those (many) instance where if only I had known for sure, I could have made some money. Ah, but how many times have I suspected some disaster only to see stock markets rise thereafter? Much better to buy and hold.

What the Fed did, in lowering the discount rate, was really quite genious. Very little additional credit will enter the economy as a result, and what does enter can be offset at an opportune time via open market operations.

But the Fed showed investors that they do understand that conditions are unusual and that there is a risk of a credit crunch. Credit crunches, panics, and runs should be prevented, and that is the job of the Fed. Bailing out mortgage bankers who loaned 100% of a home’s appraised value to buyers without verifying income is not the job of anyone.

By the way, I know folks in Hanover who had to pay for private mortgage insurance when they bought a house, and these are people with great jobs and in a great housing market. How is it that people in Florida and California are getting by with 100% loan to value mortgages, no income verification, and no PMI??

Gloom and Doom

It’s really entertaining to read the New York Times, especially Paul Krugman’s gloom and doom editorials. I have a colleague who writes an investment advisory letter that exhibits a similar “longing for disaster” tone. Another example is all the climate change advocates who I detect thirsting for some Atlantic hurricanes this year (hurry up, Dean!).

The politics and world views behind so many pundits’ analysis is just so obvious, and so weakly denied. Krugman’s columns ooze not just gloom and doom, but I get a strong sense that he wants to see things melt down, just to prove that the Bush administration has been a total failure. My colleague’s letters to his clients are very similar. It’s not just that he thinks a real estate crash might come, but one gets a very strong sense that he will be happy and fulfilled if it does happen.

Here is an example. In today’s NYT, Krugman writes, “According to data released yesterday, both housing starts and applications for building permits have fallen to their lowest levels in a decade, showing that home construction is still in a free fall…The housing slump will probably be with us for years, not months…Meanwhile, it’s becoming clear that the mortgage problem is anything but contained.”

Free fall, years not months, anything but contained, lowest levels in decade…well, that last phrase is the one factual statement out of all of them. But given what housing has done in the last decade, to say that activity is lower than it has been for ten years really does not sound too bad. And even with housing prices haven fallen of late, has anyone checked the rate of return on owner-occupied housing over recent periods? Some slowing down or even declines is not exactly a crash.

How much you want to bet that Krugman criticizes the Fed for throwing cold water on his dreams? Don’t you share my hunch that many of these Democratic analysts are hoping that the housing crunch does indeed snowball into a recession, so that the Presidency will go to….Hillary? Obama? Edwards?

Health Insurance Limitations

Someone remarked the other day that if not for the war in Iraq, health care would be topic number one in the presidential race. That might well be true.

How will we devise a system to stop insurance from creating unlimited demand for health care services, creating a non-ending escalation of costs? Somehow we will have to give consumers incentive to limit their demand for services. This is tough, because when you are sick, or a loved one is sick, it is really tough to say that you cannot get treated.

Yet this has been the norm in all other important areas, such as housing, education, transportation, and food. Prices in these cases serve their normal role of inducing people to make choices to go without certain services, or at least to choose lower cost services. Many people routinely choose cheaper schools for their children, less expensive and less safe cars for themselves, and take jobs that are riskier to life and limb but pay more (e.g., fire fighters). Also, throughout history, unlimited health care has not been the norm.

Other countries are to a great extent using some kind of nonprice rationing such as waiting for service. In the US today, we have some rationing due to geography: living close to a major medical center will get you more, and more expensive, health care.

I have always felt that a part of the answer will lie in medical insurance being differentiated by degree of coverage. Some plans will not cover certain services, such as expensive transplants, or will at least have high co-pays for certain services, such as mental health.

The new Massachusetts regime requiring everyone to have medical insurance is moving in this direction. The Blue Cross Blue Shield website for the state lists several different plans at different prices and with different coverages.

What I was not able to find in the online descriptions of the plans is a key feature: lifetime maximum benefit. I think this will be critical. There should be some plans that are cheaper but have lower lifetime maximums, or in some way put a limit on what will be covered in certain situations (heart transplant, long term hospital stays, hip transplants past a certain age, etc). It is interesting that the lifetime maximum is not prominent in the plan descriptions -- indeed it is hidden. I am pretty sure there are lifetime maximums, and that they differ across plans. What will BS BS do with patients who hit that max and still want more coverage? Will our dear friend M. Moore have yet more fodder for another movie?

Taxing Private Equity

Not too long ago, I asked an accounting colleague about the tax treatment of someone selling things on an auction site like Ebay. Suppose you are making your living buying and selling collectibles on Ebay. How does the income you make get treated for tax purposes -- is it normal income, or is it capital gains? The difference, of course, is very large, as capital gains are taxed at 15% and normal income at higher rates. Similar analogies came to mind: how about a used car dealer? If I buy and sell cars, is the money I make a capital gain or normal income? It seemed like one of those issues where tax law would draw a somewhat arbritrary line. I can see an argument that if you are essentially a dealer, i.e., making a market in a collectible, then your income could be considered normal, rather than a capital gain, as you are essentially being rewarded for the service of providing a market. But it is going to be a tough call, and in some sense, illustrates the arbitrariness of treating income differentially to begin with.

Now comes the tax issue with the partners of private equity funds. Is the money that private equity fund managers make better considered to be normal income or a capital gain? This is a great topic for discussion. The current law may well make it legal for the managers to use capital gains rate; I suspect if they are doing it, they have had great lawyers look into the legality. So the question is what the right legal tax treatment should be.

But along comes the New York Times yesterday, with a front page story on "Tax Loopholes Sweeten a Deal for Blackstone." The intent of the story is clear -- to raise all kinds of shady questions about the tax fairness of aspects of the Blackstone IPO. The tactics are the usual combination of insinuation, vague claims, and muckraking language. Here are some examples:

"“These guys have figured out how to turn paying taxes into an annuity,” Ms. Sheppard said. “What people don’t realize is
that the private equity managers, the investment bankers, all the financial intermediaries, are in control of their own
taxation."

"The Blackstone partners sold the good will from their left pocket to their right."

"The ability to provide answers to such questions is why tax lawyers can typically charge $700 an hour or more. Just as
fashion designers blend textures, colors and shapes, tax experts mix and match elements of partnerships and
corporations, and bits and pieces of the tax code, securities laws, accounting rules and economics principles."

There are some interesting issues in the Blackstone deal. But this NYT story leaves me clueless as to what actually is going on, and whether it is at all questionable. Some more facts and clear language on what is being done would go SO much further than the kind of language pointed out above. The "annuity" that is referred to seems to be nothing more than the fact that if the goodwill can be written off against income in future years, then of course it creates a tax saving (assuming there is positive income). And to say that private equity managers are in control of their own taxation is really a stretch.

Well, I guess I am in control of my taxation too. If I earn less money, I will pay less tax.

Scooter Libby Gets Clemency

Scooter Libby won't go to jail. He still has a felony on his record, and he still pays a fine and has probation. But no jail time, which must be a relief to him and his family. Bush could still pardon him, which would wipe the felony off the record.

This is fine with me, the punishment did not seem to fit the crime, and it was all a bunch of politics anyway.

Naturally NPR this morning led off the story with Joe Wilson complaining about the pardon and saying that there should be an investigation of Bush. For granting clemency? Give me a break. Go look up the list of pardons that Clinton gave.

The nice thing about Bush is that he did this one in broad daylight. You have to hand it to Bush on that front; he is not afraid to do what he thinks is right. Disagree all you want, but give the man his due for following through on some things.

Does Medical Supply Really Create its Own Demand?

Dartmouth Medical School receives over 5,000 applications for just 70 spots in its MD entering class. This is typical for medical schools across the country, and it swamps even the best business schools. That is a 1.4% acceptance rate, just amazing.

Lots of questions emerge from this, one simply being why so many students want to get an MD.

But my thoughts are more on the economics of health care. My knee jerk reaction to this unsatisfied demand is to question why medical schools don't expand and accept more students -- or why new schools don't open. I believe there are constraints put onto the expansion and opening of new schools by the American Medical Association, basically a supply restriction. My economics intuition would say that this is a monopolistic restriction that is meant to keep doctors' salaries high. Removing the restricton will get us more doctors, forcing their wages down, with the result of lower medical costs and improved patient welfare.

Not so fast, some observers say. Actually, in this market, an increase in supply will simply mean that the additional doctors will be employed, at the same wages, and therefore the medical expense bill will increase. Supply creates its own demand in this market, and the secret to keeping medical costs down is in fact to force restrictions in supply -- fewer beds in hospitals, fewer doctors, fewer exotic imaging machines.

I agree that there are problems on the demand side of this market, with insurance increasingly making patients less and less sensitive to cost.

But would expanding the supply of doctors really result in a worse situation? It should still cause doctors' wages to fall, even though the total spent might increase. This is true of any market -- the dollar size of the market after an increase in supply can rise or fall, depending upon elasticity of demand and of supply.

Is the dollar size of the market really what we care about? There is way too much focus in this country on total dollar expenditures on health care. I really find it hard to believe that the restrictions on supply of doctors is welfare-enhancing. Time to investigate the AMA.

Bad Immigration Policy

I am not sure how I stand on the immigration reform currently being debated.

I lean, however, toward letting more people come into the country legally. There are a variety of reasons for this, but mostly I want to give as many people as possible the opportunity that this country offers.

Another really important reason for a more open immigration policy can be seen in my world of MBA education. At Tuck, we now have foreign students hired by US-based employers who did not receive an H1-B visa this year. That means they will have to use their optional practical training (OPT) visa, which gives them one year. They will have to re-apply next year for the H1-B, and they will have to be out of the country for a couple months in between the time the OPT expires and an H1-B is granted (assuming it is granted). Is it any wonder that US-based employers don't want to hire non-US graduates of the Tuck School?

Meanwhile the UK gives something like 5 years of work authorization for any MBAs from top programs (as determined by the UK government). No problem.

My worry is that companies, especially the very top employers such as investment banks, private equity funds, and consultancies, will migrate to a country like the UK so they have the pick of the world's best talent. The US will suffer as top companies leave. Is this one of the reasons why the City of London is increasingly the world's financial center?

Our First Hobie Pitchpoling Experience!

It is Memorial Day 2007, and there was a good 15mph west wind, so my two boys and I went out to the lake to sail our Hobie 16 -- here is a picture of it.

We got this boat this winter, just rigged it for the first time on Saturday, and took two brief sails on the weekend. Not a lot of wind on those first trips out. Today was different, the wind was really blowing. We got out and were having a great time, with the boys taking turns going out on the trapeze.

I was just thinking I should take my hat off before losing it when the wind really started howling. Nice whitecaps were picking up, which on an inland lake means a pretty good blow. Then followed a series of errors. I saw the leeward hull starting to go underwater, and I figured that meant trouble. I told my older son to go forward, when I should have said move aft! He was also holding the mainsheet, and kept it nicely sheeted in. My youngest son was out on the wire, controlling the jib, and he had it sheeted in so it was giving us a lot of power. I think I might have turned downwind a little as well, accidentally.

Anyway, that leeward hull dug in deeper at the same time the wind picked up even more. All of a sudden, we were in a slowmotion pitchpole! The back of the boat came up, the hulls dug in, and over we went! My youngest son went for a ride up by the forestay, as he was still on the trapeze wire. I came down on my middle son's leg, and somehow I got my own leg twisted up in the jib sheet. That gave a little excitement as I lay in the water with my leg caught up in some ropes above my head. I have a nice rope burn on my shin and lost a good bit of hair. Anyway, I looked around and saw that we were all OK, although somewhat shocked.

So there we were in the middle of the lake, with the Hobie on its side and the three of us in the water. I had read about righting a Hobie, and we had a righting line (thanks to the seller of the boat for that one!) but of course reading how to right a boat is not the same as actually doing it...especially when you have just had the shi#&* scared out of you. But we all hung on the righting line and waited, and sure enough, the boat flopped back over. We jumped up, and I yelled, "Sheet in and feel the magic!" Away we went...with a little more caution.

The nice thing is, we won't be afraid of pitchpoling again, and we know how to right the Hobie. It was actually pretty fun, definitely character building. As someone once said, "It isn't a sport if it can't kill you."

Sustainability Coordinator Wanted/ Takeover Needed

Our local grocery store in Hanover is the Hanover Consumer Cooperative. It is a great store, with good selection of fresh fish, an in-store butchery department, and nice organic produce. They even had Copper River sockeye salmon this week, at $15 per pound. The only problem is that they sometimes venture a little too far into the liberal realm, like now.

The Coop is now advertising for a person to serve as Sustainability Coordinator. You have to be kidding. A GROCERY STORE, which should be operating on the thinnest of margins, wants someone to work on, among other things, "coordination with other organizations on collaborative sustainability programs."

This will probably cost the organization something like $60,000 per year, inclusive of benefits.

It is fun to dream about taking over the Coop and putting a for-profit enterprise in its place. The local market would still demand great food, and I bet we could get it at lower prices than the Çoop provides. Now there is an idea most people would not think possible: That a for-profit enterprise, with its "need" for "unnecessary" profit, could actually provide a service at lower cost than a not-for-profit.

Monty Hall Revisited

My middle school son came to me with this twist on the famous Monty Hall/Let's Make a Deal probability problem. I am looking for the answer to the problem, and want the clearest most succinct explanation.

The original Monty Hall problem goes like this: There are three doors, and behind one is a prize. A contestant picks a door, but does not get to look behind it yet. Monty Hall, the master of ceremony (who knows which door holds the prize), opens one door, showing that there is nothing behind it. He then gives the contestant the chance to switch doors: The question is, should one switch?

(There are game theoretic aspects to this problem that are often ignored. Let's assume that Monty Hall ALWAYS opens an empty door and gives the contestant the chance to switch, no matter if the contestant currently has the right door or not.)

The answer is that one should switch doors. Not the most intuitive probability exercise for many people, but correct, given our parenthetic note above.

Now here is the twist. An exam in school will be either Monday , Tuesday or Wednesday, and the teacher has not said which. A student is assessing the odds of what day the test will be in order to study the night before. The day picked by the student is Wednesday, and she has arranged her schedule to study Tuesday night. Monday comes, and the teacher announces that the test will not be that day. So...should our student switch her pick, just like the contestant in Let's Make a Deal?