As someone who is trying to sell a new PhD on the market as opposed to someone who has tenure and is trying to sell a PhD-granting program to the government, I can state that the 50% number seems much closer to reality than the 3% number. But that's without using a Markov model.

Here's an analysis I did several years ago using the numbers from the Taulbee survey:

Q: Are you better off investing your dollars in a PhD or the Lotto?
A: It depends. Here are the details
Cost of getting a PhD: $150,000- $250,000 in tuition and barebones living expenses. Most of us in the sciences have this paid by the government. Many of us have "lost" income by going to graduate school because we gave up jobs that paid substantially more than the stipend. In my case I've "lost" about $150,000 to $250,000 in the deal.

The raw odds:
How many PhDs a year in Comp. Sci. (for example): 850-1000
How many Professorships in Universities: 35-70
How many Professorships in Colleges: 70-100 (estimate)

Chance of ending up in a Professorship after you do a few
PostDocs : 1 in 10 to 1 in 5

Odds of winning the Virginia Lotto is about one chance in 7 million.
"Investing" $250,000 in the Lotto gives you 1 chance in 28 of winning.
"Investing" $500,000 in the Lotto gives you 1 chance in 14 of winning.

So the odds of just "getting" a Professorship are still somewhat better.

But what about the Payoff?

Lotto: 20 year annuity where the winning amount (usually between 3 and 10 million dollars) is paid out annually. That comes out to between $150,000 a year and $500,000 a year.)

Professorship: $40,000 to $80,000 (when you get tenure at a top-flight university)

When you normalize for this, the substantially higher payoff of the Lotto starts equalizing things.

What about the Work Load?

Lotto: Posing for pictures for the Lotto advertisement agency. Answering questions of newspaper reporters. Fending off relatives who want a slice of the action. Talking to Robin Leach.

Professorship: Posing for pictures for the Alumni news agency. Answering questions of undergraduates. Fending off relatives who want help setting up their home computer systems.

Things are starting to tilt toward the Lotto, huh? If you can handle Robin Leach.

What about the downside?

PhD: Well you can still find employment in many different places. They may not care about your dissertation or give you the chance to do research, but you can usually fool people into thinking that
the PhD makes you smart. Is this job any better than the one you could have gotten with your BS degree? Who knows...

Lotto: You're broke and out of luck. Your only chance is getting your gambling declared a "disease" that should be covered by public health care. This would probably generate a bigger monthly check than your stipend.

The PhD is definitely a win here.

What about the cost in time?

Lotto: One week of gritting your teeth. Cost: negligible. You can still watch "Studs" or the "Love Connection" during this time.

PhD: 3-7 years of your life. No TV. No friends. Old people like to say things like, "Enjoy your youth. It's the best time of your life."

Yeah, but what about the knowledge?

Lotto: PhD in the school of life. Dissertation topic: "A fool and his money are soon parted."

PhD: Lots of great knowledge. Really. You can't discount this if you're a nerd. If you're even considering graduate school then you probably place plenty of abstract value and pride in understanding and applying the calculus of variations.

What is the lesson in all of this?

The odds are pretty close. The PhD gives you a much better downside if you're risk adverse, but the upside of winning the Lotto is substantially better. Note that my numbers were taken from Computer Science-- one of the "hot" fields.

If you're one of the people that feels that government money is just "funny" money that would have just gone for bombs, then the odds get a bit harder to compute. The whole deal is just a low paying job and you're only sacrificing lost income. If you don't have a job anyways, then graduate school is a pure win that doesn't really cost you anything. It's sort of like welfare for clean-cut, middle-class kids.

What if you're a scientist-- the type who does everything rationally by the numbers? This leads to a really deep paradox. The whole job of doing science is monetarily equivalent to "investing" in a gambling scheme where the odds are heavily stacked against you. Most scientists disdain gambling because they know the math. Why do they even bother doing science? Because they "love" learning. But everyone at Gamblers Anonymous "loves" the Lotto.