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