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One million people enter a coin-flipping contest. The winner becomes a Supreme Court Justice. Everyone flips at once, and you live to flip again if your coin lands on heads. Statistically, it will take about 20 flips to crown our champion. That is because the odds of flipping a coin 20 times and landing on heads each time is one in a million.

Of course, lower probability outcomes would be possible. So 20 flips is just a statistical average, not the number that it will take every time. Because we are using the contest (and its math) as a metaphor, let's just go with 20 flips.

It would be a strange way to pick Supreme Court Justices (but see William F. Buckley, who was fond of saying that he'd rather be governed by the first 2,000 people in the Boston phone book than 2,000 Harvard professors), but it is not terribly different from what actually happens, given the long odds facing anyone who aspires to our highest court.

To begin with, no one has a realistic chance of becoming a Supreme Court Justice without being born with whatever innate gifts are necessary to permit extraordinary academic achievement later in life. Okay, science has not yet wrestled down what those things are. At present, the assumption is that intelligence is the product of some combination of nature and nurture. But no thoughtful person believes any longer that it is all nurture. So how many heads do you allocate to the gratuitous good fortune of being born with a brain that one day will allow you, not just to get into Yale Law School, but to be a star there, to be at or near the very top of the class? I'm going with eight.

And of course, you cannot just be brilliant. You have to be capable of working hard. We all know extremely bright people who prefer video games to reading Virgil in the original Latin. It truly does not matter how smart you are, you will not make it to the top unless you can put that intelligence to good use, and that means hard work. Maybe the ability to work hard is more nurture than nature. Whatever it is, it is still damn lucky. I give it two heads.

It is well known that high intelligence is correlated with mental illness. Brilliant people suffer from depression and other mental health disorders at rates higher than the population at large, which can derail a promising career at any point in its trajectory. In the modern era, it is not even necessary that the disorder inhibit performance to be disqualifying. Just the fact that one has been treated for such things can be enough (see Edmund Muskie, Thomas Eagleton). For the contrary proposition, people often point to the fact that Abraham Lincoln probably had a major depressive disorder. If he were alive today he would have been hospitalized a time or two and would be on stabilizing meds. Thus would the country be deprived of perhaps its greatest President. The sheer luck of not facing a disqualifying mental illness during one's life is worth, in my opinion, two more heads.

To be a serious contender for the Supreme Court, you must come to the notice of important people who will promote your career at propitious moments. This cannot happen only once. You must be noticed, and passed up the chain, a number of times. Yale Law School will have 10 students at the time of your graduation who are as academically talented as you are. Not all of them will get Supreme Court clerkships. Some professor of consequence must whisper in an ear for you. Then political heavy weights must do likewise several times during your post-clerkship career until you make the list of serious contenders from which the President will choose at the appropriate moment. This means that you are that rare bird who is both shockingly brilliant and so personable/attractive/connected that powerful people will want to see you promoted, typically beyond the hopes and aspirations that they harbor for themselves. The magnitude of this bit of luck is second only to your innate cognitive potential. I give it four heads.

And once you make that list, you will compete with 20 other people who have landed 16 heads. In order to be picked, you must match some profile that the specific moment requires. That profile changes moment by moment, as the political winds swirl and presidential advisors debate what they need: a member of a specific demographic group, a person identified with a cause near and dear to the political base. On top of that, you will not be on the list long. They like young people who will serve for decades. The next administration will have its own list. You are on the list for one presidency, probably not that long. You must be on the list when there is an opening and catch a fickle wind just right to be selected. Three more heads.

Nineteen heads. One more coin to flip. The Senate must approve you, but the political party of the President who picked you is in control. You are at 29,024 feet. To take your place among the 113 others who have scaled that mountain since the founding of the Republic, you need only reach up and touch the summit. Immortality. You are handed the coin.…

Samuel J. Samaro is a partner with Pashman Stein Walder Hayden in Hackensack.