A staple of the stories written by Horatio Alger is sheer, wonderful luck. Our Hero stops a runaway horse and carriage. The frightened and, of course, grateful, passenger happens to be the beautiful daughter of a rich man. Our Hero is on his way to material success. He's industrious and brave. But mostly he's lucky. The passenger could have been the ugly daughter of a poor man.

That element of luck, undeniably important in anyone's life, is nevertheless essentially unfair. On a given day, a child will be born to poor ghetto parents, and another will come into the world heir to a fortune. To a modest degree, we count on government to inject some equity into life's unfair situations. Education is one area where we expect it to do so.

But luck -- the sheer luck of birth and even of location -- now plays an even greater role in a child's chances of getting a good education and especially of going to college. Nothing illustrates that better than the exemplary work of Eugene Lang, a millionaire industrialist. Six years ago, he promised a class of New York sixth-graders, all of them poor, that if they could get to college, he would pay for it. Twenty five of the original 61 students appear ready to take up his offer. They are college-bound.

Since 1981, Lang's idea has been emulated by others. Just recently, a Philadelphia stockbroker and his wife announced they would pay the college tuition of 116 ghetto kids, all of them now in the sixth grade. A Virginia real-estate developer has made a similar offer to students at a D.C. elementary school. In fact, more than 100 classes of mostly poor kids in 15 cities have been adopted by wealthy individuals. And it seems the offers have made a difference to these students. Drop-out rates are lower than usual and an astounding number of them seem headed for college.

But this is really a Horatio Alger story in both its best and worst sense. For the kids, the key element is luck -- the sheer good fortune to attend a school adopted by a wealthy person. Lang adopted P.S. 121 because it's his old school. Others have made their choices for similar reasons. But even if they had chosen by throwing a dart at a school-board map, the outcome would have been the same: based on nothing but luck, some kids have their college tuition paid while others, maybe a block away, do not.

The program initiated by Lang and copied by others has been widely, even lavishly, praised. This is an example, we are told, of that most wonderful of all things -- private initiative. The praise in this case is not just a reflection of conservative yahooism. Most of the wealthy people who have put up their money to provide college tuition have also become involved with the schools they've adopted and the kids who attend them. They counsel, they mediate, they encourage. Nothing takes the place of a single person who cares.

But nothing -- not even good-hearted millionaires -- can substitute for government's obligation to offer what some kids receive by sheer luck. Yet over the past six years, the Reagan administration has cut the federal higher education budget by an estimated $3 billion. What remains mostly are loans which, for the poor, are often daunting. Outright stipends for poor students, the so-called Pell Grants, are limited to $2,100 a year -- hardly sufficient to cover the cost of room and board, which often exceeds $10,000 annually. In an era in which the cost of obtaining a higher education has zoomed, the federal budget for it has been cut.

Much has been made recently of competition and productivity. Our country's ability to compete internationally reflects many factors, but certainly one of them is education. Yet the administration has met this national crisis with words, exhortation and bromides, such as the need to teach values. At the same time, it has attempted to gut the Head Start program for preschoolers and has made it harder for all but the affluent to send their kids to college.

The most important resource we have is the minds of our people. It is renewable. Unlike, say, copper or oil, it cannot be depleted unless we allow it to be. The tragedy is that we are.

Lang and other good people have moved to fill a financial void that should not exist in the first place. A student's higher education should not depend on the benevolence of an alumnus or the charitable caprice of a wealthy person who may later turn to other interests or run out of money. Even in an era of limited government, when it comes to education, Horatio Alger stories are not uplifting. They're tragic.