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The envelope is big and glossy and opens wide, like an Academy award announcement. Inside, the news: Our son has been accepted to Selective University. He, and we, are thrilled — he’s had a few yeses already, but this is by far the most promising, from a highly regarded institution with academics, location and a campus vibe that are just what he’s hoping for.

While he Snapchats a picture of the envelope, I read the letter more carefully. Blah blah achievements, talents, capabilities, blah blah intellectual challenge, civic engagement. Not what I’m looking for.

A separate page lays out the financial aid timeline. Still not what I need — having been through college admissions once before with our older son, we’re already on top of the financial aid process in all its complicated glory.

I ask my son to log into the university’s admitted students’ portal. Again, nothing.

Finally, he emails the admissions office: Will merit aid be announced later? The answer comes back almost too quickly: If there was no mention of a merit scholarship in his acceptance letter, then he’s not getting one.

And just like that, a yes becomes a no. Because tuition, room, board and fees at Selective U are $64,800. Per year. The $5,500 in federal student loans, which is what we can expect in financial aid, will put only the tiniest dent in that number. So, except for bragging rights, that school is off the list.

Why allow our son to apply to colleges we can’t afford? Because, like tens of thousands of other high school seniors and their families, we’re playing Merit Aid Roulette — the maddening, often disappointing, but occasionally wildly successful game where families try to get schools to knock $10,000, $20,000 or even more off the annual price of tuition.

Colleges and universities have only limited leeway in awarding financial aid, which is need-based, as determined by the Free Application for Federal Student Aid form and, as a sometimes supplement, the College Scholarship Service Profile.

By contrast, merit aid is entirely discretionary. Colleges and universities use it to attract incoming freshmen with superior test scores and high grade-point averages. In turn, those statistics raise the school’s academic profile and its competitiveness in the market.

Two-income families like mine, which often earn too much to qualify for much federal assistance, look to merit aid to fill in the gap between what the government thinks we can pay and what we can actually pay. We hope merit aid will help us avoid taking out a parent education loan, which has a high interest rate and Draconian repayment rules. And, yes, we use merit aid as a way to make affordable the small classes, individualized instruction and brand-name cache of a private school.

The tricky part is figuring out which schools will find your child attractive, and to the tune of how many thousands off the sticker price. Awards are typically offered to a top percentage of the overall applicant pool, but the makeup of that pool can change, sometimes radically, from year to year. A superstar student one year may be only average when compared to the next year’s crop of applicants.

What’s more, institutions throw other factors into the merit mix — diversity, gender, location and artistic or athletic talent. All of which leaves high school seniors and their parents unclear on where they stand with a given school until the acceptance notification arrives — with or without that second, precious piece of paper.

“During the college search process, a family really doesn’t know if their student will receive a merit award from a particular college — or any aid for that matter,” says Paula Bishop, a certified personal accountant and longtime financial aid advisor in Bellevue, Wash.

Given the volatile nature of the merit aid slush pile, it’s natural for parents and students to think they can lobby a school for more money, but Bishop estimates that technique only works 5 to 10 percent of the time. “It’s a long road to get a college to up their merit award — I see success only on rare occasions,” she says.

Families are welcome to play Merit Aid Roulette, Bishop says, so long as they’re prepared to come up short. “I try to tell parents that sometimes they can’t have something they cannot afford, and neither can their student,” she says. “The goal is to find colleges that fit the student’s academic and social needs, as well as the family’s financial budget.”

As of April 1, college acceptances have all been distributed. With help from us, our son chose his list pretty carefully, with no “reach” schools that would only break his heart with a rejection (we’ve been down that road before). That means that, of the 14 schools he applied to (this is a game where volume matters), he was denied by only one.

But, as we feared, a good chunk of those acceptances are yeses on paper only. The numbers can be dizzying: Of the schools on his list, annual tuition, room and board ranges from $13,260 (at one of three state schools he applied to) to $65,890, and merit aid logs in between $0 and $25,000.

Which leaves us doing what thousands of other middle-class families are doing as we hurtle toward the end of the month, when students must commit to a school: Huddling over spreadsheets and poring over offers to get to a yes that we can say yes to.

Tracy Mayor has published essays and articles in The Boston Globe Magazine, Boston Magazine, The Improper Bostonian, Child Magazine, Writer’s Digest, Brain,Child, Fitness and on Salon.com. She lives outside Boston with her husband and two sons. Find her at tracymayor.com or on Twitter  @MOMMYPRAYERS.

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