Parents of prospective students who win the lottery to get into a Success Academy school are greeted with “more of a warning than a welcome.”

“It’s not Burger King. You can’t have it your way,” one principal, Shea Reeder, told moms and dads in the first meeting before kids enroll. “It’s all or nothing. Nothing is optional!”

Yet the eagerness of many low-income families of color to embrace Success Academy’s “no-excuses” methods helps explain its amazing achievements, author Robert Pondiscio says in his new book, “ How The Other Half Learns: Equality, Excellence, and the Battle over School Choice .”

His book is filled with secrets and surprises as it explores myths surrounding the controversial charter-school network, where test-prep is intense. Pondiscio saw one student vomit all over his desk during the last practice exam. But when the results come in, kids’ self-confidence soars.

Success Academy’ “scholars” crushed the competition again this year on New York state math and English Language Arts exams.

Of 7,405 Success Academy kids in grades 3 to 8 who took the exams, 99% tested proficient or higher in math, 90% in English. By contrast, in schools run by the city Department of Education, 46% of students passed math, and 47% English.

They also outscored several affluent Westchester and Long Island school districts. For instance, Success Academy, with 94% black and Hispanic students from families with an average $49,800 household income, beat Scarsdale public schools, where 8% of kids are black and Hispanic, and the average family income $291,542. There, 88% passed math and 85% English.

How does Success Academy, which runs 45 NYC charter schools with 17,000 students, produce such results?

“They do it by starting with a very exacting, demanding school culture that parents sign up for,” Pondiscio told The Post.

Pondiscio, a veteran journalist, senior fellow at the Thomas B. Fordham Institute and a former fifth-grade teacher at a city-run Bronx public school, got permission from Success Academy’s powerhouse founder Eva Moskowitz, a former City Councilwoman, to “embed” in one of her schools in 2016-17. He spent hundreds of hours observing classrooms, as well as faculty and parent meetings.

In introducing Success Academy to parents, Pondiscio writes, Reeder promises that kids will learn to think critically, get prepped for college, and never fall between the cracks: “We will support your child in every way.”

But that doesn’t mean going soft on discipline.

“We do not tolerate hitting, biting, kicking, fighting, anything,” Reeder goes on. “And we suspend kindergartners if they do that. If you have a problem with that, this might not be the school for you.”

Moskowitz calls the relationship between her schools and parents “a marriage,” Pondiscio writes.

Parents sign a “contract” pledging to abide by all Success Academy policies and values. They must get their kids to school at 7:30 a.m. — busing is not provided — in the right uniform from head to toe.

On the first day of school at Bronx 1, one mom with a neck tattoo of Mickey Mouse was irked her child was turned away for wearing the wrong color socks, black instead of navy, Pondiscio observed. “I got an infraction,” she griped.

Parents are expected to read six books aloud to their children each week through second grade, and monitor and log their kids’ reading assignments through high school.

“You’re responsible for making sure they know their spelling words. You’re responsible for making sure they know their math facts,” lectured Bronx 1 Principal Elizabeth Vandlik, the National Blue Ribbon school where Pondiscio spent most of his visits.

Staffers speak with parents on a regular basis. When testing season gets underway, teachers may call home “every night, every night,” to discuss a child’s progress and “strategy,” one dad told Pondisicio. If the parents didn’t answer the house phone, the cellphone rang, followed by a text, an email and another call.

“I thought it was overwhelming,” the dad said. “But then I’m like, ‘This is really good. This shows they care.’”

Among the most surprising things Pondiscio learned, he said, is that many families who win admission in the lottery wind up not enrolling.

“The conventional wisdom is that Success Academy has six applicants for every seat. It’s closer to 50/50,” he told The Post.

While 3,000 families were picked by lottery in the spring of 2017, another 6,000 to 7,000 applicants were put on a “likely list,” Pondiscio found. He met a mom whose son was No. 106 on the waiting list — but finally got in.

This happens, Pondiscio writes, because Success Academy requires so many preliminary steps and meetings that only the most motivated parents sign on.

“They’ve got to show up, show up and show up again to ensure they remain active in the enrollment process,” he said. “By the time August rolls around, parents are walking in with both eyes open– 100% down with the program. If they aren’t, they fell away.”

The result: a parent body dominated by active, involved families,

“The myth is that Eva Moskowitz is creaming students,” Pondiscio said.

“I don’t think that’s true, but she certainly is creaming parents.”

While critics say this gives Success Academy an unfair advantage, Pondiscio agrees, but notes that affluent parents also “self-select” when they flock to private or suburban schools. Poor or working-class people also deserve options, he notes.

But Pondiscio says “you can’t dismiss” another charge — that Success Academy gets rid of kids it finds too difficult. A damning New York Times report in 2015 revealed a principal’s “Got to Go” list of 16 students to be pushed out of his school in Fort Greene, Brooklyn. He was reprimanded.

Pondiscio tracked the case of a troubled boy, “Adama,” who frequently disrupted the class with his misbehavior and meltdowns — once standing on a chair and screaming.

One day, Adama was gone. ​Pondiscio met his mother outside the school and heard a “deeply troubling” story. She claimed the school had pressured her to withdraw Adama and enroll him in a public school where he could be in a “more restrictive classroom environment.” Worse, he wrote, the school had called 911 about a dozen times to have an ambulance take Adama to the hospital because of his behavior. The conflict between the family and the school grew so combative that Success Academy called the city’s agency that investigates parental abuse and neglect, the parents said.

“We serve many children who experience emotional trauma, and we must sometimes and repeatedly get paramedics involved to ensure that children get the treatment they need,” spokeswoman Ann Powell said.

Another Times story in 2016 dropped a bomb when it published a secretly recorded video of a teacher berating a first-grader and exiling her to a “calm-down chair.” Success Academy suspended the teacher for two weeks, calling the incident “aberrational.”

Pondiscio says he never witnessed cruelty, though teachers he observed could be stern.

“Tough love,” he found, a pattern of “high expectations, warmth and encouragement” overall.

“You cannot spend time watching these teachers and think anything other than that they are profoundly invested in their kids,” he said.

Pondiscio dubs it “the GAS factor,” which stands for “give a shit.”

The teachers, he found, are “mostly very young,” twenty-somethings, but Moskowitz has “figured out a way to get new teachers good, quickly,” he says.

Success Academy uses the exact same curriculum for each grade, so teachers don’t have to spend hours devising lessons — like city teachers do, Pondiscio said. “They spend all their time preparing how to best teach the lesson and going over students’ work.”

Supervisors heavily critique the staff. “Success Academy teachers get more feedback in their first week on the job than I got in five years teaching in the DOE,” said Pondiscio, who worked at PS 277 in the Bronx.

But teacher turnover is very high, Pondiscio says. “I don’t think I could teach there. They make extraordinary demands. There’s no pussyfooting around. You live and die by the data. It’s an intense, aggressive, performance culture.”

Some students leave, move or transfer along the way. Pondiscio says low-income Success Academy families move less than similar families in DOE schools, but leave at a higher rate than kids at competing charters.

This year, 30 out of 310 Success Academy students who took the entrance exam for the eight specialized high schools were accepted by one. Two are going to Stuyvesant HS, two to Bronx HS of Science, nine to Brooklyn Technical, and three to La Guardia HS for the arts, which requires an audition or portfolio.

In June, Success Academy graduated its second high-school class, 26 seniors, boasting that all are going to colleges including the University of Pennsylvania, Tufts, Howard University and many SUNY campuses.

But whether the Success Academy model is truly effective won’t be clear for years, Pondiscio said.

“It will take a decade or more before we can say if this brand of education helps people of color become upwardly mobile and leaders in their fields, closing the ultimate achievement gap in American life.”