OWENSBORO, Ky. — How, exactly, did Congress manage to kick 4-year-old Carli Hopkins out of her preschool?

Carli asked after it happened. Her mother didn’t try to explain. The child was still too young to learn about politicians.

“Some kids get to go to school all the time. And some kids get to stay home with Mom,” Rebecca Hopkins told her. “And you are one of those kids.”

The real answer was the “sequester,” the $85 billion budget cut that Washington lawmakers designed to be such a stupid idea it could never come true.

Then, of course, it came true.

Now — as Congress considers a deal that would end this odd experiment in blind budget-cutting — it is possible to stand back and explain how it actually worked.

The cuts were supposed to cause equal pain across a broad spectrum of Washington programs. They didn’t. Lawmakers had declined to choose austerity’s winners and losers. But they were chosen anyway by a long national scramble in which programs from Head Start to the Pentagon sought to wriggle out of their share of the cuts.

The winners — those with stored-up cash to spend or powerful friends to help — avoided painful reductions in the sequester’s first year.

THE LOSERS … LOST

The losers did not. And this year, as the cuts trickled down from Washington to a preschool classroom in Kentucky, Carli Hopkins was at the end of a long line of losers.

Congress “didn’t make the hard choices. . . . They avoided the hard choices at all costs,” said Peggy Grant, director of the Head Start preschool program, who was forced to kick Carli out. “And we had to make the hard choices, again and again.”

Sequestration was intended as an across-the-board budget cut, reducing spending on national defense and non-defense programs. It was triggered after a special “supercommittee” — and then Congress — was unable to agree on a better plan to reduce the federal deficit.

So, after two years of intense fighting about austerity, the nation’s harshest spending cuts were adopted essentially by accident.

Congress is considering a deal that would replace these across-the-board cuts with something smaller. And, it is hoped, smarter.

Senate Budget Committee Chairman Patty Murray, D-Wash., and House Budget Committee Chairman Paul Ryan, R-Wis., have agreed on a plan that would eliminate about $45 billion of the planned cuts for the current fiscal year.

If this is the sequester’s end, its epitaph will be: This was a budget cut that could be beaten.

Today, a survey of 48 specific forecasts, made by federal agencies before the cuts took effect, shows that at least 27 of those predictions did not come true. There were no furloughs of FBI agents and prison guards. Furloughs of air-traffic controllers were canceled after a few days of flight delays.

But, in other cases, the reductions turned out to be as bad as projected: At least 12 predictions about the sequester’s impact came true. There were 700 fewer grants for research scientists. And, at Head Start, officials had to eliminate services for 57,000 children, including Carli Hopkins.

How did those groups lose, while so many others found a way out?

For Carli, the answer starts with bad luck. And a list.

The list was created by the 2011 law that laid out sequester’s ground rules. It decreed which programs would be exempt from the cuts, if they ever came. The list was largely cribbed from a 1985 law, and it exempted a number of programs that help low-income families: Medicaid, food stamps, Temporary Assistance for Needy Families. Head Start helps the same kind of people. But it was not on the list.

What was the thinking behind that?

The answer seems to be: In 2011, there was not much thinking at all.

The sequester bill “hit things that sort of — in the real world — we all knew nobody would really want to [cut]. Like the air-traffic controllers, and Head Start kids, and Meals on Wheels…,” said Richard Kogan, a budget expert who worked in the Obama administration until a few months before the agreement. But, he said, the details of the list didn’t seem to matter too much then. “Experienced budget hands say, ‘There’s not going to be a sequestration. There never has been,’ “ Kogan said.

Then there was.

After it took effect in March, some agencies with powerful friends began to nudge Congress to give them a way out.

At the Agriculture Department, officials issued alarming warnings about furloughs among meat inspectors. The meat industry lobbied. Congress gave in. Lawmakers provided $55 million in new money to keep inspectors on the job.

Head Start could have tried the same me-first tactics. It didn’t.

“There is a lot of goodwill about Head Start. And I imagine if we had chosen to say, ‘Just us! Us! Us! Us!’ we might have been able to get some action,” said Yasmina Vinci, executive director of the National Head Start Association. The group didn’t think that would be right.

Instead, the organization joined a massive coalition with one of Washington’s least catchy names: NDD (for “nondefense discretionary” spending) United. It has more than 3,200 members, including from the Soil Science Society of America and the Sexuality Information and Education Council.

APPROACH HASN’T WORKED

The only problem with this approach is that it hasn’t worked. Head Start programs nationwide received no relief from Congress. They had to cut at least $401 million of their federal funding for fiscal 2013.

So then, the trouble found its way to a red-brick building in the Ohio River town of Owensboro, Ky. Here, Grant runs a Head Start program that covers 16 counties and provided free preschool, free diapers and free food to 2,086 children. This is the rugged bottom of the federal safety net: A few weeks ago, a Head Start staff member took a parent permission slip to the Union County jail so a child’s mother could sign it behind bars.

Another mother told her son to steal beanbags from the play area. The family cut open the bags and cooked the beans.

In Owensboro, Grant did the math. She had to cut $856,232.

“We did a Survey Monkey,” she said. Everybody from the top officials to the bus drivers was asked to go online and suggest places to trim. Some of the ideas worked: The program no longer paid for staffers’ lunches. That was $120,000. They cut money earmarked for new school buses. That was $103,010.

When that was done, they still had to cut about $600,000.

This is the point at which many of the sequester’s other victims found a way out. Agencies used accounting maneuvers to shift the burden — instead of cutting people, they cut into rainy-day funds, training plans, building maintenance or money left over from past years. Grant, in Owensboro, had a problem right away. Budget rules prevented her from storing up money from past years. She had no rainy-day funds. “There was no alternative than to start cutting slots,” she said, describing a decision she made in the spring. “Kid slots.”

Grant said the decision “absolutely sent a spear through my heart.” For the fourth time, the winners had to be divided from the losers. In all, 164 of the program children would have to be kicked out in the middle of the school year.

There was, once again, a list.

“I just remember taking that list and having to walk somewhere,” said Patricia Chism, the Head Start staffer who had to deliver the news. Officials had decided which children would lose their slots, using Head Start’s ranking system. The poorest kids and the oldest kids got priority. Carli Hopkins was on the list. Her mother, who was working part-time and taking night classes at Owensboro Community and Technical College, had to stay home to keep her over the summer.

Today, Carli is back in class. When the Head Start school year started this fall, she was older — and higher on the list.

But about 100 other children who were kicked out of class are still out.