Inside a sun-splashed classroom, George Kaiser folds his lanky frame into a tiny plastic chair next to a blue mat. For the dozen-plus 3- and 4-year-olds sitting on the mat in various stages of squirming, it’s afternoon story time.

Mr. Kaiser is the billionaire benefactor behind this and other preschools for the poorest children in Tulsa, Okla., and he’s the reason why this classroom looks the way it does – cozy nooks, fairy lights, play kitchens, books everywhere – and has two certified early education teachers. As one of them reads “The Gingerbread Man,” Kaiser’s face has the rapt look of a child waiting for the page to turn.

He’s been here before. He’s brought US lawmakers and presidential candidates into the classroom and plied them with data showing the effect of early education on at-risk kids.

Still, he never seems to tire of the attentive faces, the happy hubbub. One of the kids, a smiley African-American boy in a striped polo shirt, is too antsy to sit for long, so he gets up and runs over to the tall visitor in the gray suit, who stretches out his arms for a hug. The boy leans into Kaiser’s lap, and the two listen to the story of a runaway cookie’s comeuppance.

Cheryl Remache, a local mother, recalls a similarly personal encounter she had with Kaiser. A few years ago, she broke down and sobbed at a preschool board meeting because one of Kaiser’s schools had taken in her two autistic sons. He came over and hugged her. “We wouldn’t be where we are today without him,” says Ms. Remache, her eyes tearing up again.

Her younger son, Jayden, is now in sixth grade and a member of his school’s debating team. Remache says the preschool was the building block that helped him succeed. “This is not a drop-off babysitter. This is education,” she says.

If it seems as if Kaiser is everywhere in this former “oil capital of the world,” helping and hugging people, it’s because he is. The deep-pocketed philanthropist is involved in preschools and elementary schools, industrial parks and recreational parks, artists’ lofts and folk-singer museums, parenting classes and prisoner rehabilitation programs. He has, in fact, turned Tulsa into perhaps the country’s most ambitious test bed for the power of philanthropy to tackle poverty at its roots.

Across the United States, millionaires and billionaires are increasingly stepping in with private money to try to solve problems that were once largely or exclusively the purview of government. In Detroit, philanthropic dollars helped build a streetcar system. In Kalamazoo, Mich., donors are underwriting college tuition programs. Elsewhere, philanthropists are funding the mapping of all cells in the human body to try to stamp out disease and pouring money into preventing obesity.

Yet few if any of today’s megadonors are involved in as many programs targeting the poor in one city as is Kaiser. The oil and gas industrialist believes that every child deserves a chance to succeed and that effectively spent charitable dollars – his and others’ – can unlock their potential. His foundation has given away more than $1 billion over the past decade, almost all of it in Tulsa.

“God bless George Kaiser. That’s all I can say,” says Dewey Bartlett Jr., a former two-term mayor of the city.

Kaiser’s next act will be his most audacious. Over the next decade, his foundation wants to target every poor child born in Tulsa, from birth until third grade, so that a patchwork of public programs – prenatal care, parenting classes, child care – becomes a seamless quilt. The strategy reads like a welfare program from Denmark. But it’s being piloted in the reddest of red states, where limited government is a way of life.

Funding will also come from a national network of philanthropists eager to see if Kaiser’s model works. “They’re making a very big bet in one community on a comprehensive strategy that can be truly transformative,” says Nancy Roob, chief executive officer of the New York-based Edna McConnell Clark Foundation. “It’s one of the most robust of its kind anywhere in the United States.”

The idea behind all these efforts – fighting poverty with philanthropic wealth – is one that holds great promise in an era of dazzling private fortunes, yawning economic inequality, and public-sector austerity. But it comes with caveats: greater reliance on the whims of the wealthy and a potential erosion of oversight by elected officials. It also raises the question of what happens to poor communities that don’t have a rich benefactor.

Is Kaiser a glimpse of salvation for America or just a saintly anomaly in one city?

Kaiser is a tall man with a thinning shock of gray hair, an irrepressible demeanor, and a patrician air. To hear him tell it, in his Great Plains drawl, his generosity stems from “Jewish guilt” and a debt of gratitude owed to Tulsa. His father, Herman Kaiser, a German judge disbarred by the Nazis, immigrated here in 1940. Herman joined his uncle’s oil and gas company, which became Kaiser-Francis Oil. George was born two years later, the first US citizen in the family.

Growing up in Tulsa, George sensed the social change in the air. Public schools were desegregating; “colored only” signs were coming down. The whites-only country club invited Jews to join. Herman refused, believing it was a token gesture, and George hasn’t forgotten it. “I’m still uncomfortable going there,” he says.

George went to Harvard University and studied politics and international relations. He briefly considered a diplomatic career. Instead he went to business school and in 1966 moved back to Tulsa to join the family firm. Three years later his father suddenly fell ill (he would live another 23 years). George took over the company and led it through the turbulent ’70s.

But it was banking that catapulted Kaiser into the ranks of America’s richest. In 1991, he bought a Tulsa bank that was in federal receivership, one of dozens of failed lenders. Having served on its board, Kaiser knew it had potential and he led the revival of what became the Bank of Oklahoma. At the time, it had $1.8 billion in assets. Today it has $33 billion, and Kaiser is its largest shareholder. Bloomberg estimates his net worth at $12.5 billion.

Kaiser’s shift to philanthropy came gradually, from writing checks to local charities to setting up a community foundation in 1998. In the past, Tulsa had “a lot of major corporations and a lot of wealthy people, largely in the oil and gas industry. Those people had moved to Houston or retired,” he says. Kaiser began thinking about the most effective way to help the city’s disadvantaged residents.

By this time, he had read new medical research into brain development. He began to ask, what if the biggest barriers to social mobility are in plain sight, waiting to be broken down? Could this help to repair the American dream of equal opportunity for all?

The key conclusion, says Kaiser, is that experience determines the development of cognitive and social and emotional abilities in children. “What that means is that rich, smart parents have rich, smart kids not because of genetics but because they also hold their kids and read to their kids and put mobiles over their cribs,” he says. “What that means is that you can fix it.”

He smiles. “I don’t have epiphanies, but that’s as close to an epiphany as I came.”

This led Kaiser to scour the country for state-of-the-art programs to provide intensive nurturing to poor children from as young as 6 weeks. In 2006, Tulsa opened its first Educare, a nonprofit preschool, paid for by the philanthropist. The city now has three, and a fourth will open in 2019. Most of the teachers come from early education programs at the University of Oklahoma-Tulsa and Tulsa Community College, programs underwritten by Kaiser.

Each Educare has fewer than 200 students grouped in small classrooms taught by specialists. They have the look and feel of a private preschool in an elite ZIP Code. But every child is at or below the poverty line, and on Fridays, as nap mats are stowed in cubbyholes, paper bags of donated food are discreetly left for the neediest to take home. A sign on the wall reads, “Embrace. Empower. Evolve.”

Kaiser had settled on his first antipoverty fix. But his philanthropy would keep evolving.

It’s opening night at Tulsa’s annual film festival. Inside the lobby of a restored 1920s theater, Nathan Young, a bearded man in a faded denim shirt, stands in front of a blank screen. “I want to thank everyone for coming tonight,” he says, blinking at the modest crowd.

On the exposed brick walls hang several large photographs of Native American men whose eyes are blacked out, surrounded by objects used in peyote rituals. Mr. Young explains that the images are part of “Infinite Peyote Road,” a multimedia show that reimagines the persecution of the sacred.

Young is a Tulsa Artist Fellow, which entitles him to housing and studio space downtown and a $20,000 stipend, all underwritten by the George Kaiser Family Foundation (GKFF). “Cities thrive on artists,” says Julia White, who runs the fellowship. “They’re the social activists, the creators who go out into the community.”

The fellowship is one item in Kaiser’s expanding cultural portfolio. As a patron of the arts – a familiar role for philanthropists – he is more wildcatter than Medici, exploring for a cultural cachet that can help Tulsa outrun other hardscrabble heartland cities in attracting young talent.

Sure, other cities may have baristas and bike lanes, yoga studios and hiking trails. But do they have the Woody Guthrie Center? An archive of his music? A repository for Bob Dylan’s works? A 100-acre riverfront park with adventure playgrounds and a boating lake? Tulsa does, or soon will, thanks to Kaiser.

The Bob Dylan Archive, acquired by GKFF last year for a reported $20 million, will eventually open to the public at a downtown site near the Woody Guthrie Center. (Mr. Dylan, who idolized Guthrie, visited the center last year.) For now Dylan’s trove of notebooks, films, and recordings are housed at the Gilcrease Museum in Tulsa and open to scholars and Dylanologists.

Kaiser is not one of them (“I predated both the political and the sex, drugs, and rock ’n’ roll time” at college, he says). He likes the social justice message in Dylan’s songs, but he’s buying into him as a means to an end: making Tulsa the next hub of Americana cool. And that, in turn, is good for the economic prospects of the city’s neediest households.

“A vibrant community can provide better for all members of the community, and there are certain things you need to be a vibrant community,” he says.

GKFF has even bought derelict land in North Tulsa and worked with the city to develop it and look for investors to build factories, hoping to generate jobs and training for local residents. It’s an unusual role for a charitable foundation: economic development agency.

Courtesy of Nick Goodwin A Gathering Place for Tulsa, a park for families with everything from a giant ‘Reading Tree’ to fly-fishing fountains, is being built with major private funding.

While cities from New York to Detroit have tapped private donors to build public parks, none compare in scope and generosity to A Gathering Place for Tulsa. GKFF alone has committed $200 million in land and capital to design, build, and run the park. It has raised an additional $150 million in private donations to go along with a $65 million investment in public infrastructure.

Today the site is still a blur of diggers, dirt berms, and half-built playgrounds. Giant castles and animals loom over curving pathways. Kaiser reckons that American kids are too cosseted from risk-taking play and has imported equipment from Germany that will no doubt excite injury lawyers. There are also mirrored mazes, a massive cottonwood “Reading Tree,” and flying-fish fountains.

Kaiser loves that kids from across the city will mix at the park. It’s another selling point for Tulsa, which helped him tap corporate donors. But he still hesitates at the ballooning cost, the dollars not going to programs that directly improve a poor child’s well-being.

“I can’t really justify it,” he says.

Other donors might sit back and bask in the civic acclaim. Kaiser, who works 95-hour weeks, is too busy looking at spreadsheets to see if the data support his programs’ goals, whether it’s time to invest more or cut funding. That arithmetic is what drives his philanthropy, he says, not the warm buzz of story time in a classroom. “Without evidence, it’s an emotional response,” he says.

Indeed, Kaiser possesses a restless mind. He reads widely, from medical journals to economic surveys, and displays an uncanny recall of historical facts and granular data, all salted into analytical sentences delivered with a professorial tone. He has the air of a striver who knows he’s one of the smartest guys in town, but who still stops to ask: But what if I’m wrong?

Kaiser applies a cost-benefit lens to his own lifestyle, too: He usually flies coach, wears a $12 watch, and hunts for a cut-rate hotel room. Forbes called him “one of the world’s most understated billionaires.” Susie Buffett, a philanthropist who led Kaiser to Educare (Nebraska, where she lives, now has three), says he is “cut from the same cloth” as her famously unflashy father, Warren Buffett. “My father is a huge George fan,” she says.

Ms. Roob says Kaiser’s analytical bent comes with a dose of empathy. “What it takes to make someone effective in philanthropy is having the right partnership of head and heart,” she says.

Ann Hermes/Staff Ebonie Carroll (l.), Kelsey Lipp (c.), and Shay Veloquio (r.) chop ingredients during a cooking class at Women in Recovery, a treatment program for nonviolent female offenders in Tulsa.

Educare came too late to Tulsa for Kelsey Lipp. As an infant, she was neglected by her teen mother, who struggled with methamphetamine addiction, and abused by her father and stepfather. “I couldn’t trust anyone,” she says. “I knew I had to take care of myself.” At age 14, she ran away from home and was held for more than a year by a man who, she says, repeatedly forced her to have sex.

After her escape, she hid the truth from her family, dropped out of school, and turned to drugs. At 19, she found out she was HIV-positive, which led her deeper into meth addiction. “I felt my life was over,” she says. To feed her habit, she stole. Last July, a botched home robbery led to her being shot in the leg while driving away. In February she was arrested at her grandparents’ house. “I knew I was going to jail and I was angry about it,” she says.

Today Ms. Lipp, who is 22, is out of jail and enrolled in Women in Recovery, an 18-month program of drug rehab, therapy, and life skills and career training. Oklahoma leads the country in locking up women, mostly for drug-related offenses. By focusing on mothers facing prison sentences, the program tries to both rescue the women and prevent their children from taking the same path.

Kaiser started the program in 2009. He likes to point to the subsequent drop in Tulsa’s female prison admissions, compared with the statewide trend, as a measure of its efficacy. It’s also a much cheaper alternative than locking people up, given the lower rate of repeat offenses by women who stick with the program.

The initiative has gotten government buy-in: In April, Oklahoma signed a “pay for success” contract that will reimburse Women in Recovery for each individual it rehabilitates. State officials praised the arrangement as beneficial to taxpayers, especially at a time of “fiscal duress.”

A decade of tax cuts and fitful economic growth has resulted in nearly $1.2 billion in state budget cuts. Oklahoma’s per-student K-12 spending has shrunk by more than one-fifth, the deepest of any state, and dozens of schools have adopted four-day weeks to save money. The state is still struggling to fill a $215 million budget deficit in 2017-18.

For philanthropists making ambitious investments in helping the poor, such austerity poses a dilemma. Simply put, there’s not enough private capital to replace public dollars. And the long-held idea of philanthropists as risk-taking pioneers – what Kaiser calls the “R&D shop” for government – seems to work best when policymakers are willing to step up and fund worthwhile initiatives.

In 2010, Kaiser signed the Giving Pledge, a campaign led by Bill Gates and Mr. Buffett to persuade the ultrarich to give away most of their money. Like Buffett, he has called for higher taxes on the wealthy. Once a registered Republican, Kaiser swung hard to the Democratic side and raised money for the presidential campaigns of Barack Obama and Hillary Clinton.

Ann Hermes/Staff Tyson Fowler, who attended a Kaiser-funded preschool, now goes to a magnet school in Tulsa.

The ultimate test of how much his money can help the poor may come with his Birth through Eight Strategy for Tulsa. Since Educare and other quality preschools don’t have enough places to serve all of the city’s impoverished children, Kaiser wants to build out a continuum of social services to ensure that more kids are born and raised in nurturing homes.

About half of all students in Tulsa public schools enter first grade behind in math and reading. The program aims to increase kindergarten readiness and third-grade test scores. Advocates will start by targeting expectant mothers with prenatal programs and connect them with services for their children. Within a decade, it hopes to serve 32,000 low-income kids. GKFF is providing most of the estimated $200 million in private funding, along with Blue Meridian Partners, a network of individuals and foundations to which GKFF belongs.

Once implemented, GKFF believes the program will become a national model. Kaiser sees it as a way to give back to Tulsa, and, because the initiative is local, he can measure its results better than, say, those of a health-care project in India.

And Kaiser does like to gauge the results of his giving. He is not like many megadonors: He doesn’t just give money and then let others run their do-gooder projects. Both he and his staff at GKFF go deep into the operational weeds, designing, testing, and tweaking programs, and collecting data.

When the foundation opened the first Educare, Kaiser himself picked out the carpet colors and paints. “Attention to detail is a hallmark of George’s,” says Steven Dow, executive director of CAP Tulsa, a nonprofit that runs other Kaiser-funded preschools.

That engagement and the sheer breadth of Kaiser’s business and philanthropic interests has burnished his image as Tulsa’s kingmaker. It also means a steady stream of supplicants to his door inspired to “go talk to George,” as he puts it, about a project or investment. Yet none of Kaiser’s projects are named after him. There is no George Kaiser school in Tulsa. This is both modesty – “I don’t need a legacy,” he says – and savvy marketing: It allows him to sell naming rights to other donors.

Kaiser says he works hard to involve other private and public players so that his pledges don’t become an excuse for politicians to shirk their responsibilities. Local officials say Tulsa is fortunate to have Kaiser and other local benefactors, but insist that the boundaries between public and private sectors should remain clear, too. “There’s a tendency in the community that every need that people see that they don’t know how to pay for, well, we should just talk to the Kaiser [Family] Foundation,” says G.T. Bynum, Tulsa’s mayor. “But if it’s something that the city should be paying for, then I think the city should pay for it.”

As Kaiser spends down his vast fortune, the debate over his impact on Tulsa is likely to grow. The strategies that his foundation pursues, from prenatal services and early childhood education to criminal justice and cultural tourism, may have equal if not greater weight than any bond issue or city council resolution. Should Kaiser take a wrong turn, Tulsa presumably would, too.

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That tension between the vision of big donors and the fortunes of the communities they’re supporting is as old as philanthropy itself. Compared with politicians, the ultrarich are freer to put bold ideas into practice, for better or worse. “It’s like electricity: Great wealth can burn your house down or make the lights go on,” says Paul Schervish, professor emeritus at Boston College and an expert on charitable giving.

Kaiser believes that he can make the lights go on in Tulsa. It might just take a generation before the children growing up today – including those sitting on a blue mat in a preschool – will see the effects on their lives.