Jeff Bulington was new in town. He'd recently arrived from Memphis on a mission to teach chess to the children of Franklin County, Mississippi, when a man in an SUV spotted him. The man stopped the car in the middle of the street, got out, and approached Bulington, saying "I know everyone in this town, and I don't know you." Bulington explained who he was, and the man responded, "Oh, I'm the mayor," before returning to his car and driving off.

That's life in a county of only 7,000 people.

"Franklin Country is one of those places where, if you're an out-of-towner, you're going to be spotted pretty quickly," says 60 Minutes producer Laura Dodd. She co-produced this week's 60 Minutes story about what happened after Bulington arrived — and the impact he's had on the community.

Jeff Bulington, or "Dr. B" as he's known to his chess students. CBS News

"Here's this stranger coming in — nobody really knows who he is — to teach their kids chess," correspondent Sharyn Alfonsi tells 60 Minutes Overtime's Ann Silvio in the video above. "Everybody thought, like, 'What's this guy about?'"

But Bulington had a plan.

A wealthy benefactor, who wishes to remain anonymous, lured Bulington and his chess skills to Franklin County. He had seen how Bulington molded chess champions in Memphis, and he hoped to see the same success brought to Mississippi. He thought maybe a dozen kids would be interested.

A year-and-a-half later, Bulington, or "Dr. B" as he's known in town, is now teaching hundreds of Franklin County kids, showing them so much more than chess.

"We're using chess to open some doors and to help the people maybe see themselves in a way they didn't see themselves before," Bulington says, "to develop a kind of intellectual, cultural identity that didn't exist before."

Bulington's students now identify as chess players who are skilled enough to compete on the national level. Though some are only in the fifth and sixth grades, they are happy to sit at a chessboard for hours-long games. Alfonsi attributes their patience, in part, to the slower pace of life in Mississippi.

"Those kids will sit at a chessboard, and they'll take their time, and they'll think," Alfonsi says. "And they just take a minute. I think it makes them great chess players."

One of Bulington's chess students CBS News

The kids themselves have a name for the mental zone they enter as a game stretches into two and three hours: "chess dimension." When in chess dimension, there's only the board, the black and white pieces, the chair they're sitting in.

But Bulington's students continue learning even after the game is over.

"Dr. B thinks if you keep winning games, you're not getting better," Alfonsi explains, "that when you lose, you get better. It teaches them you learn from every single game. You learn when you lose. When you win, you don't examine your games in the same way."

Win or lose, Bulington has an important instruction to his students: maintain a poker face.

Bulington teaches his students to maintain a poker face, regardless if they win or lose CBS News

"He says that, like, our own mother should normally not be able to tell whether we won or lost," says Parker Wilkinson, one of Bulington's chess students.

And as Alfonsi witnessed firsthand at the national chess championship in Nashville, that's exactly what Bulington's chess players do.

"The tournament's over, and you're watching from a distance," Alfonsi recalls. "You have no idea what's going on on the board. And the kids come down this long hallway, and they're walking to you, and you're starting at their faces like, 'Did they win? Did they lose?"

But their stoic faces betrayed no information.

Bulington's students have competed nationally CBS News

For Bulington a loss means there's more to learn, and a win shouldn't be something to gloat over.

"I think it's easy to draw cheap conclusions about how good you are for winning one particular game," he says. "And it can also do damage to another person. You don't want to do that."

Bulington teaches his students that he doesn't want to see them cheering "I won!" and hoisting up a trophy, merely because they captured someone else's king. "Don't like that," he says.

For Bulington's students, knowing they can say "checkmate" on the national stage is victory enough.

"He's teaching them they can compete with anybody," Alfonsi says. "He's teaching them to be graceful when they win and just as gracious when they lose. He's teaching them quiet confidence."

Bulington is also clear with his students: Because they hail from a small Mississippi county, where the mayor stops strangers in the street, they will be underestimated.

"And that's OK," Alfonsi says. "Use that to your advantage. Surprise people."

The video above was originally published on March 26, 2017, and produced by Brit McCandless and Sarah Shafer Prediger. It was edited by Sarah Shafer Prediger.