NEW YORK — President Barack Obama is envisioning a future of playing dominoes with retiree David Letterman.

Obama joked about their quieter futures during his eighth “Late Show” appearance Monday, saying Americans have grown up with the 33-year veteran comedian.

“After a tough day at the office or coming home from work, knowing that you’ve been there to give us a little bit of joy and a little bit of laughter, it has meant so much,” Obama said. “You’re part of all of us. You’ve given us a great gift and we love you.”

Letterman is filling his CBS show with prominent guests in the lead-up to his final show May 20.

In honor of Obama’s appearance, Letterman listed “Top 10 Questions Dumb Guys Ask the President,” which included “Will you be a guest on one of my last shows?” and “Will you show us your birth certificate?” No. 1, in honor of the recent unauthorized landing on the Capitol lawn: “When will you return my gyrocopter?”

Letterman returned Obama’s praise by complimenting his “very funny” performance at the White House Correspondents Dinner last month. “I’m a pretty funny guy,” Obama said.

“You have guys writing that stuff?” Letterman asked, to which Obama threw up his hands and gave a sidelong look at the audience. “No,” Obama deadpanned. “I came up with it all myself.”

The two men also discussed the serious topic of the Baltimore riots, with the president discussing how too many minority communities don’t have a trusting relationship with police.

Letterman asked if racism is a factor. Obama said it was a residual one after a history of slavery, Jim Crow laws and discrimination, while adding society has made great strides. “I’m a testament to that,” he said to applause from the studio audience.