The commander in chief wants to play dominoes with the dean of late-night talk show hosts when they both retire — or go have coffee and swap stories.

Making his third and final visit to Late Show With David Letterman as POTUS, President Obama suggested when they’re both gone from their current gigs they, “play some dominoes together – go to the local Starbuck and swap stories.”

Letterman shot back: “I play dominoes. I’m pretty good. I know you think I’m not good at dominoes.” During a commerical break, Letterman said, Obama had told him that when he leaves office he plans to take a month off.

“Are you kidding me? After eight years of this, you’re only taking  a month off?!” Letterman marveled.

“I plan to teach law at Columbia,” Letterman said of his retirement; his final day hosting CBSLate Show is May 20.

“I’d be interested in sitting in on that class,” Obama joked. “That would be a hoot.”

Obama’s visits to the show have been “particularly meaningful to me,” Letterman said, “Like most Americans, we feel we got to know you” and “I can only wish you all the best.”

Obama returned the sentiment: “We’ve grown up with you, this country. And after … coming home from work, knowing you’ve been there to give us a little bit of joy, a little bit of laughter. It has meant so much. … You’ve given us a great gift, and we love you.”

Obama’s motorcade had pulled up to the Ed Sullivan Theatre at 4:13 PM ET today to tape his visit.

“There’s nothing like cruising around Manhattan in a presidential motorcade: traffic blocked, lights don’t matter, all clear sailing, crowds lined streets behind barricades, snapping pix,” the White House pool report noted.

Obama’s visit comes days after First Lady Michelle Obama went on the show to wish Letterman well in retirement and offer to help raise his child. He assured her all the child-rearing problems would be left to the stepfather.

President Obama last appeared on the broadcast Sept. 18, 2012, and prior to that on Sept. 21, 2009. As an Illinois senator, he appeared on the program five times, beginning in 2004 and continuing through his 2008 presidential campaign.