Dave jokes with RDJ that he doesn't know too much about the movie and says Iron Man has to win.
Letterman then mentions Spider-Man, with Robert Downey Jr. teasing, "He may well be. Yeah. I hear they are looking to cast a new Spider-Man."
Dave then asks, "Who do we root for? Captain America, Iron Man or Spider-Man?"
"That's up to the people," RDJ responds as he points to himself.
Spider-Man will first appear in a Marvel film before the 2017 standalone movie.
Said to be up for the role of Spider-Man are five actors: Nat Wolff, Asa Butterfield, Tom Holland, Timothee Chalamet and Liam James.