The Chessmen of Mars was published in 1922 and follows the next generation of Carter’s family, in this case Tara of Helium, John Carter’s daughter, who has grown up by this point in the timeline. Tara is caught in a typhoon-like Martian storm called a tempest while flying her small craft, and crash-lands in the territory of the Kaldanes of Bantoom, a race of detachable spider-shaped intelligent heads who attach to and ride headless humanoid bodies called Rykors.
The Kaldane sections are some of the most genuinely science-fictional in the Barsoom canon, with extended worldbuilding about a species that has evolved beyond bodies but still requires them. The plot eventually moves into the city of Manator, where Tara and the rescuing Gahan of Gathol must compete in a deadly version of Martian Jetan, the chess-like game from which the book takes its title. The Jetan game played with living pieces on a giant board is one of Burroughs’s most memorable set-pieces. Strongly recommended after the first three books.