Novel - Dead Earth, Spaceships, and Chess

Question

Back in middle (or was it high?) school, in the mid-2000s, I distinctly recall thumbing through some science-fiction paperback assigned to another class. Don't remember the title or even the main character's name, but I do recall:

• Earth was rendered completely uninhabitable by pollution or something like that.
• The protagonists were part of a spaceship voyage to find somewhere new to settle (I don't recall if they made it or not). I think the ship had several hundred other families packed in.
• It MAY have had a moment near the beginning where the protagonist's father explains that other, richer countries (or planets?) got the better ships, leaving them with "bottom of the barrel". Honestly, it's entire possible I'm conflating this part from something else.
• The only source of recreation on the ship is playing chess against the computer.

It’s not Checkmate by Eric T. Baker.

Answer 1

A bit of a longshot, but Checkmate by Eric T. Baker, as referenced in the answer to Novel set on a generational ship with a unique "chess"-like game, does involve a generation ship and a chesslike game which is the sole pasttime.

As part of the Contraband Unit, Aaron Hudson is sworn to protect the resources of the colony ship Jersey. But Hudson's team is on the take-and a sudden crackdown leaves him set up to take the fall. Forced into an uneasy alliance with the Artificial Intelligence out to shut the Unit down, he's now caught between loyalty and survival... with the stakes nothing short of life and death.

However, it's about a fleet of ships, and is a bit more of a crime procedural as best I can tell, whereas your book sounds more slice-of-life.