It's all in the game: Johns and Katz really play with the theme. The first official mission Booster takes once he accepts Rips' offer? Stopping Sinestro from meeting Guy Gardner too early. They fight in a football field where Booster tries to reason with the villain eluding to Dominoes to explain the butterfly effect. His second mission leads him to Jonah Hex and sure enough a bar fight starts knocking into a card game where one of the players is cheating. Hell, NO ONE plays by standard rules of superheroes/villains in this comic. The stakes are raised a higher bar by the threat of being erased from existence. The heroes are encouraged to use whatever means they can to win the day, Rip even mentions swearing an oath when he was younger to do anything to protect the timeline.
While the Flash mission is played straight it does bring up Booster throwing the game for his dad. This becomes a crossroads of sorts for Booster after the Beetles and him arrive the day he throws away his career for his father. This has him once again making choices with his heart and not his head. In a way Booster hasn't quite learned his lesson from this day, he still wants to throw everything away for something he wants. Namely love, whether it's his fathers' unattainable love or the people he loves. The results aren't much better since Booster can't reach his goal. It's actually a selfish goal since he goes against what Ted wants. In fact he's in denial on how bad it truly is for most of the Blue and Gold arc
When you think about it even Checkmate fits perfectly into the ongoing game theme. Who's the true chess master? Max? Black Beetle? Rip?
Dr. Light 2: No more games, Max. I'm playing for keeps.
After losing his faith in being a Time Master Booster tries to decide what to do, briefly considering returning to his old ways. He does this in Las Vegas while breaking up another Royal Flush robbery.
Booster Gold: All right, time to cash in your chips, fellas. Because I'm cashing in mine.
Ironically he seems to be unsure of selling out or taking a chance on Rip--who he doesn't totally trust after the Killing Joke lesson--when Hal Jordon forms green dices to save Booster from an attack from Ace. The same robot that gave Booster trouble when they first fought and defeated to join JLI.
When Michelle is returned it's not the same as Booster trying to save Ted.
Booster Gold: (Amazed) You took a risk?
Rip Hunter: I never take risks. I thoroughly calculated it to the last millisecond.
Something about this simple exchange stuck me even before the big family reveal. It's very telling for the characters and how they approach things. Where Booster is more spontaneous Rip is logical. Perhaps he learned from his fathers' mistakes. Of course Boosters' still able to do his job mostly by taking such risks. As Boosters' future self said there's no manual for being a Time Master, sometimes you have to make it up as you go along.