Finding out the favored game to play of someone tells you what they value, what skills they choose to hone, if you want that information.
Chess is the classic example. Someone plays chess, they consider their attacks, they will trade, they plan. Even if it’s just one move in the future.
Poker players, there’s some variation, sure. Some plays the cards, some play the players, but at the end of it, chance plays a part in how they see the world.
Backgammon is right in the middle of these.
But avoid Go players. They’re either insane or geniuses. Or both.