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So, I'd say colour doesn't matter for Backgammon or Ludo, White has a small advantage in Five in Line, and a big advantage in Horde Chess. Black has a big advantage in Maharajah Chess.
(hide) If you want to play a game with an opponent of a similar level, you can define a required BKR range for a new game invitation. Then nobody with a BKR outside this range will be able to see/accept it. (Katechka) (show all tips)