Both. The shuffle decides which tiles you hold. Skill shows in which tile to play, which end to play it on, when to keep a double back, and in tracking what has gone, so you can work out what your opponent cannot have. Over one hand a strong player can lose to a better draw; over hundreds of matches the better player's scoring choices add up.
Counting is the clearest example. In a standard double-six set each number appears on seven tiles, the double included. If you can see five of the seven tiles carrying a 4, on the board or in your hand, your opponent holds at most two of them, and a 4 left at an open end may block them. Good players use that to force draws or passes, and to keep scoring ends open for themselves while closing them for the other side.
That mix matters legally as well as practically. In Great Britain the Gambling Act 2005 counts any game involving both chance and skill as a game of chance (section 6), so playing dominoes for a money prize is gaming in law, unlike chess. In the US, skill-game operators run dominoes as a contest of skill and exclude the states on their own lists.
Asynchronous play adds a fairness question. When you never see your opponent play, you are trusting the platform that the opponent is a person. Papaya Gaming's terms allow matching against players who played earlier or later and paid a different entry fee, and a US jury found Papaya liable in April 2026 for false advertising over undisclosed bots. Dominoes Gold is a Skillz product, not a Papaya one, but the same question applies to any asynchronous cash match.