Service and rotation
More arguments are caused by service position than by scoring. The rules are consistent and short, but they are stated in terms of the server's score rather than whose turn it feels like, which is why players lose track.
The one rule that decides everything
At 0–0 the score is even, so the first serve is from the right service court. At 1–0 the server's score is odd and the serve comes from the left. At 4–7 the serving side has 4, which is even, so they serve from the right. The opponent's 7 is irrelevant.
Because of this, you can always reconstruct the correct service court from the scoreboard alone. If a side has lost track of where to stand, the score tells them. This is also why an umpire calling the score aloud before each serve is doing more than announcing — it is stating where the serve must come from.
The receiver stands diagonally opposite
The receiver is the player standing diagonally opposite the server. If the serve comes from the right service court, it must be received in the right service court on the other side of the net — which is diagonally across from the server's point of view. A serve into the wrong court is a fault.
Doubles: only the serving pair rotates
In doubles the two partners occupy one service court each. The rule that catches people out is this:
So a side that takes the serve back serves from whichever player is standing in the court their new score dictates — no swapping first. A side that holds the serve and wins again swaps its two players, and the same player serves once more, now from the other court. One player can therefore serve several rallies in a row, alternating sides each time, while their partner stays put.
The receiving pair never rearranges itself. Whoever happens to be standing in the service court the serve is going to receives it. Over a long rally sequence this means positions drift, and reconstructing them from memory becomes unreliable — which is the main reason to have a scoreboard that tracks who is where.
Singles: one player, both courts
Singles is the same rule with one player instead of two. The server stands in the court their own score dictates and moves between the two service courts as their score changes. There is no partner and no rotation to remember, so the even-odd rule alone is enough.
This is why a scoreboard can treat singles as a special case of doubles rather than a separate game: a singles player simply occupies both service courts, and every doubles rule then produces the correct singles behaviour on its own.
"Service over"
When the receiving side wins a rally, the umpire calls service over — the serve has passed to the other side. It is the moment the whole structure hinges on: the score changes, the serve changes hands, and the new server's own score decides which court they serve from.
The scoring rules that sit alongside this are on the how scoring works page.