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I know that you must serve from server right side to receiver right side and all that. But when exactly is the ball counted as 'in' regarding the middle line. Is it the center of the ball or is it fine if any part of the ball (seen from the top) touches? Like in regular tennis?

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From the official rules:

2.1.6 For doubles, each court shall be divided into 2 equal half-courts by a white centre line, 3mm wide, running parallel with the side lines; the centre line shall be regarded as part of each right half-court.

2.6.3 As the ball is falling the server shall strike it so that it touches first his or her court and then touches directly the receiver's court; in doubles, the ball shall touch successively the right half court of server and receiver.

That's all there is in the rules on the double serve, i.e. "out" is not defined. Generally, out does not need to be defined in table tennis, as "out" is the same as "off the table". Since there is no VAR, I guess it doesn't make too much sense to specify how much of the ball has to be above the line because the umpire would not be able to judge this anyway.

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