In table tennis, when both players are at 10. Who serves first? Does one pick who goes first? Or does it go to the first person that reached 10?
Also, in doubles table tennis how do those rules change?
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See page 27 of the Rules Handbook, specificially rule 2.13.3 which states:
After each 2 points have been scored the receiving player or pair shall become the serving player or pair and so on until the end of the game, unless both players or pairs score 10 points or the expedite system is in operation, when the sequences of serving and receiving shall be the same but each player shall serve for only 1 point in turn
Basically, you would follow the "each 2 points" sequence until both players reached 10, then you would observe the "every 1 point" sequence in serving.