Table of Contents: Guidelines | Tips and Tricks | References | Related Links
Guidelines are suggestions. They are not rules.
Here are two examples. The first uses the "singular they", the second does not. Both styles are considered acceptable.
1) "If you take black, then you will move first; your opponent will take white; and they will move first."
2) "If you take black, then you will move first; your opponent will take white; and she will move first."
The "singular they" works best when the referent is an indefinite person. For example, the "singular they" works well in the sentence, "If someone jumps into a lake, then they will get wet." It does not work as well when the referent is a definite person. For example, the "singular they" does not work at all in the sentence, "If Pat O'Keeffe jumps into a lake, then they will get wet."
If you would like references for English grammar and style, here are four good ones.