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Discover LudwigThe phrase "a third player" is correct and usable in written English.
You can use it when referring to an additional participant in a situation involving two other players, often in games, negotiations, or discussions.
Example: "In the negotiation, a third player entered the room, changing the dynamics of the conversation."
Alternatives: "an additional participant" or "a third participant".
Exact(60)
dropped a third player back to help with transition defense.
dropped a third player back to help with transition defense, slowing the Gaels.
Before the match, it seemed likely the Centre Court roof would be a third player.
All was good until last October, when a third player entered the drama.
A third player, the junior Matt Brown, also will not be on the team.
Did it mean Miami was waiting for a third player to put on the dais?
A third player, the veteran forward Miroslav Satan, is questionable with a hand laceration.
A third player drove them back, and they hit a telephone pole.
Soon they are joined by a third player, Scottish international Emma Mitchell.
A third player complicates the Soga-Jenkins drama: the United States.
But there is a third player with a French connection: Sporting's Adrien Silva.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com