Reversi

Reversi, also known as othello, was a human game in which players would try to capture their opponent's pieces and convert them.

When John Smith asked Bernice Summerfield how the Seventh Doctor did what he does, she replied that it was like judo or Reversi, in that the opposition would think they had won, and then he would make them see the situation in a different way, and it would turn out that he had won. (PROSE: Human Nature)

Colonel Joshua compared the Cyberwars to the game othello, except that the human pieces couldn't be converted back once they'd been Cyberconverted. (PROSE: One Bad Apple)