Didn't they find out a few episodes ago when they accidentally ruined her plan in the throne room? Stephanie is actually an amazing administrator and an expert in Imanity politics. She had been slowly manipulating all the nobles for years so only those allied with her lineage had any power at all. She still runs the country because Shiro and Sora can't be bothered to do it. It's only in games that she's mediocre.
Given that Shiro is presented as a strategic genius far beyond the level of Sora, I can see that she would predict he'd play Reversi/Othello as an "optimal" match. They're both smart enough to play a un-losable match, but it's probably only Shiro who could run through all those iterations of how Kurami would play. I'm not so sure that she played three straight turns either. Sora presumably set up the board for her so that Kurami could only finish the game in certain spots, and that Shiro playing from outside would win the game by a landslide.
Reversi/Othello is one of those games that was long ago "solved" by computers (it actually hasn't).
I'm quite interested in how they are going to use the ability to manipulate Fi's memory at will.