Correct me if I’m wrong, but it seems more realistic to say:

1. Playing the same game twice is unlikely because of the number of possible games, OR
2. It’s possible the same game has never been played twice, OR
3. After a certain number of moves, it’s very possible to create a never-played game

I’m certain I’ve played the same game multiple times, because I suck at chess and I fall into the same obvious traps over and over.