Lay definitions of "rare" or "unlikely" tend to break down on this type of question.

If you've ever played chess, you've had an experience that's entirely unique to you. In almost all cases, that exact game you played with the color you played in it has never in the history of the world happened to any other person. That's a rare experience. So as phrased, the answer to your question is yes.

The underlying question could be more accurately phrased as "at least one rare experience that would be categorized by a human's brain as a salient and simple experience indicative of further analysis to discern an underlying pattern where in fact none exists, and it's just statistical noise," but that's not a mathematical enough question to be analyzable within the confines of pure statistics.