This special Othello case will follow every discussion from now on. But in reality, a generic, non-specialized model hallucinates early in any non-trivial game, and the only reason it doesn’t do that on a second move is because openings are usually well-known. This generic “model” is still of a statistical nature (multiply all coeffs together repeatedly), not a logical one (choose one path and forget the other). LLMs are cosplaying these models.