Analysts have estimated the number of legal positions in Othello is at most 1028, and it has a game-tree complexity of approximately 1058. Mathematically, Othello is solved up to 8x8 board. On 4×4 and 6×6 boards under perfect play, the second player wins. On 8x8 board, the game results in draw under perfect play, according to an arXiv paper. The first of these proofs is relatively trivial, the second dates to around 1990, and the last one was done in 2023. When generalizing the game to play on an n×n board, the problem of determining if the first player has a winning move in a given position is PSPACE-complete.
Analysts have estimated the number of legal positions in Othello is at most 1028, and it has a game-tree complexity of approximately 1058. Mathematically, Othello is solved up to 8x8 board On 4×4 and 6×6 boards under perfect play, the second player wins. On 8x8 board, the game results in draw under perfect play, according to an arXiv paper. The first of these proofs is relativ?el.y trivial, the second dates to around 1990, and the last one was done in 2023. When generalizing the game to play on an n×n board, the problem of determining if the first player h.as a winning move in a given position i!s PSPACE-complete.