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| NTest - a strong othello program |
Computer Othello refers to computer architecture encompassing computer hardware and computer software capable of playing the game of Othello. It was notably included in Microsoft Windows from 1.0 to XP, where it is simply known as Reversi.
There are many Othello programs such as NTest, Saio, Edax, Cassio, Pointy Stone, Herakles, WZebra, and Logistello that can be downloaded from the Internet for free. These programs, when run on any up-to-date computer, can play games in which the best human players are easily defeated. This is because although the consequences of moves are predictable for both computers and humans, computers are better at exploring them.[1]
Computer Othello programs search for any possible legal moves using a game tree. In theory, they examine all positions / nodes, where each move by one player is called a "ply". This search continues until a certain maximum search depth or the program determines that a final "leaf" position has been reached.
A naive implementation of this approach, known as Minimax or Negamax, can only search to a small depth in a practical amount of time, so various methods have been devised to greatly increase the speed of the search for good moves. These are based on Alpha-beta pruning, Negascout, MTD(f), and NegaC*.[2] The alphabeta algorithm is a method for speeding up the Minimax searching routine by pruning off cases that will not be used anyway. This method takes advantage of the fact that every other level in the tree will maximize and every other level will minimize.[3]
Several heuristics are also used to reduce the size of the searched tree: good move ordering, transposition table and selective Search.[4]
To speed up the search on machines with multiple processors or cores, a "parallel search" may be implemented. Several experiments have been made with the game Othello, like ABDADA[5] or APHID[6] On recent programs, the YBWC[7] seems the preferred approach.
Multi-ProbCut is a heuristic used in alpha–beta pruning of the search tree.[8] The ProbCut heuristic estimates evaluation scores at deeper levels of the search tree using a linear regression between deeper and shallower scores. Multi-ProbCut extends this approach to multiple levels of the search tree. The linear regression itself is learned through previous tree searches, making the heuristic a kind of dynamic search control.[9] It is particularly useful in games such as Othello where there is a strong correlation between evaluations scores at deeper and shallower levels.[10][11]
There are three different paradigms for creating evaluation functions.
Different squares have different values - corners are good and the squares next to corners are bad. Disregarding symmetries, there are 10 different positions on a board, and each of these is given a value for each of the three possibilities: black disk, white disk and empty. A more sophisticated approach is to have different values for each position during the different stages of the game; e.g. corners are more important in the opening and early midgame than in the endgame.[12]
Most human players strive to maximize mobility (number of moves available) and minimize frontier disks (disks adjacent to empty squares). Player mobility and opponent mobility are calculated, and player potential mobility and opponent potential mobility are calculated as well.[13] These measures can be found very quickly, and they significantly increase playing strength. Most programs have knowledge of edge and corner configurations and try to minimize the number of disks during the early midgame, another strategy used by human players.[12]
Mobility maximization and frontier minimization can be broken down into local configurations which can be added together; the usual implementation is to evaluate each row, column, diagonal and corner configuration separately and add together the values, many different patterns have to be evaluated.[12] The process of determining values for all configurations is done by taking a large database of games played between strong players and calculating statistics for each configuration in each game stage from all the games.[12]
The most common choice to predict the final disc difference uses a weighted disk difference measure where the winning side gets a bonus corresponding to the number of disks.[12]
Opening books aid computer programs by giving common openings that are considered good ways to counter poor openings. All strong programs use opening books and update their books automatically after each game. To go through all positions from all games in the game database and determine the best move not played in any database game, transposition tables are used to record positions that have been previously searched. This means those positions do not need to be searched again.[12] This is time-consuming as a deep search must be performed for each position, but once this is done, updating the book is easy. After each game played, all new positions are searched for the best deviation.
Faster hardware and additional processors can improve Othello-playing program abilities, such as deeper ply searching.
During gameplay, players alternate moves. The human player uses black counters while the computer uses white. The human player starts the game.[1] Othello is strongly solved on 4×4 and 6×6 boards, with the second player (white) winning in perfect play.[14][15]
Othello 4x4 has a very small game tree and has been solved in less than one second by many simple Othello programs that use the Minimax method, which generates all possible positions (nearly 10 million). The result is that white wins with a +8 margin (3-11).[14]
Othello 6x6 has been solved in less than 100 hours by many simple Othello programs that use the Minimax method, which generates all possible positions (nearly 3.6 trillion). The result is that white wins with a +4 margin (16-20).[16]
The Othello 8x8 game tree size is estimated at 1054 nodes, and the number of legal positions is estimated at less than 1028. As of October 2023, a preprint claims that the game has been solved, with optimal result being draw.[17][18] Computation results is also shared, making it one of the largest publicly available book.[19]
Some top programs have expanded their books for many years now. As a result, many lines are in practice draws or wins for either side. Regarding the three main openings of diagonal, perpendicular and parallel, it appears that both diagonal and perpendicular openings lead to drawing lines, while the parallel opening is a win for black. The drawing tree also seems bigger after the diagonal opening than after the perpendicular opening.[20][failed verification] The parallel opening has strong advantages for the black player, enabling black to always win in a perfect play.[21][failed verification]
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