Othello, also known as Othello, is also known as Othello, and its name is derived from Shakespeare's famous play Othello - the black and white sides symbolize the protagonist Othello and his wife Desdemona;The game between the chess games symbolizes the comings and goings of the two. Now, with the help of supercomputing clusters, scientists have cracked Othello by exhausting all the variations of the game. Through more than 400 years of jealousy and betrayal, remorse and tears, the lovers finally embraced each other tightly in a reciprocal attitude.
Written by |Jiawei.
a minute to learn, a lifetime to master
A proverb that is well known to Othello fans all over the world.
I believe that most of the first encounters with Othello were in an electronic dictionary called "Wenqu Xing". At the same time, because the "social status" of Othello is far from being compared with the traditional game of Go and chess with its own elite temperament, many people may think that Othello is just a simple and easy-to-learn children's board game. As everyone knows, because of its unique rules, Othello is different from other chess games. In situations where the situation is limited, such as the endgame in backgammon or chess, players can often easily gain insight into the situation. However, even if Othello only has the last 6 squares, it is not easy to calculate. This relative complexity is dictated by the nature of Othello, which is not as easily understood as other chess games "at a glance", so it is easy to turn the tide and turn the tide by allowing a large number of opposing pieces to turn against in just a few turns later in the game.
So, Othello not only has a theoretically astonishing number of 10 28 variations, but it also requires a very deep level of thinking. Even from the early and middle stages, top players have to think about their strategy for the final battle.
The complexity of Othello can also be seen in the fact that the more popular Gomoku (Gobo) was solved by computer scientist Victor Allis back in 1993 and proved that there is a winning strategy for the first side of Goloku in the absence of special opening rules;But over the past 30 years, despite the exponential growth of computing power at our disposal, it has not been able to exhaust all the variations of Othello – until late October this year, when Japanese computer scientist Hiroki Takizawa made a landmark breakthrough and announced that Othello had been cracked
At the same time, the research on Othello has also had a wonderful connection with the "coup" of OpenAI's management, which was triggered not long ago in the AI industry.
However, before we go any further, for the convenience of those who are not familiar with Othello, let's briefly introduce the rules and history of this type of chess.
What is Othello.
Othello is also called flip chess in Chinese, and reversi in English, or othello.
The prototype of Othello was first invented by the British at the end of the 19th century, and in the 70s of the last century, it was developed and popularized by the Japanese Goro Hasegawa, who borrowed Shakespeare's famous play "Othello" to rename the game (in Japanese) Why borrow Shakespeare's famous plays?Because the male protagonist in the play, Othello, is a black man and his wife is white. Othello was provoked by the villain and suspected his wife of infidelity, and finally killed his wife with his own hands. Later, when the truth was revealed, he was remorseful and committed suicide. Reversi is named after the story of the struggle between black and white, so the pieces are both positive and negative, black and white.
Othello pieces and chessboard. Source: Reversi - Wikipedia
In some places, the chess pieces are red and green, and at this time they are also called "apple chess", because apples are divided into red apples and green apples.
Basic rules: gf]2022[ gf] The most standard opening, the 4 squares of the chessboard are placed in 4 squares separated by black and white. Usually the sunspot goes first, and the two sides take turns to drop the seed.
Othello opening.|Source: Japan's weakest Othello AI battle platform is the weakest game interface.
gf]2022[ gf] As long as the falling piece and any of your own pieces on the board are on a line (horizontal, straight, or diagonal) between the opponent's pieces, you can turn these opponent's pieces into your own pieces (you can turn them over). The position of the grip must be full of opponent's pieces, and there can be no spaces. Also, you can only play where you can flip the pieces.
gf]2022[ gf] A move can be flipped in several directions, any caught piece must be flipped over, and the player has no right to choose not to flip a piece. The opponent's piece must be clamped by the freshly played piece to be able to turn the opponent's piece over, and the piece caught by flipping the opponent's piece cannot be turned over.
gf]2022[ gf] If one side has no legal moves to play, they must let the opponent continue to play until they have a legal move. If neither player has a legal move to play, the game is over.
At the end of the game, the side with more pieces on the board wins. If the number of pieces is the same, it is a tie.
Zemelo's theorem (zermelo's theorem) with Solved Game
The study of any kind of chess game is inseparable from the famous theorem published by the German mathematician Zermelo in 1913:
In a two-player limited game, if both players have complete information and luck is not involved, either the first or second player must have a winning strategy.
Note that many people do not understand the theorem correctly and even think that it is nothing more than an obvious nonsense. In order to illustrate the significance of the theorem, please think about the game of "rock-paper-scissors".
In the absence of cheating, "rock-paper-scissors" is a game of luck, and there is no winning strategy for it. So how can we think that in a game of non-luck, there must be a winning and undefeated strategy?It is true that there is a fundamental difference between a game with a sense of luck and a game without a sense of luck, but this is by no means obvious, but needs to be mathematically proven.
Here's an easy-to-understand way of proving this: let's assume that both sides of the game are immortals with infinite wisdom. If a player loses a move (e.g. checkmate in chess), then he is still bound to lose after regretting the move, otherwise it contradicts our "infinite wisdom" (because he made a wrong move in the last move), and so on, we know that the outcome of the game is already decided at the beginning - that is, one side has a winning strategy.
In fact, Zermelo's theorem is the cornerstone of complete information game theory. From this we know that in every regular board game that can end in a limited number of moves, one side is sure to win or at least be undefeated. The follow-up question is: find the side that has an undefeated strategy.
When we confirm that there is a winning strategy in a game where the first or second player has a winning strategy, we say that the game is a solved game. At present, there is no unified standard translation of the name of solved game, but it can be translated directly as solved or cracked game very naturally.
For cracked games, there are also three intensities.
Ultra-weak solution: The theory proves that one side can guarantee to win the game, or that the game is bound to draw, but does not need to give a specific winning or tie method. This solution only requires the use of mathematical tools to analyze the abstract properties of the game, and does not need to exhaust all possibilities.
Weak solution: Gives an algorithm that starts from the initial state of the game and guarantees that one player wins the game, or that no player loses the game. This solution usually requires exhaustive enumeration of all branches of the game tree, or the use of a pre-generated database.
Strong Solution: Gives an algorithm that can start from any state of the game and give the optimal move, regardless of whether the previous move was perfect or not. This solution requires exhaustive enumeration of all nodes of the game tree, or the use of a pre-generated database.
In 1993, backgammon was cracked. In October of this year, Othello also got a weak solution. We now know that if two immortals with infinite computing power play Othello, they must be a draw forever. In other words, Othello is a very fair board game. The first or second hand did not gain a slight advantage as a result. This is in line with the feeling of a high-level Othello player.
At the same time, because it is a weak solution, Takumi Takisawa, a bioinformatician and computer scientist from Preferred Networks, a Japanese start-up AI R&D company, also exhaustively cited the best strategy for both sides to start from the beginning.
It should be noted that humans did not crack Go and chess. Although the current chess AI is far more powerful than humans, they have not found the most correct move. They have simply found a better way to move than we humans do. ）
Technology & Meaning.
In the infancy of computer science, cracking pure strategy games such as chess completely has always been considered an extraordinary achievement of human ingenuity. Since then, it has also been a major issue in the field of artificial intelligence (AI). Early researchers included Charles Babbage and Claude Elwood Shannon. With the improvement of machine learning technology and computing power, humans have created AI with super high chess power (such as the milestone AlphaGo), but these super AI cannot solve these games perfectly. Not so long ago, it was widely believed that Othello was too complex to crack. So it's always been a big challenge in the field of artificial intelligence.
In order to crack Reversi, Takumi Takisawa used modern technology to enhance EDAX, a game that was already very powerful in the 90s, and then broke down the task into more manageable parts. He first analysed the situation with the remaining 50 empty squares on the board, and then examined all the situations that made sense when there were 36 empty squares. He was pleasantly surprised to find that the existing computing power seemed to be sufficient to support a weak solution to Othello.
The path highlighted in bold is the best branch. The perfect player should play according to the bold countermeasure tree of the corresponding positionSource: othello is solved
He runs his program on a supercomputing cluster called MN-J owned by Preferred Networks. The cluster includes the supercomputing MN-3, which is currently ranked 11th in the world in terms of energy efficiency (1st in 2020).
Eventually, Takisawa announced in "Othello is Solved" that he had cracked Reversi. This is a major achievement for humanity and demonstrates the great strides in computer science and artificial intelligence technology.
Another notable point is that the actual number of positions that need to be explored to crack Othello is much smaller than the amount of evaluation in previous studies. Takizawa attributed this to the fact that his team has a more sophisticated configuration of search algorithms. Previously, it was precisely because of the amount of computation that was evaluated was so large that many people were discouraged. Perhaps the lesson of this story is that the analysis on paper is shallow, and you never know that you have to do it.
Othello vs. AI
Probably Japan is the country with the most othello enthusiasts. According to 2005 statistics, there were about 60 million Othello fans in Japan (about 15 million Japanese shogi fans;There are about 5 million Go enthusiasts;There are about 3 million chess enthusiasts).
Therefore, it is only natural that Japanese scientists will eventually crack Reversi. Takizawa is looking forward to making a breakthrough in chess in the future. Chess is 15 orders of magnitude more complex than Othello, and cracking chess is even one of the driving forces behind the development of computer and AI technology.
However, in addition to super AI, there are also people who plan to do the opposite. Sensing that today's chess AI is too powerful, the Japanese AI company **Ilen has developed a Othello game AI called "Othello", which aims to lose as much as possible to human players, rather than pursuing victory like other AIs.
The principle of this AI is to modify the AI's understanding of the rules of Othello so that the AI chooses the most unfavorable move for itself every time, while giving the human player the greatest advantage. In this way, it is very difficult for human players to lose to the AI, and even require some special strategies to do so. Othello openly challenged human players online, and as of July 29, 2019, it has played 220,000 matches and won just over 1,000 of them, with a win rate of less than 05%。It has even attracted the challenge of some professional Othello players to see if they can lose to it.
Some researchers believe that Othello has broken the conventional thinking in the field of artificial intelligence and shown another possibility of AI. It has also led to some people's thinking about AI, such as whether AI has its own will and whether AI can understand human emotions and ......
To a certain extent, the AI experiments on Othello do provide clues to the above thinking.
On November 17, OpenAI, which became a leader in the AI field due to the development of ChatGPT and GPT-4, announced without warning that former CEO Sam Altman (Sam Altman) was dismissed from his position by the board of directors. This was seen as a "coup d'état". The plot behind is even more ups and downs, and many details have not been disclosed so far.
One of the theories is that OpenAI has made another major breakthrough in the field of AI, and their chief scientist, Ilya Sutskever, has a disagreement with Ultraman Sam because he is suspicious of the latest technology and does not want to commercialize it. Eventually, the conflict intensified, triggering a purge of management. Of course, we later learned that Ilya regretted it again and decided to side with Ultraman to oppose the board's decision.
So in which direction is OpenAI most likely to get a breakthrough?In fact, not long ago Ilya revealed to ** that he thinks:
When you train a large neural network to accurately follow the next word in various texts, you're actually building a model of a world. These texts are essentially a kind of mapping of the real world. Neural networks are learning from every aspect of the world, including people, the human environment, expectations, dreams, motivations, and more. AI learns to compress and abstract the human world, and the representations that are available. ”
The above statement makes people seem to understand it, but to use a popular analogy related to the topic of this article, it is that we show the AI a chess game, but do not tell it that it is a chess game. Eventually, the AI learns to play chess, but doesn't know it's playing.
Whether OpenAI has validated this concept — proving that large language models (LLMs) ultimately re-represent the world with language by simply learning language — is unknown, but another recent Othello study supports this theory.
Source: Researchers trained a neural network called othellogpt using 20 million sequence samples sampled from a large number of real-world games. othellogpt doesn't understand the rules of the game or the game concepts that the input sequence represents, it only touches the sequence string of text tags. Similar to the training of natural language by large language models, othellogpt is trained to target the strings that may appear next in the sequence.
After obtaining enough games, othellogpt is able to accurately ** future legal moves, even for strings that have never been seen in the training data (i.e., sequences in the game)!
OthelloGPT didn't know he was playing Othello, but by reading a lot of games (strings of letters and numbers), he found the pattern and actually learned to play chess. Although for othellogpt, it's just in the ** string generation mode.
Finally, if anyone has become interested in Othello after reading this article, here is a primer book available online called the Reversi Guide (by Brian Rose).
Resources. 1] othello is solved，2310.19387.pdf (arxiv.org)
2] reversi - wikipedia
3] Japan's weakest Reversi AI battle platform: Weakest Projects ( **Ilen Co., Ltd
This article is supported by the Science Popularization China Star Program Project, produced by the Science Popularization Department of the China Association for Science and Technology, supervised by the China Science and Technology Press, Beijing Zhongke Galaxy Culture Media***
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