Endgame studies have long served as a tool for testing human creativity and intelligence. We find that they can serve as a tool for testing machine ability as well. Two of the leading chess engines, Stockfish and Leela Chess Zero (LCZero), employ significantly different methods during play. We use Plaskett's Puzzle, a famous endgame study from the late 1970s, to compare the two engines. Our experiments show that Stockfish outperforms LCZero on the puzzle. We examine the algorithmic differences between the engines and use our observations as a basis for carefully interpreting the test results. Drawing inspiration from how humans solve chess problems, we ask whether machines can possess a form of imagination. On the theoretical side, we describe how Bellman's equation may be applied to optimize the probability of winning. To conclude, we discuss the implications of our work on artificial intelligence (AI) and artificial general intelligence (AGI), suggesting possible avenues for future research.
Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory, there must be a solution, a right procedure in any position---John von Neumann The advent of computer chess engines based, such as AlphaZero, LCZero and Stockfish 14 NNUE, provides us with the ability to study optimal play. AI chess algorithms are based on pattern matching, efficient search and data-centric methods rather than rules based. Together with an objective functions based on maximising the probability of winning, we can now see what optimal play and strategies look like. One caveat is the black-box nature of these algorithms and lack of insight into the features that are empirically learned from self play.
Leela Chess Zero ID 467 takes on Stockfish 6 in a Ruy Lopez, Schliemann Defense with bullet time controls. Leela's efficient opening development is challenged early by Stockfish 6's central pawn duo. Stockfish 6's pawns give the white knights an early kick, and soon thereafter a sharpened middlegame ensues. By move 16, the pawn structure would become a key element with white acquiring a 4:2 majority on the kingside, and black acquiring a 4:2 majority on the queenside. A big question would be, how can one best demonstrate their pawn majority is a great strength?
When you think of AI or machine learning you may draw up images of AlphaZero or even some science fiction reference such as HAL-9000 from 2001: A Space Odyssey. However, the true forefather, who set the stage for all of this, was the great Arthur Samuel. Samuel was a computer scientist, visionary, and pioneer, who wrote the first checkers program for the IBM 701 in the early 1950s. His program, "Samuel's Checkers Program", was first shown to the general public on TV on February 24th, 1956, and the impact was so powerful that IBM stock went up 15 points overnight (a huge jump at that time). This program also helped set the stage for all the modern chess programs we have come to know so well, with features like look-ahead, an evaluation function, and a mini-max search that he would later develop into alpha-beta pruning.
It was a war of titans you likely never heard about. One year ago, two of the world's strongest and most radically different chess engines fought a pitched, 100-game battle to decide the future of computer chess. On one side was Stockfish 8. This world-champion program approaches chess like dynamite handles a boulder--with sheer force, churning through 60 million potential moves per second. Of these millions of moves, Stockfish picks what it sees as the very best one--with "best" defined by a complex, hand-tuned algorithm co-designed by computer scientists and chess grandmasters.