|
Piece-square Table
An evaluation function, also known as a heuristic evaluation function or static evaluation function, is a function used by game-playing computer programs to estimate the value or goodness of a position (usually at a leaf or terminal node) in a game tree. Most of the time, the value is either a real number or a quantized integer, often in ''n''ths of the value of a playing piece such as a stone in go or a pawn in chess, where ''n'' may be tenths, hundredths or other convenient fraction, but sometimes, the value is an array of three values in the unit interval, representing the win, draw, and loss percentages of the position. There do not exist analytical or theoretical models for evaluation functions for unsolved games, nor are such functions entirely ad-hoc. The composition of evaluation functions is determined empirically by inserting a candidate function into an automaton and evaluating its subsequent performance. A significant body of evidence now exists for several games l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Tree Search
In computer science, Monte Carlo tree search (MCTS) is a heuristic search algorithm for some kinds of decision processes, most notably those employed in software that plays board games. In that context MCTS is used to solve the game tree. MCTS was combined with neural networks in 2016 and has been used in multiple board games like Chess, Shogi, Checkers, Backgammon, Contract Bridge, Go, Scrabble, and Clobber as well as in turn-based-strategy video games (such as Total War: Rome II's implementation in the high level campaign AI) and applications outside of games. History Monte Carlo method The Monte Carlo method, which uses random sampling for deterministic problems which are difficult or impossible to solve using other approaches, dates back to the 1940s. In his 1987 PhD thesis, Bruce Abramson combined minimax search with an ''expected-outcome model'' based on random game playouts to the end, instead of the usual static evaluation function. Abramson said the expected-out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deepmind
DeepMind Technologies Limited, trading as Google DeepMind or simply DeepMind, is a British–American artificial intelligence research laboratory which serves as a subsidiary of Alphabet Inc. Founded in the UK in 2010, it was acquired by Google in 2014 and merged with Google AI's Google Brain division to become Google DeepMind in April 2023. The company is headquartered in London, with research centres in the United States, Canada, France, Germany, and Switzerland. DeepMind introduced neural Turing machines (neural networks that can access external memory like a conventional Turing machine), resulting in a computer that loosely resembles short-term memory in the human brain. DeepMind has created neural network models to play video games and board games. It made headlines in 2016 after its AlphaGo program beat a human professional Go player Lee Sedol, a world champion, in a five-game match, which was the subject of a documentary film. A more general program, AlphaZer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deep Neural Networks
Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be either supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supervised Learning
In machine learning, supervised learning (SL) is a paradigm where a Statistical model, model is trained using input objects (e.g. a vector of predictor variables) and desired output values (also known as a ''supervisory signal''), which are often human-made labels. The training process builds a function that maps new data to expected output values. An optimal scenario will allow for the algorithm to accurately determine output values for unseen instances. This requires the learning algorithm to Generalization (learning), generalize from the training data to unseen situations in a reasonable way (see inductive bias). This statistical quality of an algorithm is measured via a ''generalization error''. Steps to follow To solve a given problem of supervised learning, the following steps must be performed: # Determine the type of training samples. Before doing anything else, the user should decide what kind of data is to be used as a Training, validation, and test data sets, trainin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalization (statistics)
In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment. In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinforcement Learning
Reinforcement learning (RL) is an interdisciplinary area of machine learning and optimal control concerned with how an intelligent agent should take actions in a dynamic environment in order to maximize a reward signal. Reinforcement learning is one of the three basic machine learning paradigms, alongside supervised learning and unsupervised learning. Reinforcement learning differs from supervised learning in not needing labelled input-output pairs to be presented, and in not needing sub-optimal actions to be explicitly corrected. Instead, the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge) with the goal of maximizing the cumulative reward (the feedback of which might be incomplete or delayed). The search for this balance is known as the exploration–exploitation dilemma. The environment is typically stated in the form of a Markov decision process (MDP), as many reinforcement learning algorithms use dyn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lichess
Lichess (; ) is a free and open-source software, free and open-source Internet chess server run by a Nonprofit organization, non-profit organization of the same name. Users of the site can play online chess anonymously and optionally register an account to play games to earn a rating on Lichess. Lichess is ad-free and all the features are available for free, as the site is funded by donations from patrons, who receive a special badge as thanks for their support. Features include chess puzzles, computer chess, computer analysis, chess tournament, tournaments and chess variants. History Lichess was founded in 2010 by French programmer Thibault Duplessis. The software running Lichess and the design are mostly Open-source software, open source under the GNU Affero General Public License, AGPL license and other free and non-free licenses. The name ''Lichess'' is a "combination of live/light/libre software, libre and chess". On February 11, 2015, an official Lichess mobile app was r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Combination
In mathematics, a linear combination or superposition is an Expression (mathematics), expression constructed from a Set (mathematics), set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of ''x'' and ''y'' would be any expression of the form ''ax'' + ''by'', where ''a'' and ''b'' are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field (mathematics), field, with some generalizations given at the end of the article. Definition Let ''V'' be a vector space over the field ''K''. As usual, we call elements of ''V'' ''vector space, vectors'' and call elements of ''K'' ''scalar (mathematics), scalars''. If v1,...,v''n'' are vectors and ''a''1,...,''a''''n'' are scalars, then the ''linear combination of those vectors with those scalars as coefficients'' is :a_1 \mathbf v_1 + a_2 \mathbf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Network
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks. A neural network consists of connected units or nodes called '' artificial neurons'', which loosely model the neurons in the brain. Artificial neuron models that mimic biological neurons more closely have also been recently investigated and shown to significantly improve performance. These are connected by ''edges'', which model the synapses in the brain. Each artificial neuron receives signals from connected neurons, then processes them and sends a signal to other connected neurons. The "signal" is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs, called the '' activation function''. The strength of the signal at each connection is determined by a ''weight'', which adjusts during the learning process. Typically, ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Piece Relative Value
In chess, a relative value (or point value) is a standard value conventionally assigned to each piece. Piece valuations have no role in the rules of chess but are useful as an aid to evaluating an exchange of pieces. The best-known system assigns 1 point to a pawn, 3 points to a knight or bishop, 5 points to a rook and 9 points to a queen. Valuation systems, however, provide only a rough guide; the true value of a piece can vary significantly, depending on a piece's board position relative to a player's other pieces and the opponent's pieces. Standard valuations Piece values exist because calculating to checkmate in most positions is beyond reach even for top computers. Thus, players aim primarily to create a material advantage; to pursue this goal, it is normally helpful to quantitatively approximate the strength of an army of pieces. Such piece values are valid for, and conceptually averaged over, tactically "quiet" positions where immediate tactical g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Chess
Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysis, entertainment and training. Computer chess applications that play at the level of a Chess title, chess grandmaster or higher are available on hardware from supercomputers to Smartphone, smart phones. Standalone chess-playing machines are also available. Stockfish (chess), Stockfish, Leela Chess Zero, GNU Chess, Fruit (software), Fruit, and other free open source applications are available for various platforms. Computer chess applications, whether implemented in hardware or software, use different strategies than humans to choose their moves: they use Heuristic (computer science), heuristic methods to build, search and evaluate Tree (data structure), trees representing sequences of moves from the current position and attempt to execute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
