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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, Computer 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). 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-outcome model "is sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Search Algorithm
In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values. algorithms are Although search engines use search algorithms, they belong to the study of information retrieval, not algorithmics. The appropriate search algorithm often depends on the data structure being searched, and may also include prior knowledge about the data. Search algorithms can be made faster or more efficient by specially constructed database structures, such as search trees, hash maps, and database indexes. Search algorithms can be classified based on their mechanism of searching into three types of algorithms: linear, binary, and hashing. Linear search algorithms check every record for the one associated with a target key in a linear fashion. Binary, or half-interval, searches repeatedl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rome II
Rome II may refer to: * Rome II Regulation, governing choice of law in the European Union in disputes about non-contractual obligations * Rome II, part of the Rome process about the diagnosis and treatment of functional gastrointestinal disorders * '' Total War: Rome II'', a 2013 strategy video game See also * Nova Roma (other) * Second Rome (other) * New Rome (other) * Rome (other) *Second Vatican Council *University of Rome Tor Vergata Tor Vergata University of Rome, also known as the University of Rome II ( it, Università degli Studi di Roma "Tor Vergata"), is a public research university located in Rome, Italy. Located in the southeastern suburb of Rome, the university combine ..., also known as the University of Rome II *Season 2 of ''Rome'' (TV series) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go Ranks And Ratings
There are various systems of Go ranks and ratings that measure the skill in the traditional board game Go. Traditionally, Go rankings have been measured using a system of dan and kyu ranks. Especially in amateur play, these ranks facilitate the handicapping system, with a difference of one rank roughly corresponding to one free move at the beginning of the game. This system is also commonly used in many East Asian martial arts, where it often corresponds with a belt color. With the ready availability of calculators and computers, rating systems have been introduced. In such systems, a rating is rigorously calculated on the basis of game results. Kyu and dan ranks Traditionally, the level of players has been defined using ''kyu'' and ''dan'' ranks. Kyu ranks are considered ''student'' ranks. Dan ranks are considered ''master'' ranks. Beginners who have just learned the rules of the game are usually around 30th kyu. As they progress, they advance numerically downwards through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dan (rank)
The ranking system is used by many Japanese, Okinawan, Korean, and other martial art organizations to indicate the level of a person's ability within a given system. Used as a ranking system to quantify skill level in a specific domain, it was originally used at a Go school during the Edo period. It is now also used in most modern Japanese fine and martial arts. Martial arts writer Takao Nakaya claims that this dan system was first applied to martial arts in Japan by Kanō Jigorō (1860–1938), the founder of judo, in 1883, and later introduced to other East Asian countries. In the modern Japanese martial arts, holders of dan ranks often wear a black belt; those of higher rank may also wear either red-and-white or red belts depending on the style. Dan ranks are also given for strategic board games such as Go, Japanese chess (''shōgi''), and renju, as well as for other arts such as the tea ceremony (''sadō'' or ''chadō''), flower arrangement ('' ikebana''), Japanese ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rémi Coulom
Rémi Coulom (born 1974) is a French computer scientist, once an assistant professor of computer science at the Lille 3 University, and the developer of Crazy Stone, a computer Go program. In 2006, Rémi Coulom described the application of the Monte Carlo method to game-tree search and coined the term Monte Carlo tree search in his paper, “Efficient Selectivity and Backup Operators in Monte-Carlo Tree Search.” He was one of the research supervisors of Aja Huang, who later led the Google DeepMind team that developed AlphaGo AlphaGo is a computer program that plays the board game Go. It was developed by DeepMind Technologies a subsidiary of Google (now Alphabet Inc.). Subsequent versions of AlphaGo became increasingly powerful, including a version that competed .... Coulom developed the Whole History Rating system and founded goratings.org, a website providing unofficial historical ratings of Go players in the world. References External links *Rémi Coulom's Go rati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thompson Sampling
Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that addresses the exploration-exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. Description Consider a set of contexts \mathcal, a set of actions \mathcal, and rewards in \mathbb. In each round, the player obtains a context x \in \mathcal, plays an action a \in \mathcal and receives a reward r \in \mathbb following a distribution that depends on the context and the issued action. The aim of the player is to play actions such as to maximize the cumulative rewards. The elements of Thompson sampling are as follows: # a likelihood function P(r, \theta,a,x); # a set \Theta of parameters \theta of the distribution of r; # a prior distribution P(\theta) on these parameters; # past observations triplets \mathcal = \; # a posterior distribution P(\theta, \mathcal) \propto P(\mathca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Deepening
In computer science, iterative deepening search or more specifically iterative deepening depth-first search (IDS or IDDFS) is a state space/graph search strategy in which a depth-limited version of depth-first search is run repeatedly with increasing depth limits until the goal is found. IDDFS is optimal like breadth-first search, but uses much less memory; at each iteration, it visits the nodes in the search tree in the same order as depth-first search, but the cumulative order in which nodes are first visited is effectively breadth-first. Algorithm for directed graphs The following pseudocode shows IDDFS implemented in terms of a recursive depth-limited DFS (called DLS) for directed graphs. This implementation of IDDFS does not account for already-visited nodes and therefore does not work for undirected graphs. function IDDFS(root) is for depth from 0 to ∞ do found, remaining ← DLS(root, depth) if found ≠ null then return found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Theorem Proving
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. Logical foundations While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His ''Foundations of Arithmetic'', published 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential '' Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms and inf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to distinguish it from related games, such as xiangqi (Chinese chess) and shogi (Japanese chess). The recorded history of chess goes back at least to the emergence of a similar game, chaturanga, in seventh-century India. The rules of chess as we know them today emerged in Europe at the end of the 15th century, with standardization and universal acceptance by the end of the 19th century. Today, chess is one of the world's most popular games, played by millions of people worldwide. Chess is an abstract strategy game that involves no hidden information and no use of dice or cards. It is played on a chessboard with 64 squares arranged in an eight-by-eight grid. At the start, each player controls sixteen pieces: one king, one queen, two rooks, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversi
Reversi is a strategy board game for two players, played on an 8×8 uncheckered board. It was invented in 1883. Othello, a variant with a fixed initial setup of the board, was patented in 1971. Basics There are sixty-four identical game pieces called ''disks'', which are light on one side and dark on the other. Players take turns placing disks on the board with their assigned color facing up. During a play, any disks of the opponent's color that are in a straight line and bounded by the disk just placed and another disk of the current player's color are turned over to the current player's color. The objective of the game is to have the majority of disks turned to display one's color when the last playable empty square is filled. History Original version Englishmen Lewis Waterman and John W. Mollett both claim to have invented the game of Reversi in 1883, each denouncing the other as a fraud. The game gained considerable popularity in England at the end of the 19th century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tic-tac-toe
Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row is the winner. It is a solved game, with a forced draw assuming best play from both players. Gameplay Tic-tac-toe is played on a three-by-three grid by two players, who alternately place the marks X and O in one of the nine spaces in the grid. In the following example, the first player (''X'') wins the game in seven steps: There is no universally-agreed rule as to who plays first, but in this article the convention that X plays first is used. Players soon discover that the best play from both parties leads to a draw. Hence, tic-tac-toe is often played by young children who may not have discovered the optimal strategy. Because of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
