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Backgammon Opening
The first moves of a backgammon game are the opening moves, collectively referred to as the opening, and studied in the backgammon opening theory. Backgammon opening theory is not developed in as much detail as opening theory in chess, which has been widely studied. The reason for this is that following the first move in backgammon, there are 21 dice roll outcomes on each subsequent move, and many alternative plays for each outcome, making the tree of possible positions in backgammon expand much more rapidly than in chess. Despite the complications posed by this rapid branching of possibilities, over the course of many years, a consensus did develop among backgammon experts on what is the preferred opening move for each given roll. Following the emergence of self-trained backgammon-playing neural networks, the insights on what are the best opening moves have changed in some unexpected ways. Preferred opening moves The table below summarizes the most commonly preferred moves, fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backgammon
Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back nearly 5,000 years to the regions of Mesopotamia and Persia. The earliest record of backgammon itself dates to 17th-century England, being descended from the 16th-century Irish (game), game of Irish.Forgeng, Johnson and Cram (2003), p. 269. Backgammon is a two-player game of contrary movement in which each player has fifteen piece (tables game), pieces, known traditionally as 'men' (short for 'tablemen') but increasingly known as 'checkers' in the US in recent decades. These pieces move along twenty-four 'point (tables game), points' according to the roll of two dice. The objective of the game is to move the fifteen pieces around the board and be first to ''bear off'', i.e., remove them from the board. The achievement of this while the opponent is still a long way behind results in a triple wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Theory
The game of chess is commonly divided into three phases: the chess opening, opening, Chess middlegame, middlegame, and Chess endgame, endgame. There is a large body of theory regarding how the game should be played in each of these phases, especially the opening and endgame. Those who write about chess theory, who are often also eminent players, are referred to as "theorists" or "theoreticians". "Opening theory" commonly refers to consensus, broadly represented by current literature on the openings. "Endgame theory" consists of statements regarding specific positions, or positions of a similar type, though there are few universally applicable principles. "Middlegame theory" often refers to maxims or principles applicable to the middlegame. The modern trend, however, is to assign paramount importance to analysis of the specific position at hand rather than to general principles. The development of theory in all of these areas has been assisted by the vast literature on the game. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Tree
In the context of Combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such games include well-known ones such as chess, checkers, Go, and tic-tac-toe. This can be used to measure the complexity of a game, as it represents all the possible ways a game can pan out. Due to the large game trees of complex games such as chess, algorithms that are designed to play this class of games will use partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minimax algorithms such as MCTS can be used in cases where a complete game tree is not feasible. Understanding the game tree To better understand the game tree, it can be thought of as a technique for an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinforcement Learning
Reinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of 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). The environment is typically stated in the form of a Markov decision process (MDP), because many reinforcement learning algorithms for this context use dynamic programming techniques. The main difference between the classical dynamic programming methods and reinforcement learning algorithms is that the latter do not assume knowledge of an exact mathematica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called ''edges''. Neurons and edges typically have a ''weight'' that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold. Typically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rollout (backgammon)
A rollout is an analysis technique for backgammon positions and moves. A rollout consists of playing the same position many times (with different dice rolls) and recording the results. The balance of wins and losses is used to evaluate the equity of the position. Historically this was done by hand, but it is now undertaken primarily by computer programs. In order to compare two or more ways to move, rollouts can be performed from the positions after each move. Better choices will yield a more favorable position, and thus will win more times (and lose more rarely) in the end. Computer programs usually play rollouts where the number of games is a multiple of 36, and ensure that the first dice roll is uniformly distributed. That is, 1/36 of the played games will start with a roll of ''1-1'', another 36th will start with ''1-2'', and so on. This improves the accuracy of the technique. Rollouts depend on the availability of a good evaluator. If the computer makes mistakes in particular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backgammon Notation
Backgammon notation is a means for recording backgammon games, developed by Paul Magriel in the 1970s. The common way of describing the movement of checkers involves numbering the points around the board from 24 to 1 as depicted in Figure 1. The image shows the board from black's perspective, with the numbers diminishing as her checkers move counterclockwise toward her own home board at the bottom right-hand side. The reverse numbering of the points applies when white is on roll, with the 24-point referred to as the 1-point, and so forth. Dice rolls are shown either as "4-2" or "42", denoting a roll of four on one die and two on the other. Moves are recorded using the notation: :4-2: 8/4 6/4 This denotes a roll of 4-2, and the corresponding checker moves from point 8 to 4 and from 6 to 4. After this move, the board will appear as shown in Figure 2. If a move results in a checker being hit, this is indicated by adding an asterisk to the number denoting the point at which the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Backgammon Federation
The World Backgammon Federation (WBGF), formerly the European Backgammon Federation (EUBGF) until 2018, is the international body established to support and promote the tables game of backgammon worldwide. Their functions include the regulation of competition rules worldwide, the assessment and ranking of players and the establishment of regional governing bodies. Among their objectives is the legal recognition of backgammon as a mind sport at national and international levels. The WBGF is based in Schwaz, Austria.''World Backgammon Association'' at ucolours.com. Retrieved 4 March 2022. Members The national backgammon organisations of the following countries are members of the WBGF:[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backgammon
Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back nearly 5,000 years to the regions of Mesopotamia and Persia. The earliest record of backgammon itself dates to 17th-century England, being descended from the 16th-century Irish (game), game of Irish.Forgeng, Johnson and Cram (2003), p. 269. Backgammon is a two-player game of contrary movement in which each player has fifteen piece (tables game), pieces, known traditionally as 'men' (short for 'tablemen') but increasingly known as 'checkers' in the US in recent decades. These pieces move along twenty-four 'point (tables game), points' according to the roll of two dice. The objective of the game is to move the fifteen pieces around the board and be first to ''bear off'', i.e., remove them from the board. The achievement of this while the opponent is still a long way behind results in a triple wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
