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However, these proofs are not as helpful in understanding deeper reasons why some games are solvable as a draw, and other, seemingly very similar games are solvable as a win. The resulting proof gives an optimal strategy for every possible position on the board. īy contrast, 'strong' proofs often proceed by brute force-using a computer to exhaustively search a game tree to figure out what would happen if perfect play were realized. 'Ultra-weak' proofs require a scholar to reason about the abstract properties of the game, and show how these properties lead to certain outcomes if perfect play is realized.

Strong solution Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or both sides.ĭespite their name, many game theorists believe that 'ultra-weak' proofs are the deepest, most interesting and valuable. Weak solution Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any moves of the perfect play. Solving such a game may use combinatorial game theory and/or computer assistance.Ī two-player game can be solved on several levels: Ultra-weak solution Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides.

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This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance

The game has been translated into many different languages and is enjoyed by people of all ages.Game whose outcome can be correctly predictedĪ solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. Scrabble has been enjoyed by millions of people around the world and has even been the subject of tournaments and competitions. The game is played with a set of tiles, each containing a letter of the alphabet, and players take turns placing the tiles on a board to form words. The game was originally called 'Lexiko' and was renamed to Scrabble in 1948. Scrabble is a popular word game that was created in the 1930s by an American architect named Alfred Mosher Butts. Scrabble is a fun and challenging game that tests players' vocabulary and word-building skills. The player with the highest score wins the game. The game continues until all of the tiles have been placed on the board or one player has no more tiles to play.Īt the end of the game, the players count up their scores to determine the winner. If they are unable to create a word with the tiles they have, they must pass their turn and the next player takes their turn. The board also contains special squares called 'double letter score' and 'triple letter score' squares, which can double or triple the value of the letters placed on them.Īfter a player has placed their tiles on the board, they draw new tiles to replace the ones they played.

Each letter has a different point value, with common letters like 'E' and 'S' being worth one point, and less common letters like 'Z' and 'X' being worth more points. When a player places their tiles on the board, they score points based on the value of the letters in the word they formed. The tiles must form a valid word according to the rules of the game, and must be placed so that they are connected to tiles already on the board. The first player places their tiles on the board to form a word, with the tiles touching each other either horizontally or vertically. To start the game, each player draws seven tiles from a bag of tiles, which contains all of the letters in the game. The objective of the game is to use these tiles to create words on the board, and score points based on the value of the letters in the word. Each player has a set of tiles, each with a letter on it. The game is played on a board, which is divided into a 15x15 grid of squares. Scrabble is a popular word game that is played by two or more players. How many words can you create with 7 letters?

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