Scrabble against computer online full#

Games like nim also admit a rigorous analysis using combinatorial game theory. Many algorithms rely on a huge pre-generated database and are effectively nothing more.Īs a simple example of a strong solution, the game of tic-tac-toe is easily solvable as a draw for both players with perfect play (a result manually determinable). However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate a move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time. Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree.

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.

Scrabble against computer online full#

This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance It does not store any personal data.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. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. The cookie is used to store the user consent for the cookies in the category 'Performance'. This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category 'Other.

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