What are Examples of Solved Games?
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Solved games refer to games whose outcome can be correctly predicted from any position, assuming that both players play perfectly, and examples include Tic-Tac-Toe, Checkers, and Connect 4, which have all been weakly or strongly solved through combinatorial game theory and computational power. These solved games demonstrate how artificial intelligence and mathematics can be applied to understand and master complex strategic games.
Introduction to Solved Games
A game is considered solved if its outcome can be determined with certainty, regardless of the moves made by the players, and this can be achieved through strong solutions, where a winning strategy is found for all possible positions, or weak solutions, where a winning strategy is found for the initial position.
Examples of Solved Games
Tic-Tac-Toe
Tic-Tac-Toe is a classic example of a solved game, where both players can guarantee a draw with perfect play.
Checkers
Checkers is another example of a solved game, where a computational proof has shown that the game is a draw from the starting position.
Connect 4
Connect 4 is a solved game, where the first player has a winning strategy that guarantees a win.
Frequently Asked Questions
- What is a weakly solved game?: A weakly solved game is a game where a strategy has been found to achieve the game-theoretic value from the initial position, but not necessarily from all possible positions.
- What is a strongly solved game?: A strongly solved game is a game where a strategy has been found to achieve the game-theoretic value from all possible positions.
- Is chess a solved game?: No, chess is not considered a solved game, as the number of possible positions is too large to be analyzed with current computational power.
- Is poker a solved game?: No, poker is not considered a solved game, as it is a game of imperfect information, and artificial intelligence has not yet been able to solve it.
- What is the largest solved game?: Checkers is currently the largest solved game, with a search space of 5×10^20.
- Is Go a solvable game?: Yes, Go has been solved for small board sizes, such as 5×5, but not for larger board sizes.
- Can humans beat AI at chess?: No, artificial intelligence has surpassed human ability in chess, and is now considered the strongest player.
- Is pool a solved game?: No, pool is not considered a solved game, as it is a physical game that involves geometry and physics.
- What is the biggest game world ever?: Minecraft has the largest land-based open world to explore, with a size of approximately 1.5 billion sq. miles.
- What is the biggest game in gaming history?: Minecraft is the best-selling video game of all time, with over 300 million copies sold.
- Has AI beaten shogi?: Yes, artificial intelligence has beaten shogi masters, and is now considered the strongest player.
- Can a chess game never end?: No, chess games are subject to the 50-move rule, which states that if a pawn is not moved or a piece captured within 50 moves, the game is a draw.
- Is poker just math?: No, poker is a game that involves math, but also social and psychological aspects.
- How do you play Killer pool?: Killer pool is a multi-player game where each player has a set number of lives, and takes one shot per inning to attempt to pocket a ball.
- What pool game has 3 balls and no holes?: Carom billiards is a game played with three balls and no holes, where the objective is to drive one of the white balls into both of the other balls.