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A game of chess can be posed as the following decision problem: given a legal positioning of chess pieces and information about which side is to move, determine whether that side can win. Is this decision problem decidable?

User Skymon
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The decision problem of determining whether a given chess position is winnable by a specific side is undecidable. This is because there exists an infinite number of possible move sequences leading to different endgame scenarios, and it is impossible to explore all of them in a finite amount of time. Additionally, the problem cannot be reduced to a known decidable problem, making it impossible to solve using standard algorithms or formal systems. Therefore, heuristic-based methods are used to approximate the outcome of a game.

User Jeanclaude
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