{"id":236243,"date":"2024-04-23T09:42:22","date_gmt":"2024-04-23T09:42:22","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=236243"},"modified":"2024-04-23T09:42:22","modified_gmt":"2024-04-23T09:42:22","slug":"how-to-calculate-grundy-value","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-calculate-grundy-value\/","title":{"rendered":"How to calculate Grundy value?"},"content":{"rendered":"

Grundy value is a concept in combinatorial game theory that helps determine the optimal strategy in a game. It represents the nim-value of a game position, which is the minimum non-negative integer not present in the Grundy values of its immediate successors. This value can be calculated using the following recursive algorithm:<\/p>\n

1. If the current position is a losing position (i.e., Grundy value of 0), return 0.
\n2. If the Grundy value of the current position has already been calculated, return that value.
\n3. Otherwise, calculate the Grundy value by considering all possible moves from the current position and finding the Grundy value of each successor.
\n4. Calculate the Mex (minimum excluded value) of all the successor Grundy values, which is the smallest non-negative integer not present in these values.
\n5. Return this Mex value as the Grundy value of the current position.<\/p>\n

Using this algorithm, players can determine the optimal moves in a game by analyzing the Grundy values of different positions and selecting the move that leads to a position with a Grundy value of zero.<\/p>\n

\n
\n

Table of Contents<\/p>\nToggle<\/span><\/path><\/svg><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n