Problem solving strategy to determine who wins a game?

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Consider a game on a chess board with a single counter in the top right corner. You can only move this counter to a square that is adjacent. There are two competitors and the aim of the game is to get the counter to the bottom left corner. The competitor who places the counter in this corner is the winner.

A long time ago I saw a strategy where you denote the winning square as $w$. The two adjacent squares are then losing squares $L$. Then the adjacent squares to these losing squares are winning squares $w$ and so on. With this method, it becomes possible to determine which player will always win when following the correct strategy.

Unfortunately I don't remember what this method is called and I was hoping someone new the name of this cool strategy?

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The method is 'parity' and the game is 'ultra-weak solved'.