Recently I was learning about the Grundy Number (a.k.a. Nimber) about how to convert a state of impartial combinatorial games into a state of a Nim Game and I was quite amazed about this

My question on this blog would be how do we usually find a way to convert a game state to a nimber?

For example consider a look on this mini game that I found recently

Assume a game of grid tiling where two players (name it Kiki and Wiwi) can place a tile to this game grid. Kiki and Wiwi's orientation of movement can be seen here

The question is how do we get a nimber of this game state? I was thinking of something like make a grid becomes a $$$2^{16}$$$ possible state and convert each of them into a nimber

But does anyone thought of another approach? I'm interested to learn it since I'm quite fascinated about this sprague grundy theorem recently.

Thanks. Much appreciated :)