So friends, I was learning game theory and there was one example relating to grundy number representation of states. The problem is — There is a maze with floors and walls. Walls are represented by black color and you cannot go there. You can only move on the "floor". Also you can only move either up or left.
The maze figure given is :
Maze, my grundy numbers and correct grundy numbers
In the same figure above I have also shown my grundy numbers and the correct grundy numbers. And as you can see, mine are wrong. I think I am not undertanding the orange colored grundy numbers and that is from where all the error is started.
Can you please explain me where I am wrong?
Thank you.
Looks like on the 'correct' grid you can move up or left some cells, not necessarily 1.
Can you explain what you mean by "not necessarily 1"?
And also can you check how my interpretation is wrong for example for top left orange square in "my grundy numbers", from that state you can go up(grundy no = 0) or left(grundy no = 0). So according to the sprague-grundy theorem, the grundy number for the current state(top-left orange square) it should be the smallest no-negative number not in the set of grundy numbers representing the states it go to. And so it should be 1 (set = {0,0}) and not 2(as given in correct solution).
You can go k cells left or up, where k is not necessarily equal to 1.