I am learning the basics of combinatorial game theory (impartial games). After learning about decompose a game into the sum of games, I feel comfortable with games that can divided into the sum of 1 pile games. The situation is more or less clear to me: I have to find the game graph, calculate the Sprague-Grundy values and use them to find the solution to a game.
But I do not really know what to do in case when I can't decompose a game in 1 pile games. Here is an example:
You have piles of stones, people alternate turns, person who can't make a move loses. During the move, a player can select any one of the piles divide the stones in it into any number of unequal piles such that no two of the newly created piles have the same number of stones.
I have huge problem in analyzing the 1 pile subgame (calculating grundy values for the pile of $1, 2, 3, ... n$ stones in the pile), because after each move 1 piles is divided into more piles.
How should I analyze such games?