Random Nim

Alice and Bob are playing a modified version of the Nim game. There are $N$ piles of stones, where the $i^{th}$ pile contains $A_i$ stones. In each turn, Alice and Bob roll a fair $D$-sided die. The player who rolls the higher number gets to make a move. If they roll the same number, Alice gets to make the move. During their turn, a player must select **exactly one** non-empty pile and remove **