Random NIM

There are $N$ piles numbered $1, 2, \ldots, N$. The $i$-th pile initially has $A_i$ stones. Alice and Bob are playing a Nim game on these piles, but there is a twist. As per the usual rules of Nim, Alice and Bob take turns alternately choosing a pile and removing some stones from the pile, with Alice going first. The player unable to make a move loses. However, the twist is that instead of choos