Not only is it hard, it’s NP-Hard.
Technically, it’s ‘NP-hard,’ meaning that there is no efficient way to calculate the necessary moves to “win,” even if you know in advance the complete order of pieces, and are given all the time you need to make each move. At least there’s one geek classic that refuses to fall to the scrutiny of mathematicians.
Now why didn’t I think of that for a graduate thesis???