So in this game we have two piles of size $n$ and $m$ respectively. Two players take turns, in each turn the player chooses one pile to completely remove from the game and then splits the pile that is left into two non empty parts (not necessarily equal). The player that cannot make a valid move loses (by invalid move meaning he cant split the pile into non empty parts). For example the first player chooses the pile of size $n$ to remove and splits the pile of size $m$ to $\frac{m}{3}$ and $m-\frac{m}{3}$. What is the winning strategy for this game based on $n$ and $m$ values?
I'm new to these and really lost
If there are two piles, at least one of which has an even size, the winning move is to choose an even-sized pile and split it into two odd-sized piles. The opponent must split an odd-sized pile into one even-sized and one odd-sized pile. This means that the first player wins if and only if there is at least one even-sized pile.