Jealous Nobita

Shizuka and Dekisugi are playing with a binary tree rooted at $1$. In each turn, the player chooses a subtree and erases it. The erased subtree must be a perfect binary tree. Shizuka takes the first turn. The player unable to move will lose the game.


This is a companion discussion topic for the original entry at https://toph.co/p/jealous-nobita