Finally, justice has been served to Bob!! 😭

In 2272F — Tree Reduction Game, Alice still gets the first move, but Bob finally gets some compensation: he can choose the initial root of the tree!

With the right choice, Bob can guarantee his victory even when playing second. No more suffering from always going second — Bob is finally getting his chance to shine!

Come on, Bob, you got this! 🗿

Upd: Bob really cooked this game. =DD
After a lot of research, the result surprised me

It is easy to see that when n is odd, Bob always wins. If n is even, Bob's win rate increases gradually until it reaches 100%, regardless of the number of nodes (I tested n up to $$$10^5$$$).