Algorithm for token replacement game I'm having problems finding an algorithm to the following problem:

A and B take turns replacing a number $n$ of tokens with either $floor((n+1)/2)$ or $n-1$. The player who makes one token remain wins. We want to know, if there is a way for B to win the game no matter the moves of A. A begins the game.

My idea is the following:

Is n = 1 -> No way for B to win the game

We try all moves of first A then B and check for 1 -> There is a way for B to win

But this does not incorporate the "no matter the moves of A" criteria.
I'd check what happens for some small(ish) values of initial $n$, working up. If you know who wins if there are at most $n$ on the table, working out what happens with $n + 1$ is easy.