Alice and Bob play the following game that starts with $N\ge3$ green marbles on the table.
- Alice and Bob move alternatingly.
- Alice makes the first move. In this first move, Alice removes $x$ green marbles from the table; the number $x$ is chosen by Alice so that it satisfies $1\le x\le N-1$.
- In every further move, the active player removes $y$ marbles from the table. The number $y$ is chosen by the active player to satisfy $1\le y\le2z$, where $z$ denotes the number of marbles that have been removed in the preceding move of the other player.
- The player who takes the last marble wins the game.
Question: Which player is going to win this game (in dependence on $N$)?
(As usual, we assume that Alice and Bob both use optimal strategies.)