A first winning-strategy game

Some games are decided before the final move: with perfect play one side wins from a given start. In a take-away game each player removes a fixed number of tokens (here 1 or 2), and whoever takes the last token wins. Play it enough and you feel that some pile sizes are already lost for whoever must move.

The tool is modular arithmetic. With takes of size 1 or 2, the losing pile sizes are the multiples of $3$: whatever you take, the opponent can answer so that the total removed in the round is $3$, and you are left on the next multiple of $3$. A winning strategy is a rule that always hands the opponent a losing position, without relying on their mistakes.