Using strong induction (so, neither weak nor "weak++") on the number of matches in the pile, prove that if this number is of the form 4k + 1, for k ∈ N, then P2 always has a strategy to win (which they will follow, because they are smart). Otherwise, P1 always have a strategy to win (which they will also follow because they’re smart too)! To be clear, you will need to prove both facts with a single inductive proof! That is to say, you will need to prove that P2 can always win under the aforementioned condition, but whenever that condition is not met, you have to prove that it is now P1 that can always win!