Winning strategy for a matchstick game

There are $N$ matchsticks at the table. Two players play the game. Rules: (i) A player in his or her turn can pick $a$ or $b$ match sticks. (ii) The player who picks the last matchstick loses the game.

1. What should be the conditions on $N$ so that a winning strategy can be derived for the first player?

2. What should be the strategy of first player so that he or she always wins this game provided $N$ is such that a wiinning strategy can be derived?

I have solved this problem by hit and trial for small numbers one or two, but is there a general solution?
Edit : Suppose rules of the game are changed and now a player in his or her turn can pick any number of matchstick upto p < N , then how many sticks should first player pick to ensure a win

If the moves consist of taking either $a$ or $b$ sticks, with $a\lt b$ and, as clarified in a comment, $N\lt a$ is a loss, then the first player wins iff $((N-1)\bmod(a+b))\bmod(2a)\lt a$, and a winning strategy is to take $a$ sticks if $(N-1)\bmod(a+b)\gt b$, take $b$ sticks if $(N-1)\bmod(a+b)\lt a$, and take either otherwise.