Making Fifteen

[From Thinking Mathematically, p. 79. Modified by Sam Rebelsky.]

Nine counters marked with the digits 1 to 9 are placed on the table. Two players alternately take one counter from the table. The winner is the first player to obtain a set of counters that include three counters which sum to fifteen. Devise a winning strategy.

Is there a winning strategy if there are three players?

Are there interesting variants of the game with more counters (and perhaps a different goal number)?