MathNet 1999 — Part 01 Question 82

Alberto and Barbara play the following game. There are 1999 matches on a table: each player must take turns removing from the table a number of matches of their choice, as long as it is greater than or equal to one, and less than or equal to half the number of matches that are on the table at that moment. The player who leaves only one match on the table loses. Barbara is the first to play.
Determine for which of the two players there is a winning strategy and describe this strategy.