Cutting A Very Large Polygon
Dan and Sam play a game on a regular polygon of 100 sides. Each one draws a diagonal on the polygon in his turn.
When someone draws a diagonal, it cannot have common points (except the vertexes of the polygon) with other diagonals already drawn.
The game finishes when someone can't draw a diagonal on the polygon following the rules; that person is the loser. If Dan begins, who will win? In other words, who has a winning strategy?
Clarification: The diagonals of a polygon are straight lines that join non-adjacent vertexes.