Placing Coins on a Table

Source

I got this problem from Rustan Leino, who got it from Amit Rao.

I solved it and wrote up my solution.

Problem    

Two players are playing a game. The game board is a circular table. The players have access to an ample supply of equal-sized circular coins. The players alternate turns, with each turn adding a single coin to the table. The coins are not allowed to overlap. Once a coin is placed on the table, it is not allowed to be moved. The player who has no place to put his next coin loses. Develop a winning strategy for the player who starts. (The table is large enough to accommodate at least one coin.)

Solution     Reveal