The origin of my question comes from a common job interview question where two players take turns placing coins on a round table. The coins cannot overlap and can't be moved once they've been placed. The player which first has no available space on the table to place a coin, loses.
The intuitive strategy for the first player in this game is to place their first coin in the centre of the table, and then place their ensuing coins collinear to the central coin and his opponent's previously placed coin, as well as equidistant from the centre as his oppponent's coin.
I then question what would happen if the table was an equilateral triangle. The strategy as described above falls apart, and unfortunately I have not yet come up with a well defined strategy for the first player to win (if there exists one) without some pretty restricting assumptions. I am looking for some help with this.