Number of players: 2
Board: Square grid of indeterminate size. At the start of the game one segment is filled in.

Object: to get three X's or O's in a row. Sound familiar?
Sequence of play: Each player starts by choosing a symbol to represent eirself. X's and O's are traditional, but others work just fine. The players then alternate taking turns. A turn consists of placing the chosen symbol on an empty space adjacent to a board segment, followed by placing a board segment so that it is connected to a previously placed segment.
Any segment placement which leaves no square for the other player to place a symbol on the next turn is illegal.
Strategy: Try to put your own pieces in compact groups that can create a large number of threats, while making your opponent's pieces more disperse. Use threats of making three in a row to force your opponent's piece positioning, while building segments and your own pieces towards the creation of two simultaneous direct threats, (i.e., pairs of symbols with a segment in place for a group of three in a row to be formed,) guaranteeing a win. Of course, doing this as you are defending against your opponent's attempts to do the same is tricky.