Twixt is a strategy game originally published by 3M in 1961. This is one of the types of games that takes less than five minutes to learn but the strategic aspects can take years to master.
The board is a grid of points that give the game a very mathematical feel. Each player takes turns placing a peg in one of the points on the board. After a peg is placed, a link may be made between any two pegs that are exactly two points over and one peg up (or any other combination that is like a knight’s move in chess).
The first player that makes a series of links from one side of the board to the other is the winner. One player top to bottom and the other left to right. Players run into each other as they are trying to cross the board.
After a few times playing the game, both players get a pretty good idea of basic strategies. More complex mathematical strategies are used by more advanced players who have tournaments every year. These games never actually end with one player making it across the board because the other player will give up when it becomes obvious that he can’t win.
The only thing harder than mastering this game might be finding a copy of it somewhere. Good luck.