Hex
The honeycomb game
Join your two edges before the other side joins theirs. One rule, no draws, and a lifetime of strategy.
A game invented twice
In 1942 the Danish poet and mathematician Piet Hein showed a new game at the Niels Bohr Institute in Copenhagen, and readers of the newspaper Politiken soon knew it as Polygon. A few years later John Nash, then a young mathematician at Princeton, came up with the same game on his own. Parker Brothers sold it in the early 1950s under the name it has kept ever since: Hex.
Why it never ends in a draw
However a board fills up, exactly one side ends up joined edge to edge, because a wall of stones that blocks one side is itself a chain that wins for the other. So every game has a winner.
Nash also proved that whoever moves first can always win with perfect play. His proof shows the winning strategy exists without saying what it is, and on boards like 11 by 11 nobody has found it. That is why serious players use the swap rule: after the opening stone, the other side may take it as their own, so the first stone should be good, but not too good.