One of the games Ludus has used in their national tournaments is Slimetrail. This game is simple enough that it can be played by a wide age range, but there are many complicated strategies that can be used by more advanced players.
Slimetrail is played on a connected graph, with one vertex colored Blue, another colored Red, and a third vertex with a moveable piece or token which will create the trail of slime. The two players alternate turns moving the token one space, then marking the previous space (where the token was) a third color (usually green). The token can never be moved back to one of these "slimed" spaces.
A player wins when the token is moved onto the space of their color. Since we want to make sure that one player can still win, it's not allowed to move the token to a space where it can't reach at least one of the two goals.
In all the examples I've seen, Slimetrail is played on a grid, with adjacencies in all 8 directions. Apparently, it's also played on hex grids.
(Edit: the link to the game didn't auto-clickableify, so I added a clickable link.)
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