The game of Y is not on boardgamegeek as far as I can tell, so I'll tell you the rules. (Oops, yes it is.)
It's played on a triangular hex board. Each player has markers of a different colour and takes turns placing a marker on an unoccupied hex on the board. The goal is to connect all three sides of the board with a chain of your pieces. Corners count as being on both sides. That's all the rules there are, and the beauty of it is that one player must win.
Caeth Y is the same game using the caeth meta-rule. In a caeth game, rather than claiming cells you claim edges between cells. When you've claimed at least half of the edges incident with a cell, you claim the cell.
On this board, then, take turns colouring edges. If you've claimed half the edges going into a circle, colour the circle as well. When you've got a Y of circles connecting all three edges, you win. Note that the connectivity of your coloured edges is completely unrelated to whether you win the game or not!
I haven't played any of these games yet (I didn't have a board till just now!) but it seems to me that a small board would make the game too easy? So I've made some larger ones as well. Awfully smart people probably know how to force a win going first anyway, but I'm not awfully smart ye