Where to swap (y)

the red marked hexes should not be swapped
the blue marked hexes should be swapped
the star marked hexes are defining the Y board.

Regular Y / Size 2

Regular Y / Size 3

Regular Y / Size 4

Regular Y / Size 5

Regular Y / Size 6

Regular Y / Size 7

Regular Y / Size 8

Regular Y / Size 9

Up to symmetry, the only move with unknown status is the middle cell along an edge. So suppose Blue plays first here. By a strategy stealing argument, Red can not hope to win by responding with another middle edge move. This leaves only the six marked cells to be investigated.

If Red plays here, Blue wins easily with this continuation.

This red move is somewhat better, but Blue can win with the same response.

And if Red plays here himself, Blue can win as shown.

Red essentially only has one option left. This move seems promising, since it wins if Blue had played any of the marked cells instead as his first move.

However, it is currently unknown who wins if Blue plays either of the two marked cells next, as they can lead to rather complicated positions. All others are losing for Blue.

Regular Y / Size 10

Regular Y / Bent-27

This board (on which the pieces are placed on the intersections) should be within reach for computers, but no results are known so far.

Master Y

In Master Y, the first player places one piece on the board, and each subsequent move consists of placing two pieces on the board.

the red marked hexes are losing first moves
the blue marked hexes are winning first moves

Master Y / Size 2

Master Y / Size 3

Master Y / Size 4

Master Y / Size 5

Master Y / Size 6

Master Y / Bent-27

Again, status unknown but presumably within reach for computers.