Difference between revisions of "Where to swap (y)"
(Updated and edited Regular Size 9 - middle edge cell opening) |
(Updated and edited Regular Size 9 - middle edge opening) |
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| Line 98: | Line 98: | ||
3:SSSSSS___ | 3:SSSSSS___ | ||
4:SSSSS____ | 4:SSSSS____ | ||
| − | 5: | + | 5:SSSS__R__ |
6:SSS______ | 6:SSS______ | ||
| − | 7: | + | 7:SS___B___ |
8:S________ | 8:S________ | ||
9:____B____ | 9:____B____ | ||
</hex> | </hex> | ||
| − | If Red plays | + | If Red plays here, Blue wins fairly easily with this continuation. |
| Line 113: | Line 113: | ||
4:SSSSS____ | 4:SSSSS____ | ||
5:SSSS_____ | 5:SSSS_____ | ||
| − | 6: | + | 6:SSS______ |
| − | 7: | + | 7:SS___BR__ |
| − | 8: | + | 8:S________ |
| − | 9: | + | 9:____B____ |
</hex> | </hex> | ||
| − | + | The same move works for Blue if Red plays here instead. | |
| Line 126: | Line 126: | ||
3:SSSSSS___ | 3:SSSSSS___ | ||
4:SSSSS____ | 4:SSSSS____ | ||
| − | 5: | + | 5:SSSS__B__ |
| − | 6: | + | 6:SSS______ |
| − | 7: | + | 7:SS___R___ |
8:S________ | 8:S________ | ||
9:____B____ | 9:____B____ | ||
</hex> | </hex> | ||
| − | + | And if Red plays here, Blue yet again has a winning move as shown. | |
| Line 141: | Line 141: | ||
4:SSSSS____ | 4:SSSSS____ | ||
5:SSSS_____ | 5:SSSS_____ | ||
| − | 6: | + | 6:SSSPP_R__ |
| − | 7: | + | 7:SSPP_____ |
| + | 8:SPPPP____ | ||
| + | 9:PPPPB____ | ||
| + | </hex> | ||
| + | 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. | ||
| + | |||
| + | |||
| + | <hex> C9 R9 | ||
| + | 1:SSSSSSSS_ | ||
| + | 2:SSSSSSS__ | ||
| + | 3:SSSSSS___ | ||
| + | 4:SSSSS____ | ||
| + | 5:SSSS_____ | ||
| + | 6:SSS___R__ | ||
| + | 7:SS__P_P__ | ||
8:S________ | 8:S________ | ||
9:____B____ | 9:____B____ | ||
</hex> | </hex> | ||
| − | + | 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. | |
Revision as of 15:54, 6 December 2011
- the red marked hexes should not be swapped
- the blue marked hexes should be swapped
- the star marked hexes are defining the Y board.
Contents
- 1 Regular Y / Size 2
- 2 Regular Y / Size 3
- 3 Regular Y / Size 4
- 4 Regular Y / Size 5
- 5 Regular Y / Size 6
- 6 Regular Y / Size 7
- 7 Regular Y / Size 8
- 8 Regular Y / Size 9
- 9 Regular Y / Size 10
- 10 Regular Y / Bent-27
- 11 Master Y
- 12 Master Y / Size 2
- 13 Master Y / Size 3
- 14 Master Y / Size 4
- 15 Master Y / Size 5
- 16 Master Y / Size 6
- 17 Master Y / Bent-27
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 fairly easily with this continuation.
The same move works for Blue if Red plays here instead.
And if Red plays here, Blue yet again has a winning move 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.
