Difference between revisions of "Where to swap (y)"

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(Minor update)
Line 72: Line 72:
 
3:SSSSSSRRR
 
3:SSSSSSRRR
 
4:SSSSSRRRR
 
4:SSSSSRRRR
−
5:SSSS_RBR_
+
5:SSSSRRBRR
 
6:SSSRRBBRR
 
6:SSSRRBBRR
 
7:SSRRBBBRR
 
7:SSRRBBBRR
 
8:SRRRRRRRR
 
8:SRRRRRRRR
−
9:RRRR_RRRR
+
9:RRRRRRRRR
 
</hex>
 
</hex>
−
 
−
<hex> C9 R9
 
−
1:SSSSSSSS_
 
−
2:SSSSSSS__
 
−
3:SSSSSS___
 
−
4:SSSSS____
 
−
5:SSSS__P__
 
−
6:SSS__PP__
 
−
7:SS__PPP__
 
−
8:S________
 
−
9:____B____
 
−
</hex>
 
−
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.
 
−
 
−
 
−
<hex> C9 R9
 
−
1:SSSSSSSS_
 
−
2:SSSSSSS__
 
−
3:SSSSSS___
 
−
4:SSSSS____
 
−
5:SSSS__R__
 
−
6:SSS______
 
−
7:SS___B___
 
−
8:S________
 
−
9:____B____
 
−
</hex>
 
−
If Red plays here, Blue wins easily with this continuation.
 
−
 
−
 
−
<hex> C9 R9
 
−
1:SSSSSSSS_
 
−
2:SSSSSSS__
 
−
3:SSSSSS___
 
−
4:SSSSS____
 
−
5:SSSS_____
 
−
6:SSS______
 
−
7:SS___BR__
 
−
8:S________
 
−
9:____B____
 
−
</hex>
 
−
This red move is somewhat better, but Blue can win with the same response.
 
−
 
−
 
−
<hex> C9 R9
 
−
1:SSSSSSSS_
 
−
2:SSSSSSS__
 
−
3:SSSSSS___
 
−
4:SSSSS____
 
−
5:SSSS__B__
 
−
6:SSS______
 
−
7:SS___R___
 
−
8:S________
 
−
9:____B____
 
−
</hex>
 
−
And if Red plays here himself, Blue can win as shown.
 
−
 
−
 
−
<hex> C9 R9
 
−
1:SSSSSSSSP
 
−
2:SSSSSSS_P
 
−
3:SSSSSS__P
 
−
4:SSSSS____
 
−
5:SSSS_____
 
−
6:SSSPP_R__
 
−
7:SSPP____P
 
−
8:SPPPP___P
 
−
9:PPPPB___P
 
−
</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________
 
−
9:____B____
 
−
</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.
 
−
 
  
 
=== Regular Y / Size 10===
 
=== Regular Y / Size 10===
 
<hex> C10 R10
 
<hex> C10 R10
 
1:SSSSSSSSSR
 
1:SSSSSSSSSR
−
2:SSSSSSSS__
+
2:SSSSSSSSRR
−
3:SSSSSSS___
+
3:SSSSSSSRRR
−
4:SSSSSS____
+
4:SSSSSSRRRR
 
5:SSSSS_____
 
5:SSSSS_____
−
6:SSSS______
+
6:SSSS__BB__
−
7:SSS___B___
+
7:SSSR_BBB_R
−
8:SS________
+
8:SSRR_BB_RR
−
9:S_________
+
9:SRRR___RRR
−
10:R________R
+
10:RRRR__RRRR
 
</hex>
 
</hex>
  

Revision as of 05:27, 31 August 2016

  • 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

Regular Y / Size 10

Regular Y / Bent-27

Y27 bent.gif

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

Y27 bent.gif

Again, status unknown but presumably within reach for computers.

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