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

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(Updated Regular Size 9: A3 loses to D4)
(swap maps for sizes 10-13, 15, 17)
 
(18 intermediate revisions by 4 users not shown)
Line 1: Line 1:
−
*the red marked hexes should not be swapped
+
* The red marked hexes should be swapped.
−
*the blue marked hexes should be swapped
+
* The blue marked hexes should not be swapped.
−
*the star marked hexes are defining the [[Y]] board.
+
  
−
=== Regular Y / Size 2===
+
== Regular Y ==
−
<hex> C2 R2
+
−
1:SB
+
−
2:BB
+
−
</hex>
+
  
−
=== Regular Y / Size 3===
+
=== Size 2 ===
−
<hex> C3 R3
+
<hexboard size="2x2"
−
1:SSR
+
  coords="none"
−
2:SBB
+
  edges="none"
−
3:RBR
+
  visible="area(a2,b2,b1)"
−
</hex>
+
  contents="S red:all"
 +
  />
  
−
=== Regular Y / Size 4===
+
=== Size 3 ===
−
<hex> C4 R4
+
<hexboard size="3x3"
−
1:SSSR
+
  coords="none"
−
2:SSBB
+
  edges="none"
−
3:SBBB
+
  visible="area(a3,c3,c1)"
−
4:RBBR
+
  contents="S blue:all red:(b2 b3 c2)"
−
</hex>
+
  />
  
−
=== Regular Y / Size 5===
+
=== Size 4 ===
−
<hex> C5 R5
+
<hexboard size="4x4"
−
1:SSSSR
+
  coords="none"
−
2:SSSRR
+
  edges="none"
−
3:SSRBR
+
  visible="area(a4,d4,d1)"
−
4:SRBBR
+
  contents="S red:all blue:(a4 d4 d1)"
−
5:RRRRR
+
  />
−
</hex>
+
  
−
=== Regular Y / Size 6===
+
=== Size 5 ===
−
<hex> C6 R6
+
<hexboard size="5x5"
−
1:SSSSSR
+
  coords="none"
−
2:SSSSRR
+
  edges="none"
−
3:SSSRRR
+
  visible="area(a5,e5,e1)"
−
4:SSRBBR
+
  contents="S blue:all red:area(d3,c4,d4)"
−
5:SRRBRR
+
  />
−
6:RRRRRR
+
−
</hex>
+
  
−
=== Regular Y / Size 7===
+
=== Size 6 ===
−
<hex> C7 R7
+
<hexboard size="6x6"
−
1:SSSSSSR
+
  coords="none"
−
2:SSSSSRR
+
  edges="none"
−
3:SSSSRBR
+
  visible="area(a6,f6,f1)"
−
4:SSSRBBR
+
  contents="S blue:all red:area(d4,d5,e4)"
−
5:SSRBBBR
+
  />
−
6:SRBBBBR
+
−
7:RRRRRRR
+
−
</hex>
+
  
−
=== Regular Y / Size 8===
+
=== Size 7 ===
−
<hex> C8 R8
+
<hexboard size="7x7"
−
1:SSSSSSSR
+
  coords="none"
−
2:SSSSSSRR
+
  edges="none"
−
3:SSSSSRRR
+
  visible="area(a7,g7,g1)"
−
4:SSSSRBBR
+
  contents="S blue:all red:area(c6,f6,f3)"
−
5:SSSRRBRR
+
  />
−
6:SSRBBBBR
+
−
7:SRRBRBRR
+
−
8:RRRRRRRR
+
−
</hex>
+
  
−
=== Regular Y / Size 9===
+
=== Size 8 ===
−
<hex> C9 R9
+
<hexboard size="8x8"
−
1:SSSSSSSSR
+
  coords="none"
−
2:SSSSSSSRR
+
  edges="none"
−
3:SSSSSSRRR
+
  visible="area(a8,h8,h1)"
−
4:SSSSS____
+
  contents="S blue:all red:(f4--f7,g4--d7,d6--g6)"
−
5:SSSS__B__
+
  />
−
6:SSS__BB__
+
−
7:SSR_BBB_R
+
−
8:SRR____RR
+
−
9:RRR___RRR
+
−
</hex>
+
  
−
=== Regular Y / Bent-27===
+
=== Size 9 ===
 +
<hexboard size="9x9"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a9,i9,i1)"
 +
  contents="S blue:all red:area(g5,g7,e7)"
 +
  />
 +
 
 +
=== Size 10 ===
 +
The hexes marked (*) are proven to be winning or losing. The rest are highly likely but not proven.
 +
 
 +
<hexboard size="10x10"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a10,j10,j1)"
 +
  contents="S blue:all red:area(f6,h5,i6,h8,f9,e8) E *:(area(d7,d10,a10) area(j1,j4,g4) area(j7,j10,g10) area(f7,f8,g8,h7,h6,g6))"
 +
  />
 +
 
 +
=== Size 11 ===
 +
For sizes 11 and larger, the swap map maps are not proven, but a cell is only shaded red or blue if it is likely to be accurate.
 +
 
 +
<hexboard size="11x11"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a11,k11,k1)"
 +
  contents="S blue:all red:area(i9,i5,e9)"
 +
  />
 +
 
 +
=== Size 12 ===
 +
<hexboard size="12x12"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a12,l12,l1)"
 +
  contents="S blue:all red:area(j10,j5,e10)"
 +
  />
 +
 
 +
=== Size 13 ===
 +
<hexboard size="13x13"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a13,m13,m1)"
 +
  contents="S blue:all red:area(l4,k4,i8,h8,h9,d11,d12,h10,h11,i10,k12,l11,j9,k8,j8)"
 +
  />
 +
 
 +
=== Size 15 ===
 +
<hexboard size="15x15"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a15,o15,o1)"
 +
  contents="S blue:all red:area(m6,l6,k8,i9,h11,f12,f13,h12,i13,k12,l13,m12,l11,m9,l8)"
 +
  />
 +
 
 +
=== Size 17 ===
 +
Uncertain cells are shaded gray. These cells are marked (+) if they are more likely to be strong cells (that Blue should swap) and (-) if they are more likely to be weak cells (that Blue should not swap).
 +
 
 +
<hexboard size="17x17"
 +
  coords="none"
 +
  edges="none"
 +
  visible="area(a17,q17,q1)"
 +
  contents="S blue:all red:(o10 j10 j15 area(n8,n7,m8) area(h14,h13,g14) area(n14,n13,m14) area(m10 l10 j12 j13 l13 m12)) gray:(o7 m7 g13 g15 m15 o13 line(n9,l9,i12,i14,l14,n12,n9)) E +:line(n9,l9,i12,i14,l14,n12,n9) -:(o7 m7 g13 g15 m15 o13)"
 +
  />
 +
 
 +
=== Bent-27 ===
  
 
[[Image:Y27_bent.gif]]
 
[[Image:Y27_bent.gif]]
Line 85: Line 128:
 
This board (on which the pieces are placed on the intersections) should be within reach for computers, but no results are known so far.
 
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===
+
== 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.
 
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 red marked hexes are winning first moves
−
*the blue marked hexes are winning first moves
+
*the blue marked hexes are losing first moves
  
−
=== Master Y / Size 2===
+
=== Size 2 ===
−
<hex> C2 R2
+
<hexboard size="2x2"
−
1:SR
+
  coords="none"
−
2:RR
+
  edges="none"
−
</hex>
+
  visible="area(a2,b2,b1)"
 +
  contents="S blue:all"
 +
  />
  
−
=== Master Y / Size 3===
+
=== Size 3 ===
−
<hex> C3 R3
+
<hexboard size="3x3"
−
1:SSR
+
  coords="none"
−
2:SBB
+
  edges="none"
−
3:RBR
+
  visible="area(a3,c3,c1)"
−
</hex>
+
  contents="S blue:all red:area(b3,c2,b2)"
 +
  />
  
−
=== Master Y / Size 4===
+
=== Size 4 ===
−
<hex> C4 R4
+
<hexboard size="4x4"
−
1:SSSR
+
  coords="none"
−
2:SSRR
+
  edges="none"
−
3:SRBR
+
  visible="area(a4,d4,d1)"
−
4:RRRR
+
  contents="S blue:all red:c3"
−
</hex>
+
  />
  
−
=== Master Y / Size 5===
+
=== Size 5 ===
−
<hex> C5 R5
+
<hexboard size="5x5"
−
1:SSSSR
+
  coords="none"
−
2:SSSRR
+
  edges="none"
−
3:SSRRR
+
  visible="area(a5,e5,e1)"
−
4:SRRRR
+
  contents="S blue:all"
−
5:RRRRR
+
  />
−
</hex>
+
  
−
=== Master Y / Size 6===
+
=== Size 6 ===
−
<hex> C6 R6
+
<hexboard size="6x6"
−
1:SSSSSR
+
  coords="none"
−
2:SSSSRR
+
  edges="none"
−
3:SSSRRR
+
  visible="area(a6,f6,f1)"
−
4:SSR__R
+
  contents="S blue:all red:area(d4,d5,e4)"
−
5:SRR_RR
+
  />
−
6:RRRRRR
+
−
</hex>
+
  
−
=== Master Y / Bent-27===
+
=== Bent-27 ===
  
 
[[Image:Y27_bent.gif]]
 
[[Image:Y27_bent.gif]]
  
 
Again, status unknown but presumably within reach for computers.
 
Again, status unknown but presumably within reach for computers.
 +
 +
== See also ==
 +
For corresponding information on Hex, please visit [[Small boards]].
  
 
[[category:Y]]
 
[[category:Y]]

Latest revision as of 02:58, 26 June 2026

  • The red marked hexes should be swapped.
  • The blue marked hexes should not be swapped.

Regular Y

Size 2

Size 3

Size 4

Size 5

Size 6

Size 7

Size 8

Size 9

Size 10

The hexes marked (*) are proven to be winning or losing. The rest are highly likely but not proven.

Size 11

For sizes 11 and larger, the swap map maps are not proven, but a cell is only shaded red or blue if it is likely to be accurate.

Size 12

Size 13

Size 15

Size 17

Uncertain cells are shaded gray. These cells are marked (+) if they are more likely to be strong cells (that Blue should swap) and (-) if they are more likely to be weak cells (that Blue should not swap).

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

Size 2

Size 3

Size 4

Size 5

Size 6

Bent-27

Y27 bent.gif

Again, status unknown but presumably within reach for computers.

See also

For corresponding information on Hex, please visit Small boards.

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