Difference between revisions of "User:Mason"

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== Relative Coordinates ==
 
== Relative Coordinates ==
 
This is a coordinate system adapted from [https://senseis.xmp.net/?Coordinates%2FRelativeCoordinates Go] that allows us to talk about important moves in the same way, regardless of board size. We use YX instead of XY because row is more important in Hex, and because we're taking the bottom red edge as our perspective, as is customary. This also most closely resembles how people talk about certain moves already. 4-4 becomes 44. 5-4 becomes 54'.
 
This is a coordinate system adapted from [https://senseis.xmp.net/?Coordinates%2FRelativeCoordinates Go] that allows us to talk about important moves in the same way, regardless of board size. We use YX instead of XY because row is more important in Hex, and because we're taking the bottom red edge as our perspective, as is customary. This also most closely resembles how people talk about certain moves already. 4-4 becomes 44. 5-4 becomes 54'.
 +
* '''A:''' 44
 +
* '''B:''' 54'
 +
* '''C:''' 5'4
 +
* '''D:''' 4'4'
 +
* '''1:''' 2'3
 +
* '''2:''' 5'2
 +
<hexboard size="13x13"
 +
  coords="none"
 +
  contents="R A:d10 B:j9 C:d5 D:j4 1:c2 2:b5 3:b8"
 +
  />
 +
'''3''' requires some more explaining. On it's own, '''3''' would be 62. However, if stones '''1''' and '''2''' were the previous two moves, it can be better to refer to it as 8'2. This is because the sequence 2'3, 5'2, 8'2 is a common opening sequence, and referring to it as 8'2 means it won't change with board size. It also communicates the fact that '''3''''s row is based on the placement of '''1''' and '''2''', and not distance from the red edge.
  
−
44
+
=== Edges ===
−
<hexboard size="4x4"  
+
Relative coordinates naturally give rise to a very simple way of referring to the edges: red, red', blue, blue'.
−
   edges="bottom left"
+
 
 +
== Symmetrical Switchback Templates ==
 +
 
 +
<hexboard size="4x7"
 +
  visible="-area(a1,a3,c1)"
 +
   edges="bottom"
 
   coords="none"
 
   coords="none"
−
   contents="R d1"
+
   contents="R d1 g1 E +:f1--f4"
 
   />
 
   />
  
−
54'
+
<hexboard size="5x8"
−
<hexboard size="5x4"  
+
  visible="-area(a1,a4,d1)"
−
   edges="bottom right"
+
   edges="bottom"
 
   coords="none"
 
   coords="none"
−
   contents="R a1"
+
   contents="R e1 h1 E +:g1--g5"
 
   />
 
   />
  
−
5'4
+
<hexboard size="6x11"
−
<hexboard size="5x4"  
+
  visible="-area(a1,a5,e1)"
−
   edges="top left"
+
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 j1 E +:i1--i6"
 +
  />
 +
 
 +
== Templates ==
 +
<hexboard size="6x7"
 +
  visible="-area(a1,c1,c3,a5) d1 g3--g6"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R e1 g2 f3"
 +
  />
 +
 
 +
<hexboard size="5x8"
 +
  visible="-area(a1,d1,a4) g1 h1 h2"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R e1 d2 S blue:e4 blue:e5 blue:f5"
 +
  />
 +
This is actually 3 templates. Each blue-shaded cell represents a place you can put a blue stone and still have a template.
 +
=== Ladder Escapes ===
 +
 
 +
<hexboard size="5x5"
 +
  visible="-a1 a2 b1 e3 e4 e5"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="E +:a3--a5 R b2 d1 e1 B d2"
 +
  />
 +
 
 +
=== Switchbacks ===
 +
 
 +
==== 3-5 Switchbacks ====
 +
 
 +
<hexboard size="6x7"
 +
  visible="-area(a1, c1, a3) f1 g1--g3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R d1 E arrow(9):c2 arrow(9):b3 arrow(3):a4 arrow(3):a5 S red:c2 blue:b3 red:a4 blue:a5"
 +
  />
 +
 
 +
==== 4-6 Switchbacks ====
 +
 
 +
<hexboard size="6x8"
 +
  visible="-a1 a2 b1 g1 h1 h2 h3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R e1 E arrow(9):c1 arrow(9):b2 arrow(3):a3 arrow(3):a4 S red:c1 blue:b2 red:a3 blue:a4"
 +
  />
 +
 
 +
==== 5-7 Switchbacks ====
 +
 
 +
<hexboard size="7x8"
 +
  visible="-a1 a2 b1 e1--h1 f2--h2 g3 h3 h4"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R e3 E arrow(9):c1 arrow(9):b2 arrow(3):a3 arrow(3):a4 S red:c1 blue:b2 red:a3 blue:a4"
 +
  />
 +
 
 +
<hexboard size="7x4"
 +
  visible="-a1"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R d3 c4 B d4 E arrow(9):b1 arrow(9):a2 arrow(3):a3 arrow(3):a4 S red:b1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
<hexboard size="7x7"
 +
  visible="-a1 a2 b1 e1--h1 f2--h2 g3 g4"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R d2 E arrow(9):c1 arrow(9):b2 arrow(3):a3 arrow(3):a4 S red:c1 blue:b2 red:a3 blue:a4"
 +
  />
 +
==== 6-8 Switchbacks ====
 +
 
 +
<hexboard size="8x9"
 +
  visible="-a1 a2 b1 e1--i1 f2--i2 g3--i3 h4 i4 i5"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R e3 E arrow(9):c1 arrow(9):b2 arrow(3):a3 arrow(3):a4 arrow(6):a7 S red:c1 blue:b2 red:a3 blue:a4"
 +
  />
 +
 
 +
Only works if there's a second row foldback threat.
 +
 
 +
=== Foldbacks ===
 +
 
 +
==== 4-2 Foldbacks ====
 +
<hexboard size="5x4"
 +
  visible="-a1 area(c3,d3,d5,b5,b4)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R arrow(6):d2 E arrow(3):a2 arrow(3):a3 arrow(9):a4 arrow(9):a5 S red:a2 blue:a3 red:a4 blue:a5"
 +
  />
 +
 
 +
<hexboard size="6x9"
 +
  visible="-a1--c1 a2 g1--i1 h2 i2 i3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R e1 E +:b2 arrow(3):a3 arrow(3):a4 arrow(9):a5 arrow(9):a6 S red:a3 blue:a4 red:a5 blue:a6"
 +
  />
 +
 
 +
The cell with the + needs to be extended with empty cells such that it is adjacent to the red stone at the front of the ladder, with blue to move.
 +
 
 +
==== 5-2 Foldbacks ====
 +
 
 +
<hexboard size="6x7"
 +
  visible="-a1 e1--g1 f2 g2 g3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R d2 E +:b1 arrow(3):a2 arrow(3):a3 arrow(9):a5 arrow(9):a6 S red:a2 blue:a3 red:a5 blue:a6"
 +
  />
 +
 
 +
The cell with the + needs to be extended with empty cells such that it is adjacent to the red stone at the front of the ladder, with blue to move.
 +
 
 +
==== 5-3 Foldbacks ====
 +
 
 +
<hexboard size="5x5"
 +
  visible="-d1 e1 e2"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b1 E arrow(3):a1 arrow(3):a2 arrow(9):a3 arrow(9):a4 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
<hexboard size="6x3"
 +
  visible="-a2--a6"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R c3 c1 E arrow(3):b2 arrow(3):b3 arrow(9):b4 arrow(9):b5 S red:b2 blue:b3 red:b4 blue:b5"
 +
  />
 +
 
 +
<hexboard size="6x4"
 +
  visible="-a2--a6 d3--d6"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R c3 d1 E arrow(3):b2 arrow(3):b3 arrow(9):b4 arrow(9):b5 S red:b2 blue:b3 red:b4 blue:b5"
 +
  />
 +
 
 +
<hexboard size="5x3"
 +
  visible="-c1 c4 c5"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b2 c2 E arrow(9):a3 arrow(9):a4 arrow(3):a1 arrow(3):a2 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
Generalizible to any capped flank.
 +
 
 +
<hexboard size="6x4"
 +
  visible="-a2--a6"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R d2 c3 B d3 E arrow(9):b4 arrow(9):b5 arrow(3):b2 arrow(3):b3 S red:b2 blue:b3 red:b4 blue:b5"
 +
  />
 +
 
 +
<hexboard size="6x7"
 +
  visible="-a2--a6 e1--g1 f2 g2 g3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R c1 E arrow(9):b4 arrow(9):b5 arrow(3):b2 arrow(3):b3 S red:b2 blue:b3 red:b4 blue:b5"
 +
  />
 +
 
 +
==== 6-3 Foldbacks ====
 +
 
 +
<hexboard size="7x8"
 +
  visible="-a1 e1--h1 f2--h2 g3 h3 h4"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R d2 E +:b1 arrow(3):a2 arrow(3):a3 arrow(9):a5 arrow(9):a6 S red:a2 blue:a3 red:a5 blue:a6"
 +
  />
 +
 
 +
The cell with the + needs to be extended with empty cells such that it is adjacent to the red stone at the front of the ladder, with blue to move.
 +
 
 +
==== 6-4 Foldbacks ====
 +
 
 +
<hexboard size="6x5"
 +
  visible="-c1--e1 d2 e2 e3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b2 E arrow(3):a1 arrow(3):a2 arrow(9):a3 arrow(9):a4 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
<hexboard size="6x6"
 +
  visible="-d1--f1 e2 f2 f3"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b1 E arrow(3):a1 arrow(3):a2 arrow(9):a3 arrow(9):a4 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
<hexboard size="6x2"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b3 b1 E arrow(3):a1 arrow(3):a2 arrow(9):a3 arrow(9):a4 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
<hexboard size="6x3"
 +
  visible="-c3--c6"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b3 c1 E arrow(3):a1 arrow(3):a2 arrow(9):a3 arrow(9):a4 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
==== 7-5 Foldbacks ====
 +
 
 +
<hexboard size="7x3"
 +
  visible="-c4--c7 b6 b7"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R b4 c2 E arrow(3):a1 arrow(3):a2 arrow(9):a3 arrow(9):a4 S red:a1 blue:a2 red:a3 blue:a4"
 +
  />
 +
 
 +
=== Ladder ===
 +
 
 +
<hexboard size="7x7"
 +
  visible="-area(a1,a5,e1) c4--a6"
 +
   edges="bottom"
 
   coords="none"
 
   coords="none"
−
   contents="R d5"
+
   contents="R g1 d4 E arrow(9):c5 arrow(9):b6 arrow(3):g4 arrow(3):g5 S red:c5 red:g4 blue:b6 blue:g5"
 
   />
 
   />
  
−
4'4'
+
<hexboard size="7x8"
−
<hexboard size="4x4"  
+
  visible="-area(a1,a5,e1) c4--a6"
−
   edges="top right"
+
   edges="bottom"
 
   coords="none"
 
   coords="none"
−
   contents="R a4"
+
   contents="R g1 d4 E arrow(9):c5 arrow(9):b6 arrow(3):h5 arrow(3):h6 S red:c5 red:h5 blue:b6 blue:h6"
 
   />
 
   />
  
−
We don't always have to use the smallest number if the reference point for the move is on a different half of the board. Here, stone A could be labeled as 62, but it would be preferable to label it as 8'2 when talking about it in the context of the other two stones, as this is a common opening sequence. Labeling it as 8'2 insures that that pattern is always labeled the same regardless of board size.
+
=== Misc ===
  
−
<hexboard size="13x3"  
+
<hexboard size="4x6"
−
   edges="top left bottom"
+
  visible="-a1 f3 f4"
 +
   edges="bottom"
 
   coords="none"
 
   coords="none"
−
   contents="R c2 b5 A:b8"
+
   contents="R arrow(12):b1 e1 B a2 E arrow(9):a3 arrow(9):a4 *:f1 a:c3 S red:a3 blue:a4"
 
   />
 
   />
 +
Assuming * could be used for a ladder escape fork if the ladder was farther away. Blue must play at '''a'''.

Latest revision as of 19:48, 2 April 2024

Relative Coordinates

This is a coordinate system adapted from Go that allows us to talk about important moves in the same way, regardless of board size. We use YX instead of XY because row is more important in Hex, and because we're taking the bottom red edge as our perspective, as is customary. This also most closely resembles how people talk about certain moves already. 4-4 becomes 44. 5-4 becomes 54'.

  • A: 44
  • B: 54'
  • C: 5'4
  • D: 4'4'
  • 1: 2'3
  • 2: 5'2
1D2C3BA

3 requires some more explaining. On it's own, 3 would be 62. However, if stones 1 and 2 were the previous two moves, it can be better to refer to it as 8'2. This is because the sequence 2'3, 5'2, 8'2 is a common opening sequence, and referring to it as 8'2 means it won't change with board size. It also communicates the fact that 3's row is based on the placement of 1 and 2, and not distance from the red edge.

Edges

Relative coordinates naturally give rise to a very simple way of referring to the edges: red, red', blue, blue'.

Symmetrical Switchback Templates

Templates

This is actually 3 templates. Each blue-shaded cell represents a place you can put a blue stone and still have a template.

Ladder Escapes

Switchbacks

3-5 Switchbacks

4-6 Switchbacks

5-7 Switchbacks

6-8 Switchbacks

Only works if there's a second row foldback threat.

Foldbacks

4-2 Foldbacks

The cell with the + needs to be extended with empty cells such that it is adjacent to the red stone at the front of the ladder, with blue to move.

5-2 Foldbacks

The cell with the + needs to be extended with empty cells such that it is adjacent to the red stone at the front of the ladder, with blue to move.

5-3 Foldbacks

Generalizible to any capped flank.

6-3 Foldbacks

The cell with the + needs to be extended with empty cells such that it is adjacent to the red stone at the front of the ladder, with blue to move.

6-4 Foldbacks

7-5 Foldbacks

Ladder

Misc

a

Assuming * could be used for a ladder escape fork if the ladder was farther away. Blue must play at a.

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