Difference between revisions of "User:Mason"

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Line 1: Line 1:
 
== 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 ("four four") is the same: 44 ("four four"). 5-4 ("five four") becomes 54' ("five four prime"). Hyphens can be optionally included, and necessarily included when a number is more than 1 digit.
 
* '''A:''' 44
 
* '''A:''' 44
 
* '''B:''' 54'
 
* '''B:''' 54'
Line 11: Line 11:
 
   contents="R A:d10 B:j9 C:d5 D:j4 1:c2 2:b5 3:b8"
 
   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, in the context of stones '''1''' and '''2''', it is 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 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.
+
'''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 ===
 
=== Edges ===
 
Relative coordinates naturally give rise to a very simple way of referring to the edges: red, red', blue, blue'.
 
Relative coordinates naturally give rise to a very simple way of referring to the edges: red, red', blue, blue'.
−
 
−
=== Board Shading ===
 
−
Shading the 5th rows is a useful shading pattern in general, but even more so when used with relative coordinates. Every cell on the board can be referred to with very little effort. The 5th row is chosen due to it being the middle of the three rows where most interesting things happen (4, 5, and 6).
 
−
<hexboard size="13x13"
 
−
  coords="none"
 
−
  contents="S a9--m9 a5--m5 e1--e13 i1--i13"
 
−
  />
 
  
 
== Symmetrical Switchback Templates ==
 
== Symmetrical Switchback Templates ==
Line 47: Line 40:
  
 
== Templates ==
 
== 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 ===
 
=== Ladder Escapes ===
  
Line 58: Line 64:
  
 
=== Switchbacks ===
 
=== 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="6x4"
 +
  visible="-a1 a2 b1 d3--d6"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R c3 d1 E arrow(9):c1 arrow(9):b2 arrow(3):a3 arrow(3):a4 S red:c1 blue:b2 red:a3 blue:a4"
 +
  />
  
 
<hexboard size="6x8"
 
<hexboard size="6x8"
Line 65: Line 88:
 
   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"
 
   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"
 
<hexboard size="7x8"
Line 74: Line 99:
  
 
<hexboard size="7x4"
 
<hexboard size="7x4"
−
   visible="-a1"
+
   visible="-a1 a2 b1"
 
   edges="bottom"
 
   edges="bottom"
 
   coords="none"
 
   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"
+
   contents="R d3 c4 B d4 E arrow(9):c1 arrow(9):b2 arrow(3):a3 arrow(3):a4 S red:c1 blue:b2 red:a3 blue:a4"
 
   />
 
   />
  
Line 86: Line 111:
 
   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"
 
   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"
 
<hexboard size="8x9"
Line 96: Line 123:
 
Only works if there's a second row foldback threat.
 
Only works if there's a second row foldback threat.
  
−
=== Floldbacks ===
+
=== Foldbacks ===
  
−
<hexboard size="5x5"
+
==== 4-2 Foldbacks ====
−
   visible="-d1 e1 e2"
+
<hexboard size="5x4"
 +
   visible="-a1 d4 d5"
 
   edges="bottom"
 
   edges="bottom"
 
   coords="none"
 
   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"
+
   contents="R d2 d3 c4 B b4 c3 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"
 
<hexboard size="6x7"
Line 113: Line 152:
  
 
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.
 
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"
 
<hexboard size="6x4"
Line 126: Line 197:
 
   coords="none"
 
   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"
 
   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"
 
   />
 
   />
  
Line 133: Line 224:
 
   coords="none"
 
   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"
 
   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"
 +
  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"
 
   />
 
   />
  
 
<hexboard size="7x8"
 
<hexboard size="7x8"
−
   visible="-a1 e1--h1 f2--h2 g3 h3 h4"
+
   visible="-area(a1,a5,e1) c4--a6"
 
   edges="bottom"
 
   edges="bottom"
 
   coords="none"
 
   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"
+
   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"
 
   />
 
   />
  
−
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.
+
=== Ladder Caps ===
 +
 
 +
For the following templates, the walls of +s indicate empty space spreading out in that direction (update in progress)
 +
 
 +
<hexboard size="2x4"
 +
  visible="-a1 b1 d1"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R c1 E arrow(9):b2 arrow(3):c2 +:a2 +:d2 S red:b2--c2"
 +
  />
 +
 
 +
<hexboard size="3x5"
 +
  visible="-a1 b1 a2 e1 e2"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R c1 E +:e3 arrow(3):d3 S red:d3"
 +
  />
 +
 
 +
<hexboard size="3x5"
 +
  visible="-a1 b1 a2"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R c1 E +:e1--e3 arrow(9):a3 arrow(3):d1 arrow(3):b3 S red:d1 red:a3--b3"
 +
  />
 +
 
 +
<hexboard size="4x7"
 +
  visible="-a1--d1 a2 b2 a3 g1"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R e1 E +:c2--a4 +:g2--g4 arrow(9):d2 arrow(9):d4 arrow(3):e4 arrow(3):f2 S red:d2 red:d4--e4 red:f2"
 +
  />
 +
 
 +
<hexboard size="4x5"
 +
  visible="-a1 b1 a2 a3 e1 e2"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R c1 d1 E +:e3--e4 arrow(3):d3 S red:d3"
 +
  />
 +
 
 +
<hexboard size="4x6"
 +
  visible="-area(a1,c1,b3,a3) f1--f3"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R d1 e1 E +:a4 +:f4 arrow(3):e4 S red:e4"
 +
  />
 +
 
 +
Blue gets to pick between this one or the one bellow it.
 +
 
 +
<hexboard size="4x6"
 +
  visible="-area(a1,c1,b3,a3) f1--f3"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R d1 e1 E +:a4 +:f4 arrow(9):b4 S red:b4"
 +
  />
 +
 
 +
Blue gets to pick between this one or the one above it.
 +
 
 +
<hexboard size="4x6"
 +
  visible="-area(a1,c1,b3,a3) f1 f2"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R d1 e1 E +:a4 +:f3--f4 arrow(9):b4 arrow(3):e3 S red:b4 red:e3"
 +
  />
 +
 
 +
<hexboard size="5x7"
 +
  visible="-area(a1,d1,a4) c3 g1"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R e1 f1 E +:b4--a5 +:g2--g5 arrow(3):f3 arrow(3):e5 arrow(9):d5 S red:f3 red:d5--e5"
 +
  />
 +
 
 +
<hexboard size="4x6"
 +
  visible="-area(a1,c1,a3) f1 f2"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R d1 e1 E +:f3--f4 arrow(3):e3 S red:e3"
 +
  />
 +
 
 +
<hexboard size="4x7"
 +
  visible="-area(a1,d1,b3,a3) g1--g3"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R e1 f1 E +:a4 +:g4 arrow(3):f4 S red:f4"
 +
  />
 +
 
 +
<hexboard size="5x8"
 +
  visible="-area(a1,d1,a4) e1 d2 h1 h2"
 +
  edges="none"
 +
  coords="none"
 +
  contents="R f1 g1 E +:c3--a5 +:h3--h5 arrow(9):e3 arrow(9):e5 arrow(3):f5  arrow(3):g3 S red:e3 red:e5--f5 red:g3"
 +
  />
 +
 
 +
=== Misc ===
 +
 
 +
<hexboard size="4x6"
 +
  visible="-a1 f3 f4"
 +
  edges="bottom"
 +
  coords="none"
 +
  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'''.
 +
 
 +
== Handicap System ==
 +
The weaker player plays first with no swap. Difficulty is increased (for the weaker player) by increasing the size of the board.

Latest revision as of 05:25, 6 November 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 ("four four") is the same: 44 ("four four"). 5-4 ("five four") becomes 54' ("five four prime"). Hyphens can be optionally included, and necessarily included when a number is more than 1 digit.

  • 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

Ladder Caps

For the following templates, the walls of +s indicate empty space spreading out in that direction (update in progress)

Blue gets to pick between this one or the one bellow it.

Blue gets to pick between this one or the one above it.

Misc

a

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

Handicap System

The weaker player plays first with no swap. Difficulty is increased (for the weaker player) by increasing the size of the board.

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