User:Selinger - Revision history

Selinger: /* Remarks */ Caveat

2024-05-27T12:00:46Z

‎Remarks: Caveat

Selinger: More on parallel ladders

2023-10-17T02:02:33Z

Selinger: /* Connecting a 2-5 parallel ladder */

2023-10-13T00:38:56Z

‎Connecting a 2-5 parallel ladder

Selinger: /* Connecting a 2-5 parallel ladder */ typo

2023-10-11T22:00:15Z

‎Connecting a 2-5 parallel ladder: typo

Selinger: 2-5 parallel ladder

2023-10-11T21:59:27Z

2-5 parallel ladder

Selinger at 23:28, 1 May 2023

2023-05-01T23:28:30Z

Selinger: hedge

2023-02-06T21:21:13Z

hedge

Selinger: New proposed page

2023-01-08T02:34:15Z

New proposed page

Show changes

Selinger: /* D5 does not escape a 4th row ladder */ Added some climbing options.

2022-12-08T01:26:02Z

‎D5 does not escape a 4th row ladder: Added some climbing options.

Selinger: Added: Joseki "C" does not escape a 4th row ladder

2022-11-28T03:43:43Z

Added: Joseki "C" does not escape a 4th row ladder

← Older revision		Revision as of 12:00, 27 May 2024
Line 133:		Line 133:

	Also, the fact that these ladders all connect means that they are not really "ladders" in the usual sense; they are basically just templates. Note that unlike Tom's move (2-4 and 3-5 ladders), the connection requires no space above the height of the ladder, so the space in which the ladder would normally travel is already enough space to connect it.		Also, the fact that these ladders all connect means that they are not really "ladders" in the usual sense; they are basically just templates. Note that unlike Tom's move (2-4 and 3-5 ladders), the connection requires no space above the height of the ladder, so the space in which the ladder would normally travel is already enough space to connect it.
		+
		+	Also, as noted on the page [[Tom's move for 3rd and 5th row parallel ladders]], 3-5 parallel ladders can't always be pushed as 3-5 parallel ladders; the defender has the option to downgrade it to a 2nd row ladder with switchback threat. The resulting 2nd row ladder may not connect. Therefore, Tom's move may not be available if the ladder starts some distance from where there is space.

@@ Line 62: / Line 62: @@
 etc.
-= Connecting a 2-5 parallel ladder =
+= Connecting parallel ladders =
 Like 2-4 and 3-5 parallel ladders, a 2-5 parallel ladder can also connect to the edge outright, given enough space. One way to do this is to yield to a 3-5 parallel ladder and then use [[Tom's move for 3rd and 5th row parallel ladders]]. However, there is a way to do it with much less space. In fact, the amount of space shown here is minimal:
@@ Line 103: / Line 105: @@
    />
 This move isn't exactly a version of Tom's move, but it does for a 2-5 ladder what Tom's move does for a 2-4 ladder.

@@ Line 72: / Line 72: @@
    contents="R arrow(12):c1,a4 B c2 a5 R 1:d2"
    />
-The ladder stones are marked "↑", and Red's winning move is "1".
+The ladder stones are marked "↑", and Red's winning move is "1". It is Red's only winning move within this space.
 Proof of connectedness: Red's main threats is "*", using the highlighted cells:

@@ Line 81: / Line 81: @@
    contents="R arrow(12):c1,a4 B c2 a5 R 1:d2 *:c4 S red:(d1,c3,b4,b5,c4,c5,d3)"
    />
-Red's other main threat is "*", connecting via [[edge template IV2b]], and only requiring 2 or the 3 cells x, y, z:
+Red's other main threat is "*", connecting via [[edge template IV2b]], and only requiring 2 of the 3 cells x, y, z:
 <hexboard size="5x9"
    edges="bottom"

@@ Line 60: / Line 60: @@
-= Unused draft material for "Question" =
+<hexboard size="5x9"
+   edges="bottom"
-The following was a draft example for the page [[Question]], but it turned out to be too complicated to and not have a good answer.
+   coords="none"
+   visible="area(c1,a4,a5,i5,i3,g1)"
-== Example: Template intrusion ==
+   contents="R arrow(12):c1,a4 B c2 a5 R 1:d2"
-−
-Consider the following position, with Blue to move:
-<hexboard size="11x11"
-   coords="left bottom right"
-   edges="left bottom right"
-   visible="area(a7,a11,k11,k7)"
-   contents="R f7 g7 B d8 h9 S area(f7,c9,a11,g11,g7)"
    />
-Note that Red is connected to the edge by [[Fifth_row_edge_templates#V-2-b|edge template V2b]], as highlighted. Blue would like to intrude into this template to gain strength either on the left or on the right.
+The ladder stones are marked "↑", and Red's winning move is "1".
-Blue would like a 4th row ladder escape on the left. But the problem is that if Blue plays at d9 or c10, Red can reconnect by playing a [[minimax|minimaxing move]] at h7, which strenghtens Red's position.
+Proof of connectedness: Red's main threats is "*", using the highlighted cells:
-<hexboard size="11x11"
+<hexboard size="5x9"
-   coords="left bottom right"
+   edges="bottom"
-   edges="left bottom right"
+   coords="none"
-   visible="area(a7,a11,k11,k7)"
+   visible="area(c1,a4,a5,i5,i3,g1)"
-   contents="R f7 g7 B d8 h9 B 1:d9 R 2:h7 S area(f7,e8,c11,g11,h8,h7)"
+   contents="R arrow(12):c1,a4 B c2 a5 R 1:d2 *:c4 S red:(d1,c3,b4,b5,c4,c5,d3)"
    />
-Blue would also like a 4th row ladder escape on the right. But again, the problem is that if Blue moves at g10 or g9, Red can reconnect at g8, or by playing a minimaxing move, say at b10:
+Red's other main threat is "*", connecting via [[edge template IV2b]], and only requiring 2 or the 3 cells x, y, z:
-<hexboard size="11x11"
+<hexboard size="5x9"
-   coords="left bottom right"
+   edges="bottom"
-   edges="left bottom right"
+   coords="none"
-   visible="area(a7,a11,k11,k7)"
+   visible="area(c1,a4,a5,i5,i3,g1)"
-   contents="R f7 g7 B d8 h9 B 1:g10 R 2:b10 S area(f7,c9,a11,f11,g8,g7)"
+   contents="R arrow(12):c1,a4 B c2 a5 R 1:d2 *:c3 S red:c3,area(e2,b5,f5,f3) E x:b3 y:b4 z:d1"
    />
-Neither of these outcomes is great for Blue. Instead, what Blue can do is ask the template a question:
+The overlap consists of the cells marked "a", "b", and "c":
-<hexboard size="11x11"
+<hexboard size="5x9"
-   coords="left bottom right"
+   edges="bottom"
-   edges="left bottom right"
+   coords="none"
-   visible="area(a7,a11,k11,k7)"
+   visible="area(c1,a4,a5,i5,i3,g1)"
-   contents="R f7 g7 B d8 h9 B 1:f8"
+   contents="R arrow(12):c1,a4 B c2 a5 R 1:d2 E a:c3,d3 c:c4 b:b5,c5"
    />
-Basically, the question is: "How do you want to reconnect?" And based on the answer, Blue will be able to gain some strength on the left or on the right, without giving Red quite as much territory as would otherwise have been the case.
+If Blue plays at "a", Red pushes the 2nd row ladder to "c" and then uses [[Tom's move]]. If Blue plays at "b", Red responds at "c" and then uses Tom's move. Finally, if Blue plays at "c", Red plays as follows:
+<hexboard size="5x9"
-For example, if Red reconnects at e8, then Blue can play e10:
+   edges="bottom"
-<hexboard size="11x11"
+   coords="none"
-   coords="left bottom right"
+   visible="area(c1,a4,a5,i5,i3,g1)"
-   edges="left bottom right"
+   contents="R arrow(12):c1,a4 B c2 a5 R 1:d2 B 2:c4 R 3:b4 B 4:b5 R 5:e3"
-   visible="area(a7,a11,k11,k7)"
-   contents="R f7 g7 B d8 h9 B 1:f8 R 2:e8 B 3:e10 S red:(d9 d10 f9 f10 g8 g10)"
    />
+This move isn't exactly a version of Tom's move, but it does for a 2-5 ladder what Tom's move does for a 2-4 ladder.
-Now Red's [[mustplay region]] consists of the 6 highlighted cells. If Red plays at d9, Blue gets a forcing move at b10, giving Blue a 4th row escape on the left, without Red getting g8. If Red plays at d10, g8, or g10, Blue gets a forcing move at d9, giving Blue a 4th row escape on the left without Red getting g8. If Red plays at g9, Blue defends the bridge at f9 and then plays as before. Finally, if Red plays at f10, Blue can respond at g8, getting a 4th row escape on the right. Although Red can still reconnect at b10, taking away Blue's ladder escape on the left, Red does not have the option of getting g8.
-−
-To be continued... and simplified?
-−
-== To do ==
-−
-Add other illustrative examples, such as a template intrusion that forces the player to  trade-off between a stronger connection and letting the opponent get a ladder escape, etc.

← Older revision		Revision as of 23:28, 1 May 2023
Line 1:		Line 1:
		+	I have played Hex since early 2020, and I run the [[Hex clubs\|Halifax Hex Club]]. I mostly use this user page for draft articles and other random bits and pieces that aren't yet ready to go into a real HexWiki article.
		+
	= Proposed page: Eric's move =		= Proposed page: Eric's move =

@@ Line 33: / Line 33: @@
 Note that Red has formed [[edge template IV2d]], still holding Blue to a 5th row ladder. Blue still has a forcing move at x, but because Red can respond at y, this only gives Blue a 2nd row ladder escape, rather than a 3rd row escape.
-However, even this solution is not optimal for Red, as Blue still gets a 5th row ladder. It turns out that playing a different move 3 is even better for Red.
+However, even this solution is not optimal for Red, as Blue still gets a 5th row ladder. It turns out that playing a different move 3 is generally even better for Red.
 <hexboard size="5x8"
    coords="hide"

@@ Line 98: / Line 98: @@
    />
 In all other cases, Red connects outright.
 == Joseki "C" does not escape a 4th row ladder ==

← Older revision		Revision as of 03:43, 28 November 2022
Line 99:		Line 99:
	In all other cases, Red connects outright.		In all other cases, Red connects outright.

		+	== Joseki "C" does not escape a 4th row ladder ==
		+
		+	It is fairly common to play the [[Joseki#4th_row_josekis\|4th row joseki]] "C", which leaves the following position in an acute corner:
		+	<hexboard size="5x11"
		+	edges="bottom right"
		+	coords="none"
		+	visible="area(a5,k5,k1,e1)"
		+	contents="R h3 i2 B i3"
		+	/>
		+	This position obviously escapes 2nd row ladders. It is perhaps less obvious that it also escapes 3rd row ladders approaching from far enough away:
		+	<hexboard size="5x11"
		+	edges="bottom right"
		+	coords="none"
		+	visible="area(a5,k5,k1,e1)"
		+	contents="R h3 i2 B i3 B b4 R 1:c3 B 2:c4 R 3:d3 B 4:d4 R 5:f2 B 6:e3 R 7:e2 B 8:f4 R 9:f3 B 10:e4 R 11:g5 S area(c3,b5,h5,h3,i2,i1,g1)"
		+	/>
		+	Note that Red is connected by a [[Interior_template#The_span\|span]], and the connection only requires the shaded area. The "magic" move is 5. If Red just continues to push on the 3rd row, Red does not connect.
		+
		+	Does the above corner position escape a 4th row ladder? If Blue naively keeps pushing the ladder, then Red does indeed connect:
		+	<hexboard size="5x11"
		+	edges="bottom right"
		+	coords="none"
		+	visible="area(a5,k5,k1,e1)"
		+	contents="R h3 i2 B i3 B c3 R 1:d2 B 2:d3 R 3:e2 B 4:e3 R 5:f2 B 6:f3 R 7:h1"
		+	/>
		+	On the other hand, if Blue [[ladder handling\|yields]] at any point, Red connects by [[switchback]], for example like this:
		+	<hexboard size="5x11"
		+	edges="bottom right"
		+	coords="none"
		+	visible="area(a5,k5,k1,e1)"
		+	contents="R h3 i2 B i3 B c3 R 1:d2 B 2:d3 R 3:e2 B 4:e4 R 5:e3 B 6:d4 R 7:g3 B 8:f3 R 9:g1"
		+	/>
		+	Indeed, for a 4th row ladder approaching the corner, there is only one possible Blue move that prevents Red from escaping the ladder. This "magic move" is 4 in the following diagram:
		+	<hexboard size="5x11"
		+	edges="bottom right"
		+	coords="none"
		+	visible="area(a5,k5,k1,e1)"
		+	contents="R h3 i2 B i3 B c3 R 1:d2 B 2:d3 R 3:e2 B 4:f4 R 5:f3 B 6:d5 R 7:j1 B 8:g3 R 9:h1"
		+	/>
		+	Red still gets a [[foldback]] and a [[switchback]]. Instead of 7, Red could have played anywhere in the corner, but since 7 [[captured cell\|captures]] the entire corner, it is usually the [[optimal play\|best move]] in this situation.