HexWiki - Recent changes [en]

Window

Mason — Thu, 12 Nov 2026 01:52:13 GMT

Y

Hexanna — Tue, 10 Nov 2026 01:52:18 GMT

add bent-y link

Y puzzle solutions

Hexanna — Tue, 10 Nov 2026 01:51:14 GMT

add bent-y solution link

Y puzzles

Hexanna — Tue, 10 Nov 2026 01:49:14 GMT

add bent-y puzzle link

User:Mason

Mason — Tue, 03 Nov 2026 16:14:48 GMT

Signify the carrier is smaller with one of the options

User:GiB

GiB — Tue, 27 Oct 2026 02:41:17 GMT

Credit to Eric Demer

User:Hexanna

Hexanna — Fri, 23 Oct 2026 11:52:26 GMT

4x4 dark hex public-opening variant

User:StillYetAnother11

StillYetAnother11 — Wed, 21 Oct 2026 15:42:35 GMT

Window

Mason — Mon, 19 Oct 2026 13:10:23 GMT

User:Hexanna

Hexanna — Fri, 16 Oct 2026 01:10:01 GMT

non-uniqueness of 4x4 dark hex

← Older revision		Revision as of 01:52, 12 November 2026
Line 1:		Line 1:
−	A window is a loose term for the situation where a group of friendly stones, which is connected to a friendly edge, is accessible through a tiny gap in the opponents stones. They are often created ~~through sequences of moves in a corner, with a breaking move~~ from ~~the opponent to interrupt a ladder or reduce the freedom of such group~~.	+	A window is a loose term for the situation where a group of friendly stones, which is connected to a friendly edge, is accessible through a tiny gap in the opponents stones. They are often created from ladders that cannot be escaped.

	== An Example ==		== An Example ==

@@ Line 126: / Line 126: @@
 * http://www.neutreeko.net/y.htm
 * http://www.iggamecenter.com/ ('''igGameCenter''' - play "Y" online with other opponents)
-* Board editor and KataHex-like engine: https://hexanna1.github.io/hex-study/y.html
+* Board editor and KataHex-like engine
 == References ==

← Older revision		Revision as of 01:51, 10 November 2026
Line 168:		Line 168:

	[[Image:Y27puz_sol.gif]]		[[Image:Y27puz_sol.gif]]
		+
		+	You can view the lines [https://hexanna1.github.io/hex-study/benty.html#5,a3d5d6e6d7f7e7:pe5:pf6:pg7,b2a1c4(d4a2c6c7a4c5b4c4b3d3c3d2e4e3f4)a2c6d2e4d4d3c7a4b4c5b3c3e3f4 here].

	The winning move is (a). The strongest reply is (b), after which Blue has to play (c) or (d). With correct play, all the nodes will become occupied.		The winning move is (a). The strongest reply is (b), after which Blue has to play (c) or (d). With correct play, all the nodes will become occupied.

@@ Line 59: / Line 59: @@
 ==Bent-27 Y puzzle==
-[[Image:Y27puzzle.gif]]
+Blue to play (try it [https://hexanna1.github.io/hex-study/benty.html#5,a3d5d6e6d7f7e7:pe5:pf6:pg7 here]). What is the winning move, and what is Red's strongest reply?
-Blue to play. What is the winning move, and what is Red's strongest reply?
+[[Image:Y27puzzle.gif]]
 ==See also==

@@ Line 51: / Line 51: @@
     edges="bottom"
     coords="none"
-    contents="R e1 d2 S blue:e4 blue:e5 blue:f5"
+    contents="R e1 d2 S blue:e4 blue:e5 blue:f5 E *:e5 *:g2 *:h3--h5"
     />
 This is actually 3 templates. Each blue-shaded cell represents a place you can put a blue stone and still have a template.

@@ Line 1: / Line 1: @@
 __TOC__
 == Capture patterns ==
@@ Line 32: / Line 20: @@
     edges="top left"
     visible="all - (c3--f3 f2)"
-    contents="R a3 b3 e2 B b2 f1 S red:all"
+    contents="R a3 b3 e2 B b2 d2 S red:all"
     />
@@ Line 41: / Line 29: @@
     edges="top left"
     visible="all - (c3--f3 f2)"
-    contents="R a3 b3 1:e2 3:e1 5:a2 7:a1 B b2 f1 2:d2 4:c2 6:b1 S red:all"
+    contents="R a3 b3 1:e2 3:a2 B b2 d2 2:c2 S red:all"
     />
-All blue pieces are dead, so Red 1 captures the whole area
+All blue pieces are dead, so Red 1 captures the whole area.
-<br>
-<br>
+(taken from a discussion with [[User:Demer|Eric Demer]]: https://playhex.org/games/6c5a5c4a-e696-472b-9f5b-baaf56dc27c7)
-reply by [[User:Demer|Eric Demer]]:
-<br>
-The region becomes red-captured after the    blue 2  ,  red 3
+== Test diagrams ==
-<br>
-exchange, but it isn't red-captured before that exchange.
+<hexboard size="4x4"
-<br>
+   contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:a2 E *:b2 E *:c2 R a3 E *:b3 B b4 R c4 E +:a4"
-https://hexworld.org/board/#6x4c1,:pf1:pf3:pc3a3a4e2b2b3
+   /> <hexboard size="4x6"
-<br>
+  coords="none"
-is a witness position for one of the intrusions.
+  edges="bottom"

@@ Line 17: / Line 17: @@
 * Blue's optimal first-stone strategy is not unique, and the set of optimal first-stone probability distributions has dimension at least 3. (The exact dimension is an open question.)
 : <hexboard size="4x4" float="inline" contents="S red:(a2--a4 b4 d3--d1 c1) E 2:(a2 d3) 26:(b4 c1) 74:(a3 d2) 399:(a4 d1)" /> <hexboard size="4x4" float="inline" contents="S blue:-(a2 a3 d3 d2) E 10:(a1 d4) 50:(b1 c4) 56:(b4 c1) 79:(b2 c3) 151:(b3 c2) 153:(a4 d1)" />
 * 3&times;4 Classic Dark Hex: First player win probability is exactly 14279/67484 (0.211590895619702448).
-* See https://github.com/hexanna1/dark-hex for strategy certificates for 4&times;4 and 3&times;4, as well as other solved variants (3&times;4 with public first move, and 3&times;3 Abrupt Dark Hex).
+* See https://github.com/hexanna1/dark-hex for strategy certificates (and exact rational values) for all solved variants: 4&times;4/3&times;4, 4&times;4/3&times;4 with public first move, and 3&times;4/3&times;3 Abrupt Dark Hex.
 * The previous best result appears to be [1/7, 1/4] on 3&times;4, as stated in [https://www.sfu.ca/~jed/Conferences/CCC2023abstracts.pdf Notes on Dark Hex].

← Older revision		Revision as of 15:42, 21 October 2026
Line 1:		Line 1:
−	~~== log2(1.5) ratio ==~~
−
−	I was thinking about why katahex evaluates a7 as the most balanced opening on 12x12 which is very anomalous because openings in the middle of the 1st column tend to be quite strong, although in Hayward's 2003 paper, a4 on 7x7 has the highest number of nodes of all solved openings. The smallest board size after 12x12 where such an opening seems quite playable is 17x17 since katahex evaluates a10 as more balanced than its neighbors and is still one of the most balanced openings on the first column. A pattern starts to emerge where if you encode the acute corner as 0 and the obtuse corner as 1 you'll find that these openings match ratios that well approximate a particular ratio namely log2(1.5). The first semiconvergents of log2(1.5) are 1/1, 1/2, 2/3, 3/5, 4/7, 7/12, 10/17, 17/29, 24/41, 31/53 and 55/94. The next fraction after 10/17 is 17/29 so is a17 on 29x29 more balanced than its neighbors? I've run 200 engine games for each opening: a16, a17 and a18 and the results were 110 wins for a16, 102 wins for a17 and 112 wins for a18. I also ran 100 games on 41x41 for each of the following openings. The results were 57 wins for a23, 49 wins for a24 and 56 wins for a25 so the pattern seems to be consistent. This has a benefit when it comes to opening variety because most balanced openings in hex are predominantly on your own edge and not on your opponent's edge. I believe that having the denominators of semiconvergents of log2(1.5) as board sizes is the most logical and consistent way of deriving board sizes in hex.
−
−
	== The best way for red to fight in c2 opening on 11x11 ==		== The best way for red to fight in c2 opening on 11x11 ==

← Older revision		Revision as of 13:10, 19 October 2026
Line 1:		Line 1:
−	A window is a loose term for the situation where a group of friendly stones, which is connected to a friendly edge, is accessible through a tiny gap in the opponents stones. They are often created through sequences of moves on a corner, with a breaking move from the opponent to interrupt a ladder or reduce the freedom of such group.	+	A window is a loose term for the situation where a group of friendly stones, which is connected to a friendly edge, is accessible through a tiny gap in the opponents stones. They are often created through sequences of moves in a corner, with a breaking move from the opponent to interrupt a ladder or reduce the freedom of such group.

	== An Example ==		== An Example ==

@@ Line 15: / Line 15: @@
 Solution to 4&times;4 Classic Dark Hex: The first player wins with a probability of exactly 5345119702052171/6736824633547900 (0.793418263470100504) under optimal play.
 * The diagrams below show how Red and Blue should play their first stone (Blue's first stone may collide with Red's hidden stone). They are mixed strategies, and each cell's value contains the probability, in thousandths, that Red or Blue should choose that cell. For example, Red plays each of a4 and d1 39.9% of the time under optimal play. Values don't sum to 1000 because of rounding. Red's first-stone strategy is highly counterintuitive if you've only played standard Hex.
-: <hexboard size="4x4" float="inline" contents="S red:(a2--a4 b4 d3--d1 c1) E 2:(a2 d3) 26:(b4 c1) 74:(a3 d2) 399:(a4 d1)" /> <hexboard size="4x4" float="inline" contents="S blue:all E 2:(a2 a3 d3 d2) 6:(a1 d4) 54:(b1 c4) 56:(b4 c1) 77:(b2 c3) 151:(b3 c2) 153:(a4 d1)" />
+* Blue's optimal first-stone strategy is not unique, and the set of optimal first-stone probability distributions has dimension at least 3. (The exact dimension is an open question.)
 * 3&times;4 Classic Dark Hex: First player win probability is exactly 14279/67484 (0.211590895619702448).
 * See https://github.com/hexanna1/dark-hex for strategy certificates for 4&times;4 and 3&times;4, as well as other solved variants (3&times;4 with public first move, and 3&times;3 Abrupt Dark Hex).