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User:Hexanna

Hexanna — Sat, 26 Sep 2026 21:00:33 GMT

online version of hexata

Domination

Hexanna — Mon, 14 Sep 2026 03:18:53 GMT

‎Fillin with concessions: clarify

User:T0afer

Tommah — Sat, 12 Sep 2026 06:50:22 GMT

User account T0afer was created by Tommah

User:T0afer

Tommah — Sat, 12 Sep 2026 06:50:22 GMT

Creating user page for new user.

New page

User:Hexanna

Hexanna — Thu, 10 Sep 2026 03:49:07 GMT

solved 4x4 dark hex

User:GiB

Demer — Tue, 08 Sep 2026 13:16:04 GMT

‎Example 2: fixed a mis-type by me

@@ Line 5: / Line 5: @@
 I started learning Hex mid-July of 2021, about 2 weeks before I created my LittleGolem account.
-[https://github.com/hexanna1/hexata Hexata] is a GUI and CLI for analyzing Hex that I vibe-coded. It's still under active development, but I already use it as my main GUI.
+[https://github.com/hexanna1/hexata Hexata] is a GUI and CLI for Hex analysis.
-* One of the GUI's main advantages (and a primary reason I created it) is that it's fast and responsive. It's not as useful for "traditional" analysis as some other GUIs &mdash; it doesn't support adding comments to moves, for example.
-* The CLI is primarily intended for AI coding tools and scripts. For example, I have used it extensively when developing the study tools below.
-[https://hexanna1.github.io/hex-study/ Hex Study Tools] is a collection of interactive databases:
+[https://hexanna1.github.io/hex-study/ Hex Study Tools] is a collection of interactive databases and tools:
 * [https://hexanna1.github.io/hex-study/patterns.html Local pattern explorer] with up to 6-stone local patterns
 * [https://hexanna1.github.io/hex-study/openings.html Opening explorer] with opening lines on sizes 11&ndash;14 and 17
-* Of these tools, I put the most thought into the design of the local pattern explorer, and it's probably the most useful one for improving at Hex.
+* [https://hexanna1.github.io/hex-study/joseki.html Joseki explorer] with acute and obtuse corner sequences
 Solution to 4&times;4 Classic Dark Hex: The first player wins with a probability of exactly 5345119702052171/6736824633547900 (0.793418263470100504) under optimal play.

← Older revision		Revision as of 03:18, 14 September 2026
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	A note of caution about fillin: unlike capture, fillin is not closed under unions. In other words, if some set S of cells is fillin, and some other set T of cells is fillin, it does not follow that S ∪ T is fillin.		A note of caution about fillin: unlike capture, fillin is not closed under unions. In other words, if some set S of cells is fillin, and some other set T of cells is fillin, it does not follow that S ∪ T is fillin.
		+
		+	==== Fillin with concessions ====
		+
		+	In a given position, we say that X is ''Red fillin with concession Y'' if filling X red and Y blue gives a position no better for Red than the original. Here X and Y are sets of empty cells. Ordinary Red fillin is the case where Y is empty. Any superset of Y is also a concession, so we are mainly interested in minimal concession sets.
		+
		+	[[Captured cell#Generous capture\|Generous capture]] is a special case: after giving Y to Blue, X is captured by Red and can therefore be filled without changing the winner.
		+
		+	In the examples below, X (the fillin) is shaded red and Y (the concession) is shaded blue.
		+
		+	In the following two examples, Red answers a Blue move in either shaded cell by playing the other. The blue cell [[#Switch-domination\|switch-dominates]] the red cell, since a Red move in the blue cell kills the red cell. Thus either outcome is at least as good for Red as the shaded assignment.
		+
		+	<hexboard size="3x3" float="inline" coords="none" edges="none" visible="-(a1 b1 a3 c3)"
		+	contents="R c1 b3 B a2 S red:b2 blue:c2" />
		+	<hexboard size="3x3" float="inline" coords="none" edges="none" visible="c1 c2 b2 a3 b3"
		+	contents="R c1 a3 b3 S red:b2 blue:c2" />
		+
		+	In the [[crescent]] below, Red can fill a and c by conceding d. Red a kills c, and Red b captures a/c. If Blue takes b, Red answers a; the remaining d is at least as good for Red as b in the shaded position. If Blue takes a, Red answers b and pairs c with d.
		+
		+	<hexboard size="3x3" coords="none" edges="none" visible="-c3"
		+	contents="R a1 a3 b3 c2 S red:(a2 b2) blue:c1 E a:a2 b:b1 c:b2 d:c1" />
		+
		+	In the [[trapezoid]] below, Red can fill a, b, and c by conceding d. Pair a with b, and c with d. Whichever cell Red gets from each pair, the four existing Red stones become connected.
		+
		+	<hexboard size="3x3" coords="none" edges="none" visible="-c3"
		+	contents="R a1 a3 c1 b3 S red:(a2 b1 b2) blue:c2 E a:a2 b:b1 c:b2 d:c2" />
		+
		+	The diagrams below show [[Edge template IV2d\|edge template IV2d]]. The three cells shaded red are Red fillin with concession {b} or {a,c}. Both concessions have been verified by computer. The cells marked * are already captured by Red without any concession.
		+
		+	<hexboard size="4x4" float="inline" coords="none" edges="bottom" visible="area(d1,a4,d4)"
		+	contents="R d1 b3 S red:c2--c4 blue:d3 E a:d2 b:d3 c:d4 d:c2 *:a4--b4" />
		+	<hexboard size="4x4" float="inline" coords="none" edges="bottom" visible="area(d1,a4,d4)"
		+	contents="R d1 b3 S red:c2--c4 blue:(d2 d4) E a:d2 b:d3 c:d4 d:c2 *:a4--b4" />
		+
		+	Neither {a} nor {c} alone suffices, even for filling d. The following counterexamples have Blue to move. With the shaded cells empty, Blue wins by playing b in the left position, or a in the right. However, Red wins if the shaded cells are filled as indicated.
		+
		+	<hexboard size="6x6" float="inline" coords="none" edges="all"
		+	contents="R c2 d1--f1--f4 d3 b5 B a1--a5 b1--b4 c1 d2--e2 e3--e4 f5 e6--f6 S red:c4 blue:d4 E a:d4 b:d5 c:d6 d:c4 *:a6--b6" />
		+	<hexboard size="6x6" float="inline" coords="none" edges="all"
		+	contents="R c2 d1--f1--f4 d3 b5 B a1--a5 b1--b4 c1 d2--e2 e3 e5--f5 e6--f6 S red:c4 blue:d6 E a:d4 b:d5 c:d6 d:c4 *:a6--b6" />

	=== Capture-domination ===		=== Capture-domination ===

@@ Line 15: / Line 15: @@
 * Of these tools, I put the most thought into the design of the local pattern explorer, and it's probably the most useful one for improving at Hex.
-Potential exact solution to 3&times;4 Classic Dark Hex: The first player wins with a probability of exactly 14279/67484 (0.211590895619702448) under optimal play. See https://github.com/hexanna1/dark-hex for a strategy certificate. The previous best appears to be [1/7, 1/4], as stated in [https://www.sfu.ca/~jed/Conferences/CCC2023abstracts.pdf Notes on Dark Hex].
+Solution to 4&times;4 Classic Dark Hex: The first player wins with a probability of exactly 5345119702052171/6736824633547900 (0.793418263470100504) under optimal play.
 Rex+ is a second player win on 5&times;5 (and smaller board sizes). See the [https://hexanna1.github.io/hex-study/rexplus.html website] and [https://github.com/hexanna1/rexplus solver code].

← Older revision		Revision as of 13:16, 8 September 2026
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	/>		/>

−	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>
		+	reply by [[User:Demer\|Eric Demer]]:
		+	<br>
		+	The region becomes red-captured after the blue 2 , red 3
		+	<br>
		+	exchange, but it isn't red-captured before that exchange.
		+	<br>
		+	https://hexworld.org/board/#6x4c1,:pf1:pf3:pc3a3a4e2b2b3
		+	<br>
		+	is a witness position for one of the intrusions.