HexWiki - Recent changes [en]

Pivoting template

Bobson8 — Sat, 27 Jun 2026 02:51:52 GMT

Fix the flawed statement. Also extend some statement to the weak version.

User:GiB

GiB — Sat, 27 Jun 2026 01:56:51 GMT

Where to swap (y)

Hexanna — Fri, 26 Jun 2026 02:58:32 GMT

swap maps for sizes 10-13, 15, 17

Window

Bobson8 — Thu, 25 Jun 2026 03:44:26 GMT

Wording. In particular I describe the term window as a local pattern rather than a group of stone of someone.

User:Hexanna

Hexanna — Thu, 25 Jun 2026 01:43:22 GMT

moved over (and elaborated) ladders

Strategic advice from KataHex

Hexanna — Thu, 25 Jun 2026 01:42:17 GMT

improve ladders section

User:Hexanna

Hexanna — Thu, 25 Jun 2026 01:18:44 GMT

moved over "advanced strategy: leaving the question open"

Strategic advice from KataHex

Hexanna — Thu, 25 Jun 2026 01:17:58 GMT

advanced strategy: leaving the question open

Openings on 19 x 19

Hexanna — Thu, 25 Jun 2026 01:07:50 GMT

formatting

User:Hexanna

Hexanna — Thu, 25 Jun 2026 01:04:04 GMT

typos

Strategic advice from KataHex

Hexanna — Thu, 25 Jun 2026 01:02:07 GMT

typos

Show changes

Window

Mason — Wed, 24 Jun 2026 22:42:05 GMT

Window

Mason — Wed, 24 Jun 2026 22:34:35 GMT

Created page with "Windows are a class of structure where one of your stones, which is connected to one of your edges, is accessible through a tiny gap in the opponents stones. At first glance,..."

New page

Windows are a class of structure where one of your stones, which is connected to one of your edges, is accessible through a tiny gap in the opponents stones. At first glance, they seem to be not all that helpful. They feel far away from the action and often are created through sequences of moves that give the opponent a large amount of territory, which can feel like a losing exchange. However, they are actually quite strong. Their strength comes from the the fact that having a single extra move is usually enough to win the game, and a window can serve to offer you just that by creating a threat the opponent is forced to block, giving you another move.

=== An Example ===
After Blue plays '''1''' and Red plays '''2''', Blue has a window at the upper '''*'''. The red-shaded cells do not have any red stones in them at the moment, but easily could at some point in the future due to the nature of bridges.

A few moves later, Blue realizes that by starting the ladder with '''5''', Red is going to have to break at some point, giving Blue another window.
<hexboard size="17x17"
coords="hide"
contents="R e12 e13 f13 f14 f6 g14 g5 10:h14 8:j14 2:j4 6:k14 l14 m12 m4 4:m6 n14 n4 o13 B c5 d14 e15 f12 f5 g13 3:g9 9:i15 7:j15 5:k15 1:k3 l15 m14 m2 n13 n3 o12 o3 S red:l3 red:m3 E *:i14 *:k4"
/>

The final battle takes place on this board. Red has a lot of stones in Blue's way, but Blue has a couple tiny windows.
<hexboard size="17x17"
coords="hide"
contents="R b11 c10 c13 d9 e11 e12 e13 e8 f10 f13 f14 f16 f6 f8 1:g10 g14 g5 h10 h14 j14 j4 k14 l14 m12 m4 m6 n14 n4 o13 B b12 c11 c5 d10 d14 e15 e16 e9 f11 f12 f5 f9 g12 g13 g16 g8 g9 i11 i15 j15 k15 k3 l15 m14 m2 n13 n3 o12 o3"
/>

Blue starts by strengthening their upper window. Red, presumably, still feels the other direction is more threatening, so opts to block that way instead. Blue gets withing range of their window. Red will now have to block.
<hexboard size="17x17"
coords="hide"
contents="R b11 c10 c13 d9 e11 e12 e13 e8 f10 f13 f14 f16 f6 f8 g10 g14 g5 h10 h14 4:h7 2:i8 j14 j4 k14 l14 m12 m4 m6 n14 n4 o13 B b12 c11 c5 d10 d14 e15 e16 e9 f11 f12 f5 f9 g12 g13 g16 g8 g9 5:h8 i11 i15 3:i7 j15 k15 k3 1:k4 l15 m14 m2 n13 n3 o12 o3"
/>
Blue is able to use this window to get dangerously close to their other window.
<hexboard size="17x17"
coords="hide"
contents="R b11 c10 c13 d9 e11 e12 e13 e8 f10 f13 f14 f16 f6 f8 g10 g14 g5 h10 h14 h7 i8 j14 j4 1:j6 k14 5:k6 l14 3:l8 m12 m4 m6 n14 n4 o13 B b12 c11 c5 d10 d14 e15 e16 e9 f11 f12 f5 f9 g12 g13 g16 g8 g9 h8 i11 i15 i7 j15 2:j7 6:j9 k15 k3 k4 4:k7 l15 m14 m2 n13 n3 o12 o3"
/>

Without the bottom window, Red holds Blue to a ladder they cannot escape
<hexboard size="17x17"
coords="hide"
contents="R b11 c10 c13 d9 e11 e12 e13 e8 f10 f13 f14 f16 f6 f8 g10 g14 g5 h10 h14 h7 i8 1:j12 j14 j4 j6 5:k10 k14 k6 3:k9 7:l10 l14 l8 m12 m4 m6 n14 n4 o13 B b12 c11 c5 d10 d14 e15 e16 e9 f11 f12 f5 f9 g12 g13 g16 g8 g9 h8 i11 i15 i7 4:j11 j15 j7 j9 6:k11 k15 k3 k4 k7 l15 2:l9 m14 m2 n13 n3 o12 o3 E 8:l11 9:n10 S blue:l11 red:n10"
/>

Instead, Blue is able to use the window to their advantage, setting up a double threat to win the game, making use of a [[trapezoid]] (shaded).
<hexboard size="17x17"
coords="hide"
contents="R b11 c10 c13 d9 e11 e12 e13 e8 f10 f13 f14 f16 f6 f8 g10 g14 g5 h10 h14 h7 i8 j12 j14 j4 j6 k10 k14 k6 k9 l10 l14 l8 m12 m4 m6 n14 n4 o13 B b12 c11 c5 d10 d14 e15 e16 e9 f11 f12 f5 f9 g12 g13 g16 g8 g9 h8 i11 i15 i7 j11 j15 j7 j9 k11 1:k12 k15 k3 k4 k7 l15 l9 m14 m2 n13 n3 o12 o3 E +:i13 *:i14 +:j13 *:m11 S area(i13,g13,g12,h11,i11) blue:i14 blue:m11"
/>

User:Mason

Mason — Wed, 24 Jun 2026 20:07:40 GMT

Handicap

Mason — Wed, 24 Jun 2026 16:16:23 GMT

‎Progressive board size

Where to swap (y)

Hexanna — Sun, 21 Jun 2026 02:47:22 GMT

flip red/blue convention, for consistency with hex pages

Show changes

Y puzzles

Hexanna — Sat, 20 Jun 2026 23:42:26 GMT

typo

Y puzzle solutions

Hexanna — Sat, 20 Jun 2026 23:22:02 GMT

typos

Y puzzles

Hexanna — Sat, 20 Jun 2026 22:00:54 GMT

"see also" section

Y puzzle solutions

Hexanna — Sat, 20 Jun 2026 21:59:25 GMT

fix typos

Y puzzle solution

Hexanna — Sat, 20 Jun 2026 21:51:32 GMT

Hexanna moved page Y puzzle solution to Y puzzle solutions there are multiple puzzles now

Y puzzle solution

Hexanna — Sat, 20 Jun 2026 21:51:22 GMT

add a few solutions

Y puzzle

Hexanna — Sat, 20 Jun 2026 21:42:02 GMT

Hexanna moved page Y puzzle to Y puzzles there are multiple puzzles now

User:Hexanna

Hexanna — Sat, 20 Jun 2026 21:41:39 GMT

moved Y puzzles over

Y puzzle

Hexanna — Sat, 20 Jun 2026 21:41:04 GMT

add puzzles

User:Hexanna

Hexanna — Sat, 20 Jun 2026 21:34:33 GMT

basic 1-2* hex strategy

Conventions

Hexanna — Sun, 31 May 2026 16:48:52 GMT

add hexata, update playhex

@@ Line 179: / Line 179: @@
    contents="R A:h1 E B:j1 R h3"
    />
 == Weak pivoting templates ==
@@ Line 247: / Line 214: @@
              S area(b9,h9,h5,e5,c7)-g5"
    />
 == Pivoting ladder creation templates ==

← Older revision	Revision as of 01:56, 27 June 2026
Line 1:	Line 1:
−	+	<hexboard size="4x4"
	+	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"
	+	/>

@@ Line 69: / Line 69: @@
 === Size 10 ===
 <hexboard size="10x10"
    coords="none"
    edges="none"
    visible="area(a10,j10,j1)"
-   contents="S blue:all none:area(e5,e11,k5) red:area(f7,f8,g8,h7,h6,g6)"
+   contents="S blue:all red:area(f6,h5,i6,h8,f9,e8) E *:(area(d7,d10,a10) area(j1,j4,g4) area(j7,j10,g10) area(f7,f8,g8,h7,h6,g6))"
    />

← Older revision		Revision as of 01:43, 25 June 2026
Line 140:		Line 140:

	* [part 3: talk about the edges, simple edge patterns, and how opposing stones influence the strength of your stones, both proactively and retroactively?]		* [part 3: talk about the edges, simple edge patterns, and how opposing stones influence the strength of your stones, both proactively and retroactively?]
−
−	~~===Ladders===~~
−
−	* Ladders are tricky. Here's a first-order approximation — there are many exceptions, but this is still a useful baseline:
−	** As the defender of the ladder, you have two main options: push, or let your opponent connect in exchange for territory. Look ahead to see whether pushing seems good for you.
−	*** Generally, yield if and only if pushing would allow your opponent to adjacent-cut through two of your stones (which happens if you have a stone above the ladder).
−	*** If the attacker fails to push, you should either bridge or play adjacently on the attacker's row to cut in front of the ladder. In other words, Blue should play at (*) or (+) below:
−	**: <hexboard size="4x5" float="inline" edges="bottom" coords="none" contents="R arrow(12):a2 B a3 R b2 B b3 E :d2 +:c2" />
−	** As the attacker of the ladder, your main options are to push or pivot. If you're close to an acute corner, you can either pivot, or if the corner is empty, play a cornering move.
−	*** Most of the time, pushing is good until you reach a corner.
−	*** If you have stones above the ladder, try to make use of them, mostly by jumping and pivoting early enough so that the stones aren't "wasted".

	==bullet hex strategy?==		==bullet hex strategy?==

@@ Line 64: / Line 64: @@
 ===Ladders===
-* Don't worry about switchbacks, climbing, or ladder creation templates on 15&times;15 or larger. They can be theoretically interesting and make for good puzzles, but games are rarely close enough for these to matter. I personally don't think about them on any board size, but others may reasonably disagree with this approach.
-* Q: When should the defender of a ladder yield? A: Usually, don't yield unless your opponent can cut through two of your stones, one above and one below the ladder. In that case, consider yielding.
+Ladders are tricky. Here's a first-order approximation &mdash; there are many exceptions, but this is still a useful baseline:
-** [https://hexworld.org/board/#13nc1,c2e9c10d8b9c11d10d12 Here] is an example. If Blue instead plays 8. d11, Red 9. e10 cuts through e9 and d11.
+* As the defender of the ladder, you have two main options: push, or let your opponent connect in exchange for territory. Look ahead to see whether pushing seems good for you.
-** In [https://playhex.org/games/66b8a125-bf02-42d2-8900-af3042a8ccf8 this game] from the [[Tournaments#Hex_Monthly | Hex Monthly 21]] ([https://hexworld.org/board/#14c1,c2d11k10k4b5f10g9i9i8g10h9h10j8j9b12c10l8k8l7k7l6k11j11h12m5k6l4m4l5l9k9h13i13l3k5i5j5j4i6h6f8h7i7f9g8f7e8e7d8d7b8c8b9c9a11b13d10c11c12,c13d12d13e11:rw HexWorld link]), the yielding move 60. c14 is winning, while the played 60. c13 (which allows Red d12, cutting through Blue's c13 and d11 stones) is losing.
+** A third option is to yield. Generally, yield when pushing would allow your opponent to cut through two of your stones, one above and one below the ladder; otherwise, don't yield.
 ===Other===

@@ Line 1: / Line 1: @@
-Windows are a class of structure where one of your stones, which is connected to one of your edges, is accessible through a tiny gap in the opponents stones. At first glance, they seem to be not all that helpful. They feel far away from the action and often are created through sequences of moves that give the opponent a large amount of territory, which can feel like a losing exchange. However, they are actually quite strong. Their strength comes from the the fact that having a single extra move is usually enough to win the game, and a window can serve to offer you just that by creating a threat the opponent is forced to block, giving you another move.
+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.
 === An Example ===
-After Blue plays '''1''' and Red plays '''2''', Blue has a window at the upper '''*'''. The red-shaded cells do not have any red stones in them at the moment, but easily could at some point in the future due to the nature of bridges.
+At first glance, a window seems to be not so helpful for connection due to its lack of accessibility. However, it can usually serve to offer an extra move by creating a threat that the opponent is forced to block, giving you another move to win the game.
-A few moves later, Blue realizes that by starting the ladder with '''5''', Red is going to have to break at some point, giving Blue another window.
+After Blue plays '''1''' and Red plays '''2''', there is a window at the upper '''*'''. The red-shaded cells do not have any red stones in them at the moment, but easily could at some point in the future due to the nature of bridges.
 <hexboard size="17x17"
     coords="hide"
@@ Line 10: / Line 12: @@
     />
-The final battle takes place on this board. Red has a lot of stones in Blue's way, but Blue has a couple of windows.
+The final battle takes place on this board. Red has a lot of stones in Blue's way, but Blue also has a couple of windows to connect to.
 <hexboard size="17x17"
     coords="hide"
@@ Line 16: / Line 18: @@
     />
-Blue starts by strengthening their upper window. Red, presumably, still feels the other direction is more threatening, so opts to block that way instead. Blue gets withing range of their window. Red will now have to block.
+Blue starts by breaking through the window above. Red, presumably, still feels the other direction is more threatening, so opts to block that way instead. Blue gets closer to the upper group. Red will now have to block.
 <hexboard size="17x17"
     coords="hide"
     contents="R b11 c10 c13 d9 e11 e12 e13 e8 f10 f13 f14 f16 f6 f8 g10 g14 g5 h10 h14 4:h7 2:i8 j14 j4 k14 l14 m12 m4 m6 n14 n4 o13 B b12 c11 c5 d10 d14 e15 e16 e9 f11 f12 f5 f9 g12 g13 g16 g8 g9 5:h8 i11 i15 3:i7 j15 k15 k3 1:k4 l15 m14 m2 n13 n3 o12 o3"
     />
-Blue is able to use this window to get dangerously close to their other window.
+Blue is able to use this group to get dangerously close to the other window.
 <hexboard size="17x17"
     coords="hide"

@@ Line 151: / Line 151: @@
 *** Most of the time, pushing is good until you reach a corner.
 *** If you have stones above the ladder, try to make use of them, mostly by jumping and pivoting early enough so that the stones aren't "wasted".
 ==bullet hex strategy?==

@@ Line 207: / Line 207: @@
 * See more discussion of acute corner joseki at [[Openings_on_19_x_19#Acute_corner_theory]]. For the obtuse corner, see [[Openings_on_19_x_19#Obtuse_corner_theory]] which covers responses to the 4-4 and 5-5 obtuse corner in great detail. Most of this is applicable to 13&times;13 and larger, and not just 19&times;19.
-==Specific tactics==
+==Miscellaneous topics==
 ===Threatening a bridge cut===
 One of my favorite tactics is threatening a bridge cut, where the opponent needs to play too close to their own edge to defend:

@@ Line 1: / Line 1: @@
 &times;19 is the most popular of the "large" board sizes. This board size offers a lot of room for strategic freedom (unlike 11&times;11 or 13&times;13), but tactics and local play remain highly important.
-An average well-played game lasts about 72-90 moves before one side resigns, or 20-25% of the board, though it varies considerably from game to game. This article covers opening strategy that is most relevant in the first 10-30 moves of the game. Some of it is specific to 19&times;19, but much of it is applicable to other large board sizes.
+An average well-played game lasts about 72&ndash;90 moves before one side resigns, or 20&ndash;25% of the board, though it varies considerably from game to game. This article covers opening strategy that is most relevant in the first 10&ndash;30 moves of the game. Some of it is specific to 19&times;19, but much of it is applicable to other large board sizes.
 The advice in this guide is heavily influenced by [[KataHex]], the strongest known (and easily superhuman) bot as of 2024.
@@ Line 60: / Line 60: @@
 * The middle of the board is also quite strong, though it's important to spread out your moves across the board, instead of concentrating too many stones near the middle.
-There are certainly exceptions to the above; feel free to experiment with moves in the middle of Blue's 3rd row or elsewhere. The presence of other stones even moderately nearby can affect which moves are strong or weak. Nevertheless, I think these guidelines hold up surprisingly well in the first 5-10 moves or so.
+There are certainly exceptions to the above; feel free to experiment with moves in the middle of Blue's 3rd row or elsewhere. The presence of other stones even moderately nearby can affect which moves are strong or weak. Nevertheless, I think these guidelines hold up surprisingly well in the first 5&ndash;10 moves or so.
 ==General principles==
@@ Line 621: / Line 621: @@
 ===Third and fourth row openings===
 According to KataHex, the fairest openings in this category are e3 (mentioned above) and n3.
 Openings in the middle of Red's 4th row are surprisingly playable, but most people prefer not to have their opening stone swapped, and playing against a 4th row opening stone can seem daunting, so a 3rd row opening is often preferable. If you strongly prefer having the first stone, or you think your opponent is overly eager to swap, you can play a weaker opening like f3 or g3.
@@ Line 633: / Line 633: @@
    />
-[[category: Opening]]
+[[category:Opening]]
-[[category: Advanced Strategy]]
+[[category:Advanced Strategy]]

@@ Line 6: / Line 6: @@
 [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.
-* 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 GUI's &mdash; it doesn't support adding comments to moves, for example.
+* 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 to proofread and validate some of the KataHex eval claims made in my articles.
@@ Line 72: / Line 72: @@
 It's a good idea to first study patterns in a '''vacuum''', meaning in the absence of nearby stones. This provides a useful baseline when evaluating a move &mdash; if you only study patterns in the context of real games or on smaller boards, it's difficult to tell whether a move was good because the resulting pattern was inherently good, or because the rest of the board worked in your favor. A few points worth mentioning first:
 * We'll sometimes use quantitative language, such as "fractions" of a stone. That doesn't mean you need to memorize the numbers or do a bunch of math while playing Hex. Numbers are just less ambiguous than words.
-* Hex strategy is largely about making the right tradeoffs and avoiding blunders, not finding "the best move." Real games are messy. There's local/global considerations and the possibility of overlapping patterns or regions. For each pattern, try to learn not only the "optimal" move(s), but also roughly how bad the suboptimal moves are, so you can properly weigh moves that look strong in one dimension but weak in another.
+* Hex strategy is largely about making the right tradeoffs and avoiding blunders, not finding "the best move." Real games are messy. There are local/global considerations and the possibility of overlapping patterns or regions. For each pattern, try to learn not only the "optimal" move(s), but also roughly how bad the suboptimal moves are, so you can properly weigh moves that look strong in one dimension but weak in another.
 * You won't remember everything here, and this guide isn't exhaustive. Your goal is to build a parsimonious mental model of Hex: what good/bad Hex looks like, and ''why'', so that your intuition generalizes well to new positions.
 ** One mental model we'll use: you can quantify how much a position/pattern/move favors one side in terms of ''fractions of a stone''. The basic idea is that [[passing]] is like giving up "1 stone" (and so it's worth 0 stones), the best move is worth 1 stone, a fair swap move is worth 0.5 stones, and moves can also be worth >0.5 or <0.5 stones. The same idea can be extended to patterns. The crux of the mental model is that empirically, the [https://en.wikipedia.org/wiki/Superposition_principle superposition principle] ''approximately'' applies, especially when multiple patterns are sufficiently far apart and independent. That is, if Red made a 0.2-stone mistake somewhere and Blue made a 0.1-stone mistake elsewhere, in some sense, your best guess is that Blue is ahead by 0.1 stones.
@@ Line 115: / Line 115: @@
 :** (c): This is congruent to case (c) in the adjacent 2-stone pattern (which was a 0.35-stone mistake), but we're starting from a 0.05 higher baseline, so this is a 0.4-stone mistake.
 :** (d) and (e): Most simply, these Red replies are weak because they're adjacent to Red's existing stone, and Blue's existing stone isn't sufficiently close enough to make the second red stone useful. KataHex says this is a 0.4-stone mistake.
-:** (f): This is a long bridge allow-cut. According to our mental model, this should be 0.3-stone mistake &mdash; 0.2 from the tenuki baseline, and 0.1 from the allow-cut. KataHex nearly agrees and says it's a 0.35-stone mistake.
+:** (f): This is a long bridge allow-cut. According to our mental model, this should be a 0.3-stone mistake &mdash; 0.2 from the tenuki baseline, and 0.1 from the allow-cut. KataHex nearly agrees and says it's a 0.35-stone mistake.
 :** (g): This is a (short) bridge allow-cut. KataHex says it's roughly a 0.5-stone blunder.
@@ Line 222: / Line 222: @@
 If Red plays a3, some older strategy guides recommend that Blue respond d6 or e7 if she wants to play in the acute corner. However, KataHex considers this an inaccuracy; even though d6 and e7 are attacking stones in the sense that Blue would win a [[bridge ladder]] towards the acute corner, they don't do a good job blocking Red's edge the way e4 does in an empty corner.
-If you want to play the acute corner, 5-5, or 4-4 on smaller boards, is a good choice. (There are other options further away from the corner on larger boards.) KataHex and other bots consistently prefer these moves:
+If you want to play in the acute corner, 5-5 or 4-4 is a good choice on smaller boards. (There are other options further away from the corner on larger boards.) KataHex and other bots consistently prefer these moves:
 * https://www.littlegolem.net/jsp/game/game.jsp?gid=2175191&nmove=4
 * https://www.littlegolem.net/jsp/game/game.jsp?gid=2033243&nmove=2
@@ Line 247: / Line 247: @@
 * e5: In some ways, these resemble the low intrusion 5-4 joseki, shifted up one row.
 ** https://hexworld.org/board/#14nc1,a3e5c5c6d6d5 Red 5 is optional but actually an acceptable bridge peep, because intruding on the other side of the bridge would be too much strength near the top and almost never a good idea.
-** Red must still avoid b5 for the same reason as before: https://hexworld.org/board/#14nc1,a3e5c5c4b5b4d4f3d3 is very favorable to Blue. Observe that Blue 8 at f3 is more efficient than at e2, because e2 is followed by Red f3 which is a bridge cut
+** Red must still avoid b5 for the same reason as before: https://hexworld.org/board/#14nc1,a3e5c5c4b5b4d4f3d3 is very favorable to Blue. Observe that Blue 8 at f3 is more efficient than at e2, because e2 is followed by Red f3 which is a bridge cut.
 ** https://hexworld.org/board/#14nc1,a3e5c5c4d4c6d6e6d5d7b8c7a7b6a6b5a5a4b4c2c3f3d2 Red peeps the bridge with 7. d6; Blue 8. e6 may be a stronger reply than connecting directly. While this variation represents strong play by both sides, and Red is doing just fine, Blue 20 and the sequence leading up to it is a good illustration of how Blue can play efficiently around Red's a3 stone.
 ** https://hexworld.org/board/#14nc1,a3e5c5d4c4c6f5h3 There are too many variations after Blue d4 to list them all. Blue 6 at d3 leads to a fun minimaxing sequence but is perhaps a slight inaccuracy: https://hexworld.org/board/#14nc1,a3e5c5d4c4d3b6d2c3d7
 ==Notation for distances==
-When analyzing patterns, it's useful to have a way to express various distances concisely. There are terms like adjacent, bridge, "classic block," but larger distances are hard to describe. Distances like "two hexes away" are ambiguous, does it mean a distance of 2 (like a1 and c1) or two hexes in between (like a1 and d1)? Everyone has their own way of thinking about it. Here's the one I use:
+When analyzing patterns, it's useful to have a way to express various distances concisely. There are terms like adjacent, bridge, "classic block," but larger distances are hard to describe. Distances like "two hexes away" are ambiguous: does it mean a distance of 2 (like a1 and c1) or two hexes in between (like a1 and d1)? Everyone has their own way of thinking about it. Here's the one I use:
 * Pretend that the hex grid consists of regular hexagons, and adjacent hexagons' centers have distance 1. (Equivalently, the centers of the hexes form a triangular lattice; pretend these triangles are equilateral with side length 1.)
-* It's not hard to show that a "bridge" (like a1 and b2) has length sqrt(3) if you connect the centers, and a "classic block" (like a1 and c2) has length sqrt(7). A fun exercise is to show that the distances between the centers of two hexes is always the square root of an integer. Which integers are possible as squared distances? Answer: [https://oeis.org/A003136 Löschian numbers.]
+* It's not hard to show that a "bridge" (like a1 and b2) has length sqrt(3) if you connect the centers, and a "classic block" (like a1 and c2) has length sqrt(7). A fun exercise is to show that the distance between the centers of two hexes is always the square root of an integer. Which integers are possible as squared distances? Answer: [https://oeis.org/A003136 Löschian numbers.]
 * The fact that squared distances are integers is notationally convenient. Let Δn denote a ''squared'' distance of n (I like this because it looks nicer than a square root symbol, and a letter like "d" can be confused with a coordinate).
 * "Adjacent" is Δ1; "bridge" is Δ3; "classic block" is Δ7; the distance between a1 and c1 is Δ4; "two bridges away" is Δ12.
@@ Line 373: / Line 373: @@
 *** a10 is the weakest of a4&ndash;a10, while a5 is the strongest.
 *** b10 is stronger than all of its neighbors, because Blue cannot fit the ziggurat in the obtuse corner.
-** That this bot picked up on all these subtleties, and assigns a win percentage close to 100% for most moves on 13&times;13, suggest to me that it is probably stronger than leela_bot and gzero_bot. I can't know for sure, though.
+** That this bot picked up on all these subtleties, and assigns a win percentage close to 100% for most moves on 13&times;13, suggests to me that it is probably stronger than leela_bot and gzero_bot. I can't know for sure, though.
-** On the other hand, and the author seems to agree, the 37&times;37 map looks very unreliable. I see percentages as low as 37% but only as high as 54% (for a move like f1, which should almost certainly be a losing move).
+** On the other hand, the author seems to agree that the 37&times;37 map looks very unreliable. I see percentages as low as 37% but only as high as 54% (for a move like f1, which should almost certainly be a losing move).
 ** The 27&times;27 map looks more reliable. I'm personally very skeptical that moves on Red's 6th row are among the most balanced moves, but there are some interesting (if somewhat noisy) insights to be had still.

← Older revision		Revision as of 20:07, 24 June 2026
Line 391:		Line 391:
	== Handicap System ==		== Handicap System ==
	The weaker player plays first with no swap. Difficulty is increased (for the weaker player) by increasing the size of the board.		The weaker player plays first with no swap. Difficulty is increased (for the weaker player) by increasing the size of the board.
		+
		+	== Windows ==

@@ Line 92: / Line 92: @@
 == Progressive board size ==
-For beginners, it is often difficult to win against experienced players even with a large handicap. [[User:Mason|Mason Mackaman]] suggested the following procedure to keep the game enjoyable: Play with handicap 0.5 (i.e., without swap), starting from the smallest board size (even 1x1, if it is available). Each time the beginner wins, increase the board size by 1. The players will typically move through the smallest board sizes very quickly, and then slow down somewhere near 6x6 or 7x7. This ensures that the beginner is always on the verge of winning, and can clearly measure their improvement. This method might be more fun than starting with a large handicap on a typical board size. The steps up in difficulty are also potentially more fine-grained than the half-stone decrements of the Demer system, though no testing has been done to confirm this.
+For beginners, it is often difficult to win against experienced players even with a large handicap. [[User:Mason|Mason Mackaman]] suggested the following procedure to keep the game enjoyable: Play without swap, starting from the smallest board size. Each time the beginner wins, increase the board size by 1. The players will typically move through the smallest board sizes very quickly, and then slow down somewhere near 6x6 or 7x7. This ensures that the beginner is always on the verge of winning, and can clearly measure their improvement. This method might be more fun than starting with a large handicap on a typical board size. The steps up in difficulty are also potentially more fine-grained than the half-stone decrements of the Demer system, though no testing has been done to confirm this.
 === Why not use second player advantage instead? ===
 Another way to do a board size handicap is by using swap and leveraging the natural second player advantage. While this certainly can be done, it is generally not as enjoyable for the following reasons:

@@ Line 50: / Line 50: @@
 ===Puzzle 6===
-Red to play and win (try it [https://hexanna1.github.io/hex-study/y.html#7,a2d4d1c2d2 here]):
+Blue to play and win (try it [https://hexanna1.github.io/hex-study/y.html#7,a2d4d1c2d2 here]):
 <hexboard size="7x7"
    edges="hide"

@@ Line 6: / Line 6: @@
    edges="hide"
    visible="area(a1,a4,d1)"
-   contents="R a1 B b1 R 1:a3"
+   contents="R a1 B b1 R 1:a3 B 2:a2 R 3:c2"
    />
 ===Puzzle 2===
 <hexboard size="5x5"
    edges="hide"
    visible="area(a1,a5,e1)"
-   contents="R b1 c3 B d2 1:b2"
+   contents="R b1 c3 B d2 1:b2 R 2:c2 B 3:c1 R 4:d1 B 5:a4"
    />
@@ Line 25: / Line 51: @@
    />
-If Blue plays e2 too early on move 3, it is losing due to Red 4. c3. If Blue 5. b2, then Red 6. d2. If Blue 5. d2, then Red 6. b3.
+If Blue plays e2 too early, on move 3, it is losing due to Red 4. c3. If Blue 5. b2, then Red 6. d2. If Blue 5. d2, then Red 6. b3.
 <hexboard size="6x6"
@@ Line 39: / Line 65: @@
    visible="area(a1,a6,f1)"
    contents="R a2 c1 B b4 1:c2 R 2:c3 B 3:b2"
    />

@@ Line 63: / Line 63: @@
 Blue to play. What is the winning move, and what is Red's strongest reply?
-Solution: [[Y puzzle solution]]
+==See also==
-Back to the game of Y: [[Y]]
+* [[Y puzzle solutions]]
 [[Category:Y]]
 [[Category:Puzzle]]

@@ Line 25: / Line 25: @@
    />
-If Red plays e2 too early on move 3, it is losing. If Red 5. b2, then Blue 6. d2. If Red 5. d2, then Blue 6. b3.
+If Blue plays e2 too early on move 3, it is losing due to Red 4. c3. If Blue 5. b2, then Red 6. d2. If Blue 5. d2, then Red 6. b3.
 <hexboard size="6x6"
@@ Line 33: / Line 33: @@
    />
-If Blue plays 2. c3 instead, Red's unique winning reply is 3. b2!
+If Red plays 2. c3 instead, Blue's unique winning reply is 3. b2!
 <hexboard size="6x6"

← Older revision		Revision as of 21:51, 20 June 2026
Line 1:		Line 1:
		+	==Standard Y puzzles==
		+
		+	===Puzzle 1===
		+
		+	<hexboard size="4x4"
		+	edges="hide"
		+	visible="area(a1,a4,d1)"
		+	contents="R a1 B b1 R 1:a3"
		+	/>
		+
		+	===Puzzle 2===
		+
		+	<hexboard size="5x5"
		+	edges="hide"
		+	visible="area(a1,a5,e1)"
		+	contents="R b1 c3 B d2 1:b2"
		+	/>
		+
		+	===Puzzle 3===
		+
		+	<hexboard size="6x6"
		+	edges="hide"
		+	visible="area(a1,a6,f1)"
		+	contents="R a2 c1 B b4 1:c2 R 2:d1 B 3:b2 R 4:b1 B 5:e2"
		+	/>
		+
		+	If Red plays e2 too early on move 3, it is losing. If Red 5. b2, then Blue 6. d2. If Red 5. d2, then Blue 6. b3.
		+
		+	<hexboard size="6x6"
		+	edges="hide"
		+	visible="area(a1,a6,f1)"
		+	contents="R a2 c1 B b4 1:c2 R 2:d1 B 3:e2 R 4:c3"
		+	/>
		+
		+	If Blue plays 2. c3 instead, Red's unique winning reply is 3. b2!
		+
		+	<hexboard size="6x6"
		+	edges="hide"
		+	visible="area(a1,a6,f1)"
		+	contents="R a2 c1 B b4 1:c2 R 2:c3 B 3:b2"
		+	/>
		+
		+	==Bent-27 Y puzzle==
		+
	[[Image:Y27puz_sol.gif]]		[[Image:Y27puz_sol.gif]]

@@ Line 57: / Line 57: @@
 * In regular Hex, the a2-b3-c4 diagonal is strong for Red. In 1-2* Hex, the a3-b4-c5 diagonal appears strong for Red. See 3. c5 or 23. k9, for example.
 * Sometimes, the game partially collapses to single-turn Hex, where one side plays a move that would be an irrelevant but forcing move in regular Hex (like a [[time tesuji]]). A player with the initiative could use time tesujis to decide the tempo of play, choosing between one or two real moves per turn.
 ==draft of more strategy stuff==

← Older revision		Revision as of 21:41, 20 June 2026
Line 1:		Line 1:
		+	==Standard Y puzzles==
		+
		+	Each of the following puzzles has a unique winning first move.
		+
		+	===Puzzle 1===
		+
		+	Red to play and win (try it [https://hexanna1.github.io/hex-study/y.html#4,a1b1 here]):
		+	<hexboard size="4x4"
		+	edges="hide"
		+	visible="area(a1,a4,d1)"
		+	contents="R a1 B b1"
		+	/>
		+
		+	===Puzzle 2===
		+
		+	Blue to play and win (try it [https://hexanna1.github.io/hex-study/y.html#5,b1d2c3 here]):
		+	<hexboard size="5x5"
		+	edges="hide"
		+	visible="area(a1,a5,e1)"
		+	contents="R b1 c3 B d2"
		+	/>
		+
		+	===Puzzle 3===
		+
		+	Blue to play and win (try it [https://hexanna1.github.io/hex-study/y.html#6,a2b4c1 here]):
		+	<hexboard size="6x6"
		+	edges="hide"
		+	visible="area(a1,a6,f1)"
		+	contents="R a2 c1 B b4"
		+	/>
		+
		+	===Puzzle 4===
		+
		+	Blue to play and win (try it [https://hexanna1.github.io/hex-study/y.html#6,c2c3a4 here]):
		+	<hexboard size="6x6"
		+	edges="hide"
		+	visible="area(a1,a6,f1)"
		+	contents="R c2 a4 B c3"
		+	/>
		+
		+	===Puzzle 5===
		+
		+	Red to play and win (try it [https://hexanna1.github.io/hex-study/y.html#6,a1b5e1d2 here]):
		+	<hexboard size="6x6"
		+	edges="hide"
		+	visible="area(a1,a6,f1)"
		+	contents="R a1 e1 B b5 d2"
		+	/>
		+
		+	===Puzzle 6===
		+
		+	Red to play and win (try it [https://hexanna1.github.io/hex-study/y.html#7,a2d4d1c2d2 here]):
		+	<hexboard size="7x7"
		+	edges="hide"
		+	visible="area(a1,a7,g1)"
		+	contents="R a2 d1 d2 B d4 c2"
		+	/>
		+
		+	==Bent-27 Y puzzle==
		+
	[[Image:Y27puzzle.gif]]		[[Image:Y27puzzle.gif]]

@@ Line 14: / Line 14: @@
 * [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.
 ==draft of more strategy stuff==

@@ Line 219: / Line 219: @@
 | black
 | any
 |-
 | Board Game Arena
@@ Line 263: / Line 272: @@
 | red/blue
 | red
-| any positive
+| positive diamond / positive flat / positive flat II
 |-
 | AbstractPlay