User:Hexanna - Revision history

Hexanna at 23:47, 1 July 2026

2026-07-01T23:47:03Z

Hexanna: moved over (and elaborated) ladders

2026-06-25T01:43:22Z

moved over (and elaborated) ladders

Hexanna: moved over "advanced strategy: leaving the question open"

2026-06-25T01:18:44Z

moved over "advanced strategy: leaving the question open"

Hexanna: typos

2026-06-25T01:04:04Z

typos

Hexanna: moved Y puzzles over

2026-06-20T21:41:39Z

moved Y puzzles over

Hexanna: basic 1-2* hex strategy

2026-06-20T21:34:33Z

basic 1-2* hex strategy

Hexanna at 04:15, 18 June 2026

2026-06-18T04:15:43Z

Hexanna: some Y puzzles

2026-06-18T02:23:47Z

some Y puzzles

Hexanna at 19:30, 24 May 2026

2026-05-24T19:30:57Z

Hexanna: tweak stone fraction claims to match the local pattern explorer

2026-04-08T02:43:28Z

tweak stone fraction claims to match the local pattern explorer

@@ Line 7: / Line 7: @@
 [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 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.
+* 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:

← Older revision		Revision as of 01:43, 25 June 2026
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	* [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 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 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.

@@ 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==

@@ 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.
 ==some [[Y]] puzzles==

@@ Line 54: / Line 54: @@
    />
-. Red to play and win (try it [https://hexanna1.github.io/hex-study/y.html#7,a2d2 here]):
+. 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 B d2"
+   contents="R a2 d1 d2 B d4 c2"
    />

@@ Line 10: / Line 10: @@
 [https://hexanna1.github.io/hex-study/ Hex Study Tools] is a collection of interactive databases:
-* [https://hexanna1.github.io/hex-study/patterns.html Local pattern explorer] with up to 5-stone local patterns
+* [https://hexanna1.github.io/hex-study/patterns.html Local pattern explorer] with up to 6-stone local patterns
 * [https://hexanna1.github.io/hex-study/joseki.html Joseki explorer] with acute and obtuse corner sequences
 * [https://hexanna1.github.io/hex-study/openings.html Opening explorer] with opening lines on sizes 11&ndash;14 and 17

@@ Line 52: / Line 52: @@
 :* ''Answers:''
 :** Tenuki: The simplest response to analyze. If Red tenukis instead of playing (a), then by symmetry Blue could play (a) herself! That flips a 0.05-stone advantage into a 0.05-stone disadvantage, implying that tenuki is a 0.1-stone mistake. Indeed, KataHex agrees when you check the evals. In a way, the strength of (a) is why Blue's earlier choice to play adjacent to the Red stone is locally slightly inaccurate. And because tenuki is suboptimal, the local pattern is slightly tactical; this contributes to Hex games feeling like lots of local fights rather than a "cold" game.
-:** (b): This is an adjacent allow-cut. We haven't quantified these precisely, but you should expect (b) to be a blunder. KataHex says it's a 0.5-stone mistake, and Blue's best reply is cutting through at the adjacent (a).
+:** (b): This is an adjacent allow-cut. We haven't quantified these precisely, but you should expect (b) to be a blunder. KataHex says it's a 0.4-stone mistake, and Blue's best reply is cutting through at the adjacent (a).
-:** (c): This is a mistake because Blue can respond at the non-adjacent (a), rendering (-) below relatively useless. KataHex quantifies (c) as a 0.4-stone mistake.
+:** (c): This is a mistake because Blue can respond at the non-adjacent (a), rendering (-) below relatively useless. KataHex quantifies (c) as a 0.35-stone mistake.
 :**: <hexboard size="3x2" float="inline" edges="none" coords="none" visible="-(b1 b3)" contents="R -:a2 B b2 R a1 B a3" />
-:** (d): Blue can respond at either (a) and create a pattern congruent to the one when Red plays (c), so this is also a 0.4-stone mistake.
+:** (d): Blue can respond at either (a) and create a pattern congruent to the one where Red plays (c), so this is at least a 0.35-stone mistake. KataHex says Blue can do even better responding with tenuki or (e), so it thinks (d) is actually a 0.4-stone mistake.
-:** (e): The start of a [[bottleneck]], but more importantly, it's a near allow-cut. Applying our mental model: a near allow-cut is a 0.1-stone mistake, but given that Red didn't play (a), we should think of this on top of a tenuki baseline, which adds another 0.1 (total 0.2). KataHex actually says it's a 0.25-stone mistake. This kind of deviation is unsurprising and doesn't invalidate the mental model &mdash; our reasoning was a bit handwavy, Blue has alternatives to the near-cut, KataHex evals are inherently noisy, and we probably didn't account for all nonlinearities.
+:** (e): The start of a [[bottleneck]], but more importantly, it's a near allow-cut. Applying our mental model: a near allow-cut is a 0.1-stone mistake, but given that Red didn't play (a), we should think of this on top of a tenuki baseline, which adds another 0.1 (total 0.2). KataHex says it's a 0.2-stone mistake.
-:** (f): This is a retroactive near allow-cut. Similar to (e), it's a 0.25-stone mistake.
+:** (f): This is a retroactive near allow-cut. Blue can play at (a) or (b) to reach a position congruent to the one where Red plays (e), so it's at least a 0.2-stone mistake. Blue tenuki may be slightly stronger; KataHex says (f) is a 0.25-stone mistake because of that.
 :** (g): This and similar Red moves further away from the blue stone are harder to reason about. KataHex thinks these moves are generally 0.15- to 0.2-stone mistakes; working backwards, you could decompose that into a 0.1 tenuki baseline, and attribute the remaining portion to the "non-tactical" component of the move's strength. Also, it should be intuitive that the further away the Red move, the more it "looks like" tenuki, where the non-tactical component tends to zero in the limit. (Again: while this is handwavy, the general approach of "fuzzy reasoning" we used here &mdash; taking the heuristics you know to imply conclusions that aren't necessarily "correct" in some theoretical sense, but that are much better than blind guessing &mdash; is a powerful tool when thinking about real games.)
 :* If you understand the above, you only have to memorize that (a) is the optimal reply, because you can reconstruct nearly all of the rest from first principles and fuzzy reasoning.
 * Let's consider the other important two-stone pattern, a stone of your color and an opposing stone a bridge away. Suppose it's Red's turn. We can do a similar exercise and evaluate (a)&ndash;(g) and tenuki.
@@ Line 68: / Line 69: @@
 :* ''Answers:''
 :** Tenuki: By symmetry, if Red tenukis, Blue can play at (a), turning a 0.1-stone advantage into a 0.1-stone disadvantage, so tenuki is a 0.2-stone mistake. KataHex agrees, and just like in the adjacent case, this pattern is tactical.
-:** (b): This is a near allow-cut, and after Blue responds at the adjacent (c), the resulting pattern is congruent to case (e) in the previous discussion of the adjacent 2-stone pattern (where KataHex said it was a 0.25-stone mistake). However, unlike the previous case, our baseline is higher: Red is ahead by 0.1 with the optimal response, not 0.05. It's worse (by 0.05) to start from a 0.05-stone higher baseline and reach the same result, so this is actually a 0.3-stone mistake.
+:** (b): This is a near allow-cut, and after Blue responds at the adjacent (c), the resulting pattern is congruent to case (e) in the previous discussion of the adjacent 2-stone pattern (where KataHex said it was a 0.2-stone mistake). However, unlike the previous case, our baseline is higher: Red is ahead by 0.1 with the optimal response, not 0.05. It's worse (by 0.05) to start from a 0.05-stone higher baseline and reach the same result, so this is actually a 0.25-stone mistake.
-:** (c): This is congruent to case (c) in the adjacent 2-stone pattern (which was a 0.4-stone mistake), but we're starting from a 0.05 higher baseline, so this is a 0.45-stone mistake.
+:** (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 0.45-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 agrees.
+:** (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.
-:** (g): This is a (short) bridge allow-cut. KataHex says it's roughly a 0.6-stone blunder.
+:** (g): This is a (short) bridge allow-cut. KataHex says it's roughly a 0.5-stone blunder.
 That was a pretty dense section, so let's take a breather and summarize.