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• Swap rule
  ...o weak, the second player will not swap (and therefore also be in a strong position). Therefore, the swap rule creates an incentive for the first player to pla ...eans the initial red piece is replaced by a blue piece in the mirror image position, where the mirroring takes place with respect to the board's long diagonal.
  9 KB (1,588 words) - 14:53, 18 November 2023
• Weakest link
  A player's position is only as good as the '''weakest''' potential '''link''' in their best con For example, in the position below, f6 is the weakest point in [[Red]]'s best connection across the boar
  690 B (126 words) - 00:11, 17 January 2023
• Basic (strategy guide)
  Another try from the original position would be to block at a bridge distance away at f8 (see diagram below). This A good block in the original position is to block at one hex farther back than the bridge block at either e9 or f
  15 KB (2,693 words) - 23:24, 12 October 2022
• Useless triangle
  ...nnot have any effect on the rest of the game regardless of the rest of the position. Notice that any red path through c5 must pass through b6 and c6. But b6
  1 KB (230 words) - 01:47, 12 September 2021
• Forcing move
  ...ete an immediate [[strong connection]] or [[win]]. Consider the following position with Red to move. At first glance, the position looks bad for Red, but she can win by making a couple of forcing moves. She
  6 KB (1,139 words) - 15:33, 7 October 2023
• Multiple threat
  ...[double threat]] connecting two of a player's [[group]]s. In the following position, Red's two groups are connected by double threat at the two cells marked "*
  3 KB (451 words) - 01:49, 18 May 2022
• A3 escape trick
  Consider the following position, with Red to move:
  2 KB (298 words) - 00:56, 16 March 2022
• Cornering
  ...]] at the cells marked "*". If Blue instead plays 6 on the second row, the position transposes to one commonly encountered with the D3 corner move (described b
  4 KB (799 words) - 14:57, 18 November 2023
• Ladder escape
  The two red stones on the right in the following position can be used to escape Red's third row ladder and enable Red to win the game
  4 KB (815 words) - 02:00, 8 January 2023
• Ladder escape fork
  In the following position, Red has no [[edge template]].
  1 KB (228 words) - 01:53, 18 May 2022
• Parallel ladder
  Consider the following position with [[Red]] to play.
  5 KB (973 words) - 00:36, 29 December 2021
• Climbing
  ...r (see the illustration on the right). For example, consider the following position, with Red to move:
  14 KB (2,655 words) - 12:53, 27 April 2024
• A1 opening
  In the following, when we say that a position is "winning" or "losing", we always mean under [[optimal play]] by both pla ...1 and b1 is a losing opening move, we will prove a stronger statement: the position with red pieces in ''both'' a1 and b1 (and no other pieces on the board), w
  4 KB (667 words) - 16:28, 25 May 2023
• Wall
  ...But instead, she plays at y and ladders to the right, giving the following position:
  1 KB (269 words) - 22:32, 19 May 2022
• Intermediate (strategy guide)
  ...nnot have any effect on the rest of the game regardless of the rest of the position. Consider the same position as before but suppose Red has an additional piece at h8.
  26 KB (4,694 words) - 01:56, 18 May 2022
• Local play
  ...t of Hex strategy. By making local moves, a player is able to defend their position and maintain control of one area of the board. This type of play is often u ...that will be useful later, and for exploiting weaknesses in the opponent's position.
  1 KB (255 words) - 02:46, 23 January 2023
• Tips and tricks
  ...ctly. Blue is still too focused on the bottom (unavoidably, given the weak position), but after having obtained a reasonable amount of influence on the right s
  1 KB (257 words) - 18:35, 7 September 2023
• Strategy
  ...trategy refers to a player's overall plan of action considering the global position on the board, whereas tactics refers to specific moves and actions taken in
  3 KB (429 words) - 00:43, 8 May 2023
• Handicap
  ...i.e., when a player swaps, the player keeps the same color, but the board position is mirrored. If the [[Conventions#Swapping|swap-sides convention]] is used ...lay without the swap rule, but to place Red's first piece in a pre-defined position (rather than allowing Red to place the piece freely). A piece placed in the
  11 KB (1,806 words) - 03:07, 5 April 2023
• Opening
  ...not too weak, as the second player will decline the swap and have a better position. Therefore, the first player must find a move that gives both players an ap
  2 KB (325 words) - 18:04, 19 March 2023
• The Hungarian (opening)
  ...nd the [[outpost]] at the bottom right helps to connect to the bottom. The position is very difficult for [[Blue (player)|Blue]] at the moment.
  882 B (161 words) - 04:58, 28 May 2023
• Foiling
  Consider the following position: ...d he also intrudes on its [[edge template]] to the bottom. In fact in this position Blue [[win]]s.
  6 KB (1,124 words) - 02:36, 8 January 2023
• Wheel
  ...then restore the connection between her pieces by playing at any A. Red's position improves, while Blue's piece is not very useful. Although Blue still has to ...hem, it is not a wheel and it is not a template. The U-turn is a very weak position. The U-turn sometimes arises when a player tries to connect via [[bridge]]s
  3 KB (482 words) - 17:33, 18 April 2023
• Ladder handling
  ...to connect, but the defender wants to get the most compensation out of his position. The most common way to jump is on the same row as the attacker's ladder an
  4 KB (815 words) - 02:07, 9 May 2024
• Hex theory
  ...pass. If the second player to move had a winning strategy for a symmetric position, then the first player to move could simply steal that strategy by passing * The problem of determining the winner of a given Hex position (on a board of size ''n''×''n'') is '''PSPACE-complete'''. The fact that i
  10 KB (1,742 words) - 02:23, 14 May 2024
• Open problems
  * Is the following true? Assume one player is in a winning position (will win with [[optimal play]]) and the opponent plays in a hex X. Let the
  4 KB (645 words) - 02:14, 9 November 2023
• Advanced (strategy guide)
  ...wn minimax move d5 (d6 is the other minimax option) yielding the following position. ...central group with e6, my opponent responds with d5 yielding the following position.
  31 KB (5,861 words) - 00:58, 9 February 2022
• Puzzles
  Note that this position is [[Equivalent patterns|equivalent]] to the position with the pieces at a5 and a6 removed. This could arise in response to the
  5 KB (1,001 words) - 12:23, 5 January 2024
• Solutions to puzzles
  The following seem like horizontal's (Blue's) best tries from the above position. ...s to intrude Red's upward connection at 3.b4. This leaves Blue in a strong position.
  34 KB (6,464 words) - 23:41, 14 February 2024
• Equivalent patterns
  Any position on an <em>nxm</em> board is equivalent to the same position on the interior (i.e. the cells non-adjacent to the edges) of an <em>(n+2)x ...e in the left pattern is [[captured cell|captured]] by Red. Therefore, the position is equivalent to one where this stone is actually red.
  13 KB (2,546 words) - 02:17, 9 May 2023
• Computer Hex
  ...also contain variations (several different games played out from the same position), as well as comments on every move in the game.
  5 KB (756 words) - 02:08, 10 February 2024
• Draw
  ...dary of ''T'' form a [[chain]] connecting the left and right edges, so the position is winning for Blue.
  3 KB (508 words) - 04:09, 30 May 2023
• Variants using the same equipment
  ...randomly filled with black and white stones. A consequence is that in each position, Black's optimal move is the same as White's optimal move, and is the cell
  7 KB (1,237 words) - 17:18, 7 May 2023
• Games from the 13th Little Golem TwixtPP Championship
  <tr><td>Position after 8 moves</td><td>Position after 15 moves</td></tr></table><BR> [[Image:605389_11.gif]]<BR>Position after 11 moves<BR><BR>
  21 KB (3,875 words) - 14:30, 18 April 2008
• Smart Game Format
  ...ition, for example, a special starting position for a game or puzzle, or a position that is used to explain some point in a game comment. A node is a setup nod
  16 KB (2,720 words) - 14:16, 8 January 2023
• Winning strategy
  ...player is a rule that specifies the player's next move from every possible position. If we fix a strategy for Red and a strategy for Blue, then the winner of t ...winning strategy for this position with Blue to move next". We say that a position is a ''first-player win'' for a player if that player has a winning strateg
  5 KB (901 words) - 01:06, 12 September 2021
• Games from the 14th Little Golem TwixtPP Championship
  ...ead, 21.s13 had some complicated variations. Black was already in a better position, and I didn't see any way white could win here, but s13 would have required ...the same position in the same tournament. Anyway, I think in this game my position was better. 16.o22 was too low. The key point is 17.n15 here, which allows
  23 KB (4,233 words) - 14:30, 18 April 2008
• Proverbs
  * ''Your position is only as good as your [[weakest link]].''
  2 KB (285 words) - 04:31, 26 July 2021
• Ladder puzzle 1/Solution
  ...e red stone at e7 is connected up via * and down via +, so it is a winning position.
  4 KB (732 words) - 03:43, 16 June 2021
• Glenn C. Rhoads vs. unknown
  ...d with 1. a3 and my opponent responded with 1... e4 yielding the following position.
  6 KB (1,061 words) - 00:31, 9 February 2022
• Edge template V1a
  ...ng in a 2nd row [[ladder]]. Red's 2 acts as a [[ladder escape]]. The final position is
  5 KB (953 words) - 13:44, 27 August 2022
• Irrelevant move
  ...rrelevant move''' or '''wasted move''' is a move that does not improve the position of the player who makes the move. It is considered as a waste of time and s ...makes it, it can sometimes happen that it does not improve the opponent's position either. Thus, the effect of such a move is in the best case neutral for the
  3 KB (503 words) - 23:36, 28 August 2022
• Strong connection
  ...[[template]]s and [[double threat]]s. For example, consider the following position:
  3 KB (517 words) - 15:25, 1 October 2023
• Dead cell
  ...our does not affect the outcome of the game. More formally, in a given Hex position, a cell is ''dead'' if for every way of filling all empty cells of the boar ...d a blue piece or a red piece, without changing the strategic value of the position. This often simplifies the analysis of Hex positions. In particular, dead c
  5 KB (925 words) - 16:30, 25 May 2023
• Bridg-It
  ...ample, 6x6 Brid-it, shown on the right, is equivalent to the following Hex position: However, since this position never arises during a normal game of Hex, the usual elements of Hex strateg
  6 KB (1,060 words) - 04:11, 30 May 2023
• Bill LeBoeuf vs. Universidad de Oviedo
  ...playing into a simple losing position. This leaves playing into an unclear position but in which your side seems to be as strong as possible.
  10 KB (1,993 words) - 14:36, 11 May 2023
• Mustplay region
  Consider the following position, with Blue to move: ...y region, the player is losing. To illustrate this, consider the following position, with Blue to move.
  14 KB (2,723 words) - 01:16, 4 October 2023
• Switchback
  ...a useful situation for the defender to be aware of. Consider the following position, with Blue to move: This position is complicated to analyze, with many possible lines of play, but it can be
  17 KB (3,207 words) - 22:47, 18 March 2024
• Niall vs Daniel Sepczuk - Dec 2011
  This is the position I (Red) am considering when these notes start, move 25:
  6 KB (1,272 words) - 02:24, 11 May 2023
• The new HexWiki
  ...current state at http://hexwiki.amecy.com/board_gui.html. You can build a position there, and the page generates markup that you can paste into your wiki arti
  4 KB (712 words) - 21:17, 28 December 2020
• Jonathan Rydh's strategy guide
  ...se cases you can fill in the gaps with stones and still have an equivalent position. ...his rule is if you have enough ground already and are sitting on a winning position. In that case, care should instead be taken to minimize the opponent's gain
  14 KB (2,557 words) - 20:29, 11 September 2021
• Open problems about edge templates
  ...ong the 4th row and Blue suddenly decides to play elsewhere (move 1 in the position below). ...ht imagine that custom computer code could be used to analyse this sort of position, and of course computers get faster over time so perhaps this problem will
  7 KB (1,215 words) - 02:29, 9 November 2023
• Theory of ladder escapes
  ...w ladder escape means (among other things) that Red must win the following position: and now we are back at the previous position with the ladder right next to the escape, where we have already seen that R
  123 KB (22,870 words) - 19:37, 2 April 2024
• Peep
  ...with suitable surrounding conditions. For example, consider the following position, where Red is connected to the bottom edge by a [[ziggurat]].
  8 KB (1,413 words) - 00:27, 16 August 2022
• Tenuki
  ...te new opportunities on the board and exploit weaknesses in the opponent's position. As more and more stones are played in an area, that area becomes less attr ...While local play is important for maintaining control and defending one's position, tenuki allows players to expand their influence on the board and exploit o
  2 KB (309 words) - 04:06, 23 January 2023
• Joseki
  ...ing on how far from an edge the first move by player A was. When the final position is reached, player A has a fixed escape on one side of the corner and playe This position might be reached if both players want an escape on the top.<br/>
  10 KB (1,802 words) - 20:09, 9 March 2024
• David Boll Hex FAQ
  ...the key to the best defense from 4 rows out, it's also typically the best position from which to defend on a wide open board. threatens to connect to F6, and is in the 'classic' defensive position
  15 KB (2,732 words) - 19:08, 28 December 2020
• GTP
  | Show the list of all legal moves for the current position.
  6 KB (848 words) - 00:23, 25 March 2022
• Conventions
  * '''Swap sides:''' Upon playing a swap move, the board position stays the same and the players change colors. ...:''' Upon playing a swap move, the players keep their colors and the board position is mirrored (ranks and files interchanged) and the color of the pieces is i
  11 KB (1,867 words) - 17:44, 4 February 2024
• Captured cell
  ...turing player's pieces, as this does not change the strategic value of the position. ...can play at a, killing b. Therefore, both cells are captured and the above position is strategically equivalent to the following.
  10 KB (1,893 words) - 23:42, 14 February 2024
• Domination
  ...as good. In Hex, we say that a cell X dominates another cell Y in a given position (and from a particular player's point of view) if playing at X is at least For example, in the following position, each of the cells marked "*" dominates the other two. So any of these move
  21 KB (3,995 words) - 22:37, 18 November 2023
• Optimal play
  For the purpose of the following definitions, by a '''position''', we mean an arrangement of pieces on the Hex board, together with the in ...ition'''. A move is called a '''winning move''' if it results in a winning position for the player who made the move; otherwise it is called a '''losing move''
  3 KB (470 words) - 23:15, 28 August 2022
• Passing
  ...ece (no matter which piece) always leaves the player in an equal or better position than passing would do. Nevertheless, there are a number of good reasons for ...player may choose to pass as a way of demonstrating the strength of their position to the opponent. In a friendly or teaching game, this can have a pedagogica
  8 KB (1,507 words) - 21:23, 5 November 2021
• Tidiness
  To illustrate that this can make a difference, consider the following position, with Blue to move. In this situation, "a" is winning, but "b" and all othe To illustrate that this can make a difference, consider the following position, with Red to move. In this situation, "a" is winning, but "b" and all other
  3 KB (510 words) - 03:21, 16 June 2021
• Flank
  ...er, they usually do not hurt and may be useful to Red by solidifying Red's position below the flank.
  17 KB (3,144 words) - 05:31, 1 December 2022
• Pivoting template
  ...hand, if we use a proper pivoting template in the analogous situation, the position is winning for Red:
  9 KB (1,667 words) - 08:02, 1 March 2024
• FIFI25 vs. murasawa, October 2021
  22. d8 ​ ​ ​ ​ Very Good: ​ ​ Before I saw Blue play this, the position looked good for Red. ​ With this move, I am almost-certain that Blue wins
  12 KB (2,029 words) - 23:16, 28 August 2022
• Reverse Hex
  For example, consider the following position, with Blue to move: Consider the pairs (c,b) and (d,f). Blue, the first player to move in this position, can occupy c, force Red to occupy b, and force Red to occupy at least one
  11 KB (1,957 words) - 15:22, 10 July 2022
• Theorems about templates
  ...any position containing A is winning for Red, then so is the corresponding position containing B.
  29 KB (4,992 words) - 05:51, 21 April 2024
• Bolstered template
  ...spond at x, [[dead cell|killing]] Blue's stone. This never improves Blue's position, and often makes it worse. Consider the following position, with Blue to move:
  5 KB (974 words) - 11:41, 6 May 2022
• Near ladder escape
  ...[[Joseki#4th_row_josekis|4th row joseki]] "C", which leaves the following position in an acute corner: This position obviously escapes 2nd row ladders. It is perhaps less obvious that it also
  7 KB (1,441 words) - 10:27, 25 November 2023
• Openings on 11 x 11
  ...and b8 cutting up Blue's edge. For example, if Blue plays as follows, the position is completely winning for Red: ...an b10, ''Red'' can play b10 which combines efficiently with a9, and Red's position actually seems quite strong. For example:
  11 KB (2,022 words) - 14:15, 22 October 2022
• Efficiency
  ...ding does not work in every situation. For example, consider the following position with Red to move. Red cannot fast forward the ladder. ...layer's moves). For example, from Red's point of view, the efficiency of a position is the worst-case number of turns that Red must play before Red wins. Small
  7 KB (1,138 words) - 03:24, 1 December 2022
• Question
  ...ng in the center of a [[wheel#U-turn|U-turn]]. The U-turn is the following position, consisting of two [[Multiple_threat#Overlapping_threats|overlapping]] brid The following is a position where asking this question is the only winning move for Blue:
  6 KB (1,073 words) - 16:05, 27 November 2022
• Openings on 19 x 19
  ...not play 4-4, because then Red could play 5-4, and he would be in the same position that he would've been, had he played the first move correctly (via the Red ...en more so. Anecdotally, when KataHex thinks '''H''' is the best move in a position, it rarely assigns a high policy to the move, only liking the move after so
  31 KB (5,546 words) - 14:54, 18 November 2023
• Reading
  ...her strategy games, '''reading''' is the mental process of analyzing a Hex position by considering the possible moves and variations than can occur. By explori
  1 KB (218 words) - 20:04, 6 May 2023
• Strategic advice from KataHex
  Most of the time, you should play at Red 1 in the position below when given the opportunity, because you capture the hexes marked (*). ...hite resigned in a winning position according to the bot, though the final position is highly tactical). KataHex actually thinks Black has only an 18% win rate
  21 KB (3,605 words) - 16:08, 14 January 2024
• Losing play
  ...mplify.'' Don't play any moves that would unnecessarily simplify the board position and clarify the situation for your opponent. For example, if your opponent ...shing move is a bad idea, because when the opponent foils, it worsens your position. But in losing play you literally have nothing else to lose, so you may as
  5 KB (818 words) - 02:58, 2 October 2023
• Combinatorial game theory
  Consider a region of the Hex board. By a ''position'' in the region, we mean the state of the region after zero or more moves h Players change positions by making moves. In a given position, we say that ''Red's options'' are all positions that Red can reach by maki
  23 KB (4,007 words) - 00:18, 12 May 2024
• KataHex
  ...ents Monte Carlo tree search with a convolutional neural network providing position evaluation and policy guidance. ...starting position. It seems to be particularly thrown off if the starting position does not have the same number of black and white stones.
  3 KB (422 words) - 23:49, 16 January 2024
• Inferiority
  ...s response, Red's stone could be removed without changing the value of the position. ...er than X, then by [[monotonicity]], the same move is also winning for the position (Empty,Empty), proving the claim. If that winning move is X, then (Red,Blue
  4 KB (767 words) - 02:05, 26 April 2024
• Monotonicity
  ...r of cells from Blue to Empty and/or from Empty to Red, then the resulting position is still winning for Red. Of course, the analogous property holds from Blue ...ing path in Red's pretended position, Red has a winning path in the actual position as well.
  2 KB (302 words) - 02:21, 26 April 2024