Difference between revisions of "Basic (strategy guide)"
Hex player1 (Talk | contribs) m (+category) |
m ((14*14)/6 is 33 moves per side) |
||
| (6 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| − | ''Adapted with permission from Glenn C. Rhoads strategy guide.'' | + | ''Adapted with permission from [http://www.gcrhoads.byethost4.com/GamesPuzzles/Basic.html Glenn C. Rhoads's basic strategy guide].'' |
== Rules of Hex == | == Rules of Hex == | ||
| Line 18: | Line 18: | ||
<hex>R4 C4 Q1</hex> | <hex>R4 C4 Q1</hex> | ||
| − | === The | + | === The bridge === |
''(See also the article [[Bridge]])'' | ''(See also the article [[Bridge]])'' | ||
| − | The formation consisting of two pieces that are non-adjacent but have two empty neighboring hexes in common is referred to as a [[ | + | The formation consisting of two pieces that are non-adjacent but have two empty neighboring hexes in common is referred to as a [[bridge]]; e.g. the pieces on b2 and c3, and the empty hexes b3 and c2 in the following diagram form a bridge. |
<hex>R4 C4 Q1 Vb2 Vc3</hex> | <hex>R4 C4 Q1 Vb2 Vc3</hex> | ||
| − | The two pieces are almost as strongly connected as a solid chain from b2 to c3. The opponent can attempt to break this connection only by playing a piece at either b3 or c2, and no matter which one the opponent plays, you can play the other and restore the link. For most purposes you can think of the | + | The two pieces are almost as strongly connected as a solid chain from b2 to c3. The opponent can attempt to break this connection only by playing a piece at either b3 or c2, and no matter which one the opponent plays, you can play the other and restore the link. For most purposes you can think of the bridge pieces as already being connected. By connecting pieces via bridges, you can spread across the board twice as fast as by playing adjacent hexes. |
{| border="0" cellpadding="2" | {| border="0" cellpadding="2" | ||
| <hex>R7 C7 Q1 Ve1 Ve2 Vd3</hex> || <hex>R7 C7 Q1 Ve2 Vd4 Vc6</hex> | | <hex>R7 C7 Q1 Ve1 Ve2 Vd3</hex> || <hex>R7 C7 Q1 Ve2 Vd4 Vc6</hex> | ||
|- | |- | ||
| − | | <center>''Expanding by adjacent moves''</center> || <center>''Expanding by | + | | <center>''Expanding by adjacent moves''</center> || <center>''Expanding by bridges''</center> |
|} | |} | ||
| − | Considered in isolation the pieces in a | + | Considered in isolation the pieces in a bridge are [[strong connection|connected]] but sometimes a bridge can be broken by playing a piece in the middle of a bridge that contains some other [[threat]] that must be immediately answered. After the opponent answers the threat, you can then play in the other hex in the bridge breaking the connection. |
| − | Also, playing in the middle of a | + | Also, playing in the middle of a bridge can be a good play even when the opponent should and does respond by saving the link. The reason being that the piece played may be useful later. |
=== Blocking moves === | === Blocking moves === | ||
| − | When you have no pieces in the area, it is usually best to start blocking | + | When you have no pieces in the area, it is usually best to start blocking not too close to the opponent's piece. |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
If you block too close to the opponent, then he can simply flow around the attempted block. For example, suppose you are trying to stop the vertical player from connecting to the bottom in the following diagram. | If you block too close to the opponent, then he can simply flow around the attempted block. For example, suppose you are trying to stop the vertical player from connecting to the bottom in the following diagram. | ||
| − | <hex>R11 C11 | + | <hex>R11 C11 labels red h1 h2 h3 g4 g5 g6</hex> |
If you try to block by playing adjacent to the [[leading piece]], say by playing at g7, then the vertical player can simply step around it at f7 (see diagram below). Then the attempted block at say e8, could similarly be met by playing at f8. Obviously, you are not making any progress here. | If you try to block by playing adjacent to the [[leading piece]], say by playing at g7, then the vertical player can simply step around it at f7 (see diagram below). Then the attempted block at say e8, could similarly be met by playing at f8. Obviously, you are not making any progress here. | ||
| − | <hex>R11 C11 | + | <hex>R11 C11 labels red h1 h2 h3 g4 g5 g6 blue play numbered g7 f7 e8 f8</hex> |
| − | Another try from the original position would be to block at a | + | Another try from the original position would be to block at a bridge distance away at f8 (see diagram below). This is better than the [[adjacent block]] but sometimes the opponent can flow around this too by bridging at an angle — e.g. by playing h7 in response to f8. (h7 should be met by either h8 or g9.) |
| − | <hex>R11 C11 | + | <hex>R11 C11 labels red h1 h2 h3 g4 g5 g6 blue play numbered f8 h7</hex> |
| − | Another possibility is to combine the above two ideas by first doing an adjacent block at g7 and then if the vertical player responds with f7, you block at a | + | Another possibility is to combine the above two ideas by first doing an adjacent block at g7 and then if the vertical player responds with f7, you block at a bridge distance away at e9. Then your opponent cannot bridge towards the right because of the initial g7 piece. |
| − | <hex>R11 C11 | + | <hex>R11 C11 labels red h1 h2 h3 g4 g5 g6 blue play numbered g7 f7 e9</hex> |
| − | A good block in the original position is to block at one hex farther back than the | + | A good block in the original position is to block at one hex farther back than the bridge block at either e9 or f9 (sometimes this is referred to as the [[classic block]]). For example suppose H blocks at f9 (see diagram below). Bridging to f8 is met by e9. Bridging to the lower right (h7) is met by h8 and bridging towards the lower-left (e7) is met by d8. By blocking at a distance, you have a move or two before the advancing head reaches the blocking pieces. Note that when the board size is smaller than 11 × 11, then the classic block is much less useful due to the lack of space. |
| − | <hex>R11 C11 | + | <hex>R11 C11 labels red h1 h2 h3 g4 g5 g6 blue play numbered f9 f8 e9 h7 h8 e7 d8</hex> |
Suppose Red opens with G4 and Blue plays E6 yielding the following. | Suppose Red opens with G4 and Blue plays E6 yielding the following. | ||
| − | <hex>R10 C10 | + | <hex>R10 C10 labels play numbered g4 e6</hex> |
| − | Blue's play is what I call an | + | Blue's play is what I call an '''indirect block'''; it does not directly block the Red G4 from the bottom rather it threatens to block it on the next move. Red |
cannot afford to ignore this threat. If for example Red plays G3, Blue responds | cannot afford to ignore this threat. If for example Red plays G3, Blue responds | ||
with G5 completely cutting off Red's pieces from the bottom. | with G5 completely cutting off Red's pieces from the bottom. | ||
| − | <hex>R10 C10 | + | <hex>R10 C10 labels play g4 e6 numbered g3 g5</hex> |
Instead Red can play towards the bottom with F6 and blue can complete his block | Instead Red can play towards the bottom with F6 and blue can complete his block | ||
by playing E8 for example. | by playing E8 for example. | ||
| − | <hex>R10 C10 | + | <hex>R10 C10 labels play g4 e6 numbered f6 e8</hex> |
| − | + | '''Blocking Summation'''<br> | |
The most important thing for a beginner to do is to avoid the mistake of repeatedly trying to block by playing adjacent to the head of the chain as shown in the first example. Playing ahead of the chain as in the classic block gives you a move or two to place your pieces before the advancing chain meets your pieces. | The most important thing for a beginner to do is to avoid the mistake of repeatedly trying to block by playing adjacent to the head of the chain as shown in the first example. Playing ahead of the chain as in the classic block gives you a move or two to place your pieces before the advancing chain meets your pieces. | ||
| Line 103: | Line 93: | ||
In Hex, good [[offense]] and good [[defense]] are entirely equivalent. If you complete a connection between your sides, then your opponent is prevented from completing theirs. Conversely, if your opponent is prevented from completing a connection, then you must have completed yours (draws cannot occur in Hex). Furthermore, the only way to complete a connection is to prevent your opponent from making a connection and the only way to prevent your opponent from connecting is to complete your connection. In a very real sense, you don't have to worry about whether you should play offensively or defensively since they are the same. The critical point to remember is that unless you are making a sequence of [[forcing move|forcing plays]], it is generally easier to think in terms of good defense than good offense regardless of whether you are currently winning or losing. This point about thinking defensively should frequently be used with point 3.1 above. Often it is best to look for the connection that your opponent is going to have the toughest time making (point 3.1 above). For example, suppose that my opponent's most difficult connection to complete looks like the connection to the right edge of the board. Then I'll look for good defensive moves that make it even more difficult for my opponent to connect up to the right edge. | In Hex, good [[offense]] and good [[defense]] are entirely equivalent. If you complete a connection between your sides, then your opponent is prevented from completing theirs. Conversely, if your opponent is prevented from completing a connection, then you must have completed yours (draws cannot occur in Hex). Furthermore, the only way to complete a connection is to prevent your opponent from making a connection and the only way to prevent your opponent from connecting is to complete your connection. In a very real sense, you don't have to worry about whether you should play offensively or defensively since they are the same. The critical point to remember is that unless you are making a sequence of [[forcing move|forcing plays]], it is generally easier to think in terms of good defense than good offense regardless of whether you are currently winning or losing. This point about thinking defensively should frequently be used with point 3.1 above. Often it is best to look for the connection that your opponent is going to have the toughest time making (point 3.1 above). For example, suppose that my opponent's most difficult connection to complete looks like the connection to the right edge of the board. Then I'll look for good defensive moves that make it even more difficult for my opponent to connect up to the right edge. | ||
| − | === | + | === Initiative === |
| − | ''(See also the page [[ | + | ''(See also the page [[Initiative]])'' |
| − | The player who is dictating the play is said to have the ''' | + | The player who is dictating the play is said to have the '''initiative'''. Alternatively, a player who is being forced to respond to the opponent lacks the initiative. The player with the initiative usually has the advantage and this advantage is often decisive. You should generally not hand over the initiative to the opponent unless you have a very good reason for doing so. In well played close matches, the initiative often swings between the two players with each move. |
=== Multiple threats per move === | === Multiple threats per move === | ||
| Line 149: | Line 139: | ||
* 10 × 10: 16 moves per side | * 10 × 10: 16 moves per side | ||
* 11 × 11: 20 moves per side | * 11 × 11: 20 moves per side | ||
| − | * 14 × 14: | + | * 14 × 14: 33 moves per side |
* 17 × 17: 48 moves per side | * 17 × 17: 48 moves per side | ||
* 19 × 19: 60 moves per side (this is the standard size in Go) | * 19 × 19: 60 moves per side (this is the standard size in Go) | ||
Latest revision as of 23:24, 12 October 2022
Adapted with permission from Glenn C. Rhoads's basic strategy guide.
Contents
Rules of Hex
(See also the article Rules)
Hex is a two player board game played on an n × n grid of hexagons.
A turn in Hex consists of placing a piece of your color on a hexagon. The first player's goal is to form an unbroken chain of hexes of his color that connects the top to the bottom while the second player tries to form an unbroken chain connecting the left and right sides.
Swap rule: After the initial play only, the second player has the option of either responding with his turn or swapping sides taking the initial play as his first turn.
Without the swap rule, the first player has a strong advantage. The swap rule equalizes this advantage by forcing the first player to make a move that leads to a roughly equal game. If the first player makes a very strong opening move, the second player will swap sides and start with an advantage. If the first player makes a very weak opening move, the second player won't swap and again will start with an advantage.
Basic strategy
Notation: the rows of the board are indexed by numbers and the columns are indexed by letters. Individual hexes are referred to by listing the column index followed by the row index; e.g. hex c2 is the one in column c row 2. Here at HexWiki, red pieces belong to the "vertical" player, and blue pieces belong to the "horizontal" player. An empty 4 × 4 board looks like follows.
The bridge
(See also the article Bridge)
The formation consisting of two pieces that are non-adjacent but have two empty neighboring hexes in common is referred to as a bridge; e.g. the pieces on b2 and c3, and the empty hexes b3 and c2 in the following diagram form a bridge.
The two pieces are almost as strongly connected as a solid chain from b2 to c3. The opponent can attempt to break this connection only by playing a piece at either b3 or c2, and no matter which one the opponent plays, you can play the other and restore the link. For most purposes you can think of the bridge pieces as already being connected. By connecting pieces via bridges, you can spread across the board twice as fast as by playing adjacent hexes.
| |
|
Considered in isolation the pieces in a bridge are connected but sometimes a bridge can be broken by playing a piece in the middle of a bridge that contains some other threat that must be immediately answered. After the opponent answers the threat, you can then play in the other hex in the bridge breaking the connection.
Also, playing in the middle of a bridge can be a good play even when the opponent should and does respond by saving the link. The reason being that the piece played may be useful later.
Blocking moves
When you have no pieces in the area, it is usually best to start blocking not too close to the opponent's piece.
If you block too close to the opponent, then he can simply flow around the attempted block. For example, suppose you are trying to stop the vertical player from connecting to the bottom in the following diagram.
If you try to block by playing adjacent to the leading piece, say by playing at g7, then the vertical player can simply step around it at f7 (see diagram below). Then the attempted block at say e8, could similarly be met by playing at f8. Obviously, you are not making any progress here.
Another try from the original position would be to block at a bridge distance away at f8 (see diagram below). This is better than the adjacent block but sometimes the opponent can flow around this too by bridging at an angle — e.g. by playing h7 in response to f8. (h7 should be met by either h8 or g9.)
Another possibility is to combine the above two ideas by first doing an adjacent block at g7 and then if the vertical player responds with f7, you block at a bridge distance away at e9. Then your opponent cannot bridge towards the right because of the initial g7 piece.
A good block in the original position is to block at one hex farther back than the bridge block at either e9 or f9 (sometimes this is referred to as the classic block). For example suppose H blocks at f9 (see diagram below). Bridging to f8 is met by e9. Bridging to the lower right (h7) is met by h8 and bridging towards the lower-left (e7) is met by d8. By blocking at a distance, you have a move or two before the advancing head reaches the blocking pieces. Note that when the board size is smaller than 11 × 11, then the classic block is much less useful due to the lack of space.
Suppose Red opens with G4 and Blue plays E6 yielding the following.
Blue's play is what I call an indirect block; it does not directly block the Red G4 from the bottom rather it threatens to block it on the next move. Red cannot afford to ignore this threat. If for example Red plays G3, Blue responds with G5 completely cutting off Red's pieces from the bottom.
Instead Red can play towards the bottom with F6 and blue can complete his block by playing E8 for example.
Blocking Summation
The most important thing for a beginner to do is to avoid the mistake of repeatedly trying to block by playing adjacent to the head of the chain as shown in the first example. Playing ahead of the chain as in the classic block gives you a move or two to place your pieces before the advancing chain meets your pieces.
General principles
A position is only as good as the weakest link
(See also the page Weakest link)
Thus, with each move you should attempt to either improve your weakest link or make your opponent's weakest link even weaker. A move which does both is a strong move. For example, in the position below the hex f6 is the weakest point in the Red's best connection across the board. It is also the weakest link in the Blue's best connection across the board. Thus, the player whose turn it is to move would be wise to play at f6. In fact, whoever plays next has a forced win after playing f6.
Offense equals defense
(See also the page Offense equals defense)
In Hex, good offense and good defense are entirely equivalent. If you complete a connection between your sides, then your opponent is prevented from completing theirs. Conversely, if your opponent is prevented from completing a connection, then you must have completed yours (draws cannot occur in Hex). Furthermore, the only way to complete a connection is to prevent your opponent from making a connection and the only way to prevent your opponent from connecting is to complete your connection. In a very real sense, you don't have to worry about whether you should play offensively or defensively since they are the same. The critical point to remember is that unless you are making a sequence of forcing plays, it is generally easier to think in terms of good defense than good offense regardless of whether you are currently winning or losing. This point about thinking defensively should frequently be used with point 3.1 above. Often it is best to look for the connection that your opponent is going to have the toughest time making (point 3.1 above). For example, suppose that my opponent's most difficult connection to complete looks like the connection to the right edge of the board. Then I'll look for good defensive moves that make it even more difficult for my opponent to connect up to the right edge.
Initiative
(See also the page Initiative)
The player who is dictating the play is said to have the initiative. Alternatively, a player who is being forced to respond to the opponent lacks the initiative. The player with the initiative usually has the advantage and this advantage is often decisive. You should generally not hand over the initiative to the opponent unless you have a very good reason for doing so. In well played close matches, the initiative often swings between the two players with each move.
Multiple threats per move
(See also the page Multiple threats)
Whenever possible, a player should make each move achieve at least two different goals or threats. Moves that contain only a single threat are generally not hard to meet. If a move contains multiple threats, the opponent may not be able to stop all the threats with a single move.
The center
The central region of the board is strategically the most important area. From the center, connections can spread out in many directions giving you more flexibility and options than starting from an edge. Furthermore, centrally played pieces are more nearly equidistant from both of your edges — this is related to point 3.1 about improving your weakest link. The greater distance apart two pieces are, the harder they are to connect up, i.e. their potential link is weaker.
The opening
Without the swap rule, the initial move would be easy. Playing in the center hex is the strongest opening move. The weakest opening move is to play in one of the acute corners (a1 and the opposite corner) and is one of only two opening moves that are a proven loss (without the swap option). The other is right next to it at b1. Suppose the vertical player moves first. Which opening moves should you swap and which should you not swap? The following is my personal rules for the 10 × 10 board.
10 × 10 swap rules
- Don't swap any of Vertical's border row moves except for the obtuse corner.
- Don't swap a2, or b2 (nor the symmetrically equivalents i9 and j9).
- Swap all other initial moves.
Note: the possible theoretical exceptions to these rules are the opening moves a2, b2, c2 and a3 (and their symmetric equivalents). The winning/losing margin with these moves is so razor thin that nobody has been able to determine with any confidence whether these moves should theoretically be swapped or not.
Good opening moves on the 10 × 10
The best opening moves against an experienced player are the border hexes (except don't open a1!) and b2 and c2. b2—d2 are probably the only good non-border moves against an experienced player (b2 is essentially equivalent to the move a2 which is a popular opening choice and there is almost no difference between b2 and c2). Against lesser experienced players you can play something stronger such as one out from the obtuse corner (b9/i2) because they might not realize its strength and even if they do swap, they may not be capable of taking advantage of it anyway.
a2/b2 and a3 both lead to a balanced game and seem to be the most popular choices. Except for games between expert players, you can safely play either side of a2/b2 or a3 and have an equal chance of winning (and similarly for other opening plays). Also some variation in opening play is generally good. Varying your opening is the first thing to try against an opponent that seems to have your number. Sometimes you can find a weakness in a player's personal swap rules by trying out different openings.
The second and third moves
A very common but not the only good response to a border opening is to play in one of the two central hexes e6 or f5. The third move in response to a central reply should be a blocking move on the side of e6/f5 that is farthest from the edge. e6 is one hex closer to the left edge and f5 is one hex closer to the right edge. In accordance with the principle of exploiting your opponent's weakest link, you should therefore block f5 on the left and e6 on the right. Thus, a typical opening sequence would be a2, swap, f5, c6. In my opinion, the strength of the central response is overrated; practically any move that is not in one of the 3 rows closest to your border rows and that is also not too close to the opponent's border, is a near equally good response. If there is any difference in strength, it is for all practical purposes non-existent.
Update: The top players now show a definite preference for non-central responses. On the 13 by 13 game at littlegolem, most of the top players prefer to respond to a border opening with something on the 5'th row from one of their edges over the central response G7. I.e. the consensus is that responding to a border opening by playing in the center is NOT the best reply!
Board size
Hex can be played on any size board. If the board is too small, the game becomes trivial and uninteresting. The "standard" size at the online site PlaySite is 10 × 10 but in my opinion, this is just a little too small and the "standard" size should really be 11 × 11 (11 × 11 is the standard size at the PBM play by email site). Some experienced players prefer a larger board such as 14 × 14 or 17 × 17. As the board size gets larger and larger, the game becomes more subtle and strategic. Hex is actually of comparable complexity and depth to the oriental board game Go played on the same size board (many Go players consider Go to be the deepest and most complex perfect information strategy game ever invented).
A typical hex game fills about one-third of the board. We can use this to get a good estimate of the average number of moves for any board size.
- 10 × 10: 16 moves per side
- 11 × 11: 20 moves per side
- 14 × 14: 33 moves per side
- 17 × 17: 48 moves per side
- 19 × 19: 60 moves per side (this is the standard size in Go)
One of the pleasant aspects of Hex is that games generally do not last as long as in other strategy games of comparable complexity (e.g. Go typically lasts around 140 moves per side). The 11 × 11 game is very good and takes only about 20 moves per side. For those wanting a more complex game, the 14 × 14 game provides it without having the length of the game blow up to marathon proportions.
Reference bibliography
Hex Strategy: Making the Right Connections, by Cameron Browne, A.K. Peters Ltd., 2001. — The strategy part of this book is generally very sound. The primary exception is that the suggested opening swap rules are not correct at all.
