Difference between revisions of "Basic (strategy guide)"

Revision as of 06:23, 8 February 2005

Adapted with permission from Glenn C. Rhoads strategy guide.

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 Two-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 two-bridge; e.g. the pieces on b2 and c3, and the empty hexes b3 and c2 in the following diagram form a two-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 two-bridge pieces as already being connected. By connecting pieces via two-bridges, you can spread across the board twice as fast as by playing adjacent hexes.

Considered in isolation the pieces in a two-chain are connected but sometimes a two-chain can be broken by playing a piece in the middle of a two-chain 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 two-chain breaking the connection.

Also, playing in the middle of a two-chain 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 at a distance. If you block too close, then the opponent 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 two-chain distance away at f8 (see diagram below). This is better than the adjacent block but sometimes the opponent can flow around this too by two-chaining at a 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 two-chain distance away at e9. Then your opponent cannot two-chain 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 two-chain 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). Two-chaining to f8 is met by e9. Two-chaining to the lower right (h7) is met by h8 and two-chaining 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.

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 I will look for the connection that my opponent is going to have the toughest time making (point 3.1 above), e.g 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. This is very sound strategy.

Momentum

(See also the page Momentum)

The player who is dictating the play is said to have the momentum. Alternatively, the momentum is against the player who is being forced to respond to the opponent. The player with the momentum usually has the advantage and this advantage is often decisive. You should generally not hand over the momentum to the opponent unless you have a very good reason for doing so. In well played close matches, the momentum 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

1. Don't swap any of Vertical's border row moves except for the obtuse corner.
2. Don't swap a2, or b2 (nor the symmetrically equivalents i9 and j9).
3. 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.

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: 28 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 100 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.