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SOMA News |
14 Oct 1999
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In 1942, Piet Hein invented the game Con-Tac-Tix. That game is now
called Hex.
Piet invented the game while he was contemplating
the famous four-color theorem of topology. The theorem, which
was then unproved, is that four colors are sufficient to make
any map so that no two countries of the same color have a
common boundary.
The game became popular in Denmark under the name Polygon.
The game was printed on pads of paper; and sold as a paper &
pencil game.
Albert Einstein kept the game on a shelf in his study.
The game pictured above was marketed by Piet Hein in 1968.
This beautiful game consisted of an exotic hardwood board.
The board was inlaid with black & white discs which indicated
the respective player's borders. Playing pieces were polished
black & white wooded dowels kept in leather pouches.
The bottom of the board had the 'Piet Hein' magic egg symbol
and Piet's signature.
This game was marketed under the name Con-Tac-Tix.
The rules of the game are simple.
For a Deeper rule insight, See this description.
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Example of game play. |
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Black wins game by connecting pieces. |
The swapping rule
Black always starts the game. After black makes the first move, white
has the option of either playing a white piece OR taking the black
piece already played. In that case, the black piece is turned white and
"swapped into white's coordinates", meaning that the piece is in its
mirror image position on the board. Then black plays a black piece and
the game proceeds normally.
The pegs do not have to form a straight line, as long as the connection is closed. In the game shown here, black has won.
Hex can never be a draw. Therefore, the best defence equals the best attack. As soon as you have grasped this aspect of the game, you will see the beauty of the game and you will be a better player.
Thinking Hex is much like thinking Go. In Hex, the best strategy is to defend (or attack) area's. Most of the times, it's best to occupy a field that is far apart from the stones of the enemy.
The best strategy to use is (a) determining your best chain and (b) strengthening the weakest link in that chain. OR to weaken the weakest link in your enemy's strongest chain.
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Hex can also be played on a piece of paper.
(Place your pieces at the intersections.) |
Some parts of this description was copied:
With permission: from 'Bob Finn', History of HEX, and photo.
rfinn@wge.com.
http://members.iex.net/~rfinn/gameshlf/abstract/hex/hex.htm
Bob's home:
http://members.iex.net/~rfinn/
With permission: Dave Boll's Hex FAQ 1994
dboll@frii.com.
http://www.frii.com/~dboll/hexfaq.txt
Dave's home:
http://www.frii.com/~dboll/
With permission from Tijs Krammer: Description and Links.
tijs@krammer.nl.
Tijs' home:
http://www.krammer.nl/hex
Tijs Krammer has also invented a game called Trinidad, If you like 'Hex' then 'Trinidad' is the best board game you could select.
http://members.iex.net/~rfinn/gameshlf/abstract/hex/hex.htm
Site on the history of the game and productions
of it including pictures of the game as sold in
the sixties and seventies.
http://www.gamerz.net/~pbmserv/hex.faq.html
FAQ Site with rules, strategy, openings and an
example game.
http://www.cs.cmu.edu/People/hde/hex/hexfaq
OR
http://www.cs.cmu.edu/~hde/hex/hexfaq
Bert Enderton's Hex FAQ
http://www.playsite.com/games/board/hex/index.html
Site of the Playsite on hex, with history,
rules and links.
http://www.uio.no/~jkleiser/hex/hexboard.html
Site with a way to make hex boards on the net.
http://www.stratogems.com/Hex.html
Small site on Hex using the american depiction
of the board.
http://www.math.niu.edu/~rusin/uses-math/games/hex/
Another site on Hex.
http://www.frii.com/~dboll/hexfaq.txt
David Boll's Hex FAQ
http://huizen.dds.nl/~krammer/hex.htm
The abstract board game Hex
This text is copyrighted 1994 by David Boll.
dboll@frii.com.
http://www.frii.com/~dboll/hexfaq.txt
Copied here with permission.
CONTENTS:
1) Origin/Background of Hex, Literature on Hex
2) Rules of Hex
3) Elementary concepts: the 2-bridge
4) Edge techniques
5) Advanced strategy: Forced moves, ladders, etc.
6) The opening
7) Sample Game
1) Origin/Background of Hex
Hex was invented/discovered by Piet Hein. It is a connectivity game,
in the same family of games as Twixt, Bridge-It, and connection.
It is a perfect example of one of those 'a
minute to learn, a lifetime to master' games.
2) Rules of Hex
Hex is a two player strategy game played on a NxN rhombus of hexagons, as
illustrated below for N=4:
Top
. . . .
. . . . Right
Left . . . .
. . . .
Bottom
Players alternately mark hexes. The goal of the first player is to form
a unbroken chain of his hexes that connects the top to the bottom,
while the second player attempts to form an unbroken chain of her hexes
connecting the left side and the right. To make subsequent diagrams
clearer, the 2 players will be referred to as H)orizontal and V)ertical,
with Vertical having the first move. For notational purposes, the board
is indexed by letter and number, like so:
A B C D
1 . . . .
2 . . . .
3 . . . .
4 . . . .
If uneven players are playing, the game can be made more fair by
letting the weaker player start with 1 or two peg's, before the actual game.
3) Elementary concepts: the 2-bridge
Connectivity is the key to hex, consider the following game with V to
move next:
A B C D
1 V . . .
2 . . . H
3 . H . .
4 . . . V
No matter where V moves, H has the game won! There are only four hexes
that matter in this game: A4, A3, C3, and C2 and H has a response to all
four of these moves. If V moves A4, H moves A3 (and vice versa), and if V
moves C3, H moves C2 (and vice versa). So, hex players consider
hexes such as B3 and D2 to be connected, even though they do not touch,
because a connection can be trivially forced. By playing moves of this
type, you can extend two rows at a time rather than one. This document
will refer to hexes 'connected' in this manner as a 2-bridge.
A B C D E F G H I
1 . . . . . . . . .
2 . . . . . . . V .
3 . . V . . . . V .
4 . . . V . . . . .
5 . . . . . . V . .
6 . . V H H H V . .
7 . . . . . . H . .
8 . H . V . H . . .
9 . H . . . . . . .
Although the game might appear close at first glance, V has a clear win.
V is connected from the north edge to hexes C6 and G6 (if you don't see
this, refer to the section on edge tactics). And, each of these hexes
are one move away from being connected to hex D8. Hex D8 is connected to
the south edge (clearly), and one move away from being connected to the
north edge in two different ways. H can't stop both of these connections
with only a single move. So, if H and V were good players, H would
resign. Of course, if H and V were good players, the game wouldn't
look like this, but that's beside the point!
4) Edge techniques
It's handy to know when a hex is connectable to an edge regardless of
what the other player does. This section discusses connection to an
edge from 2, 3, and 4 rows out, using a connection template. A
connection template is a pattern of OPEN hexes that will allow
connection even if the opponent moves first, regardless of what the
opponent does.
2 rows away: This hardly needs explaining, but suppose V was one row from
the bottom edge, the template looks like this:
. V
- - <- edge
If the 2 hexes below V are clear, V is connected. If H moves to one of the
dashed hexes, V moves to the other. If H moves elsewhere, V should
also, since this connection is guaranteed.
A B C D
1 . . . .
2 . . V -
3 . - - -
4 - - - -
If the dashed hexes (or their mirror image) are clear, V has a connect-
ion. The basic idea is that either B3 or D3 will connect, and H can't
stop both. V need not defend this connection unless H moves into one
of the dashed hexes.
A B C D E F G
1 . . . . . . .
2 . . . . . . .
3 . . . . . . .
4 . . . - V - .
5 . . - - - - -
6 . - - - - - -
7 - - - - - - -
If H moves into this region, but doesn't move to one of {D5,E5,D6,C7,D7},
V simply moves to D6 for an easy connect.
5) Advanced strategy: Forced moves, ladders, etc.
We discussed earlier how a 2-bridge is a fundamental connection concept
in Hex. As we saw, if a player moves in one of the two link hexes, the
other player moves to the other link hex to maintain the connection.
Interetingly enough, however, there are cases where moving into your
opponent's 2-bridge can be a good move - because the hex is valuable
to you later. Here's a rather contrived example: (V to move and win)
A B C D E F G H I
1 . . . . . . . . .
2 . . . . . . . . .
3 . . . . . . . . .
4 . . . . V . . . .
5 . . . V . V . . .
6 . . . . . . . . .
7 . . . H . H . . .
8 . H . . . . . . .
9 . . . . . . . . .
From our study of edge connection techniques, we know that the hexes
D7 and B8 are effectively connected to the left, and F7 is connected
to the right. So, as V, we better jump in between these two links and
play E7, right? Wrong! E7 is easily defensed by D9. The correct move
by V (one of 'em, anyway, there's at least 2 others) is C8. A move
to C8 pretty much forces a response of C7 by H, and now V plays E7.
A B C D E F G H I
1 . . . . . . . . .
2 . . . . . . . . .
3 . . . V . . . . .
4 . . . . . . . . .
5 . . . . . . . . .
6 . . V . . . V . V
7 . . . H . . H . .
8 . H . . H . . . V
9 . . . . . . . . .
Note that H is connected from the left almost all the way across, but
was one hex shy of having a valid 3-template on the right side with
hex G7, prior to V moving to I6. H could force a ladder here with a
sequence like (H6-I5-H5-I4-H4-I3-H3-I2-H2-I1) - but there would be no
point in it. Worse, after a continuation of (I7-H7), H loses the game.
But, suppose the situation was ever so slightly different: suppose H
has an additional piece at H2, so the board looks like this:
A B C D E F G H I
1 . . . . . . . . .
2 . . . . . . . H .
3 . . . V . . . . .
4 . . . . . . . . .
5 . . . . . . . . .
6 . . V . . . V . V
7 . . . H . . H . .
8 . H . . H . . . V
9 . . . . . . . . .
Now H can play the same ladder sequence as before - but this time,
H 'ladders down' to the piece at H2 to win the game.
6) The opening
If you're the first player, the opening move is easy: open in the center
hex. The second person has a few semi reasonable choices, marked with
small letters in the diagram below:
A B C D E F G H I J K
1 . . . . . . . . . . .
2 . . . . . . h . . . .
3 . . . . . . f g . . .
4 . . . . . d c e . . .
5 . . . . . a b . . . .
6 . . . . . V . . . . .
7 . . . . . . . . . . .
8 . . . . . . . . . . .
9 . . . . . . . . . . .
10 . . . . . . . . . . .
11 . . . . . . . . . . .
So, if both players move typically, the opening will be 1. F6 G3, or some rotated version of this. After this, it's hard to say. D5 is tempting, it threatens to connect to F6, and is in the 'classic' defensive position with respect to G3. D4 looks OK also - it establishes a edge link at the cost of weaker defense on G3. H3 and I3 have possibilities as well, they both establish a link and play defense on the weaker side of G3. I tend to lean toward D4 and I3; one of my playing partners (who is a stronger player than me) seems to prefer D5.
Opening variations: The advantage of the first move is quite strong, and sometimes you want to neutralize this advantage. The following are some ways in which this can happen:
7) Sample Game (11x11 board)
The following is an annotated transcript of a hex game. Follow along
with this on a board, and you could learn all kinds of stuff. The
players are H and V, V moves first. H is a bit weak in the opening,
but the mid game is wide open after a questionable move by V. V ends
up preserving the win by carefully maintaining the winning line
throughout some tricky positions.
Moves Comments
1. F6 The center hex, the strongest opening move for V.
F5 H chooses a weaker line of defense, G3 is usual.
2. H4 V presses the attack on the north edge.
I1 H plays the "classic" defensive move. Note that G5 may look
tempting here, but H is in trouble after H5.
3. E4 V shifts focus to the right side, threatening, but not estab-
lishing, a link to the north.
E3 H's piece at I1 allows this defense, but F1 might have been
better.
4. G2 H can stop V's connection to E4 or H4, but not both!
G3
5. I3 V is now connected from the north. J2 or H2 both get the link,
and H can't stop both.
E9 H shifts sides and tries to play defense on the south.
6. H7 Nice, aggressive, offensive and defensive move.
G10 H's game is all defense at this point.
7. I9 V connects to the south, choosing to fight for the link in the
middle rather than along the edge.
J2 H's first sign of life on offense. H threatens H2 or I2, which
links H from the right out to F5...
8. H2 But, V shuts the door on that!
H6 This piece is linked to the right, even though it's not the
usual 4th row template, thanks to the H piece at H2,
9. J5 V tries to block,
I4 And H saves the link.
10. G7? Not a terrible move, but D9 was probably better. V links up in the
center with this move.
G6! If V responds with a knee-jerk F7 to save the link, H looks
pretty good after G5.
11. D6! A nice reply to H's strong move. V de-fuses F5, and extends from
E4, which could end up being connected to the north.
G5 H makes the link anyway. Perhaps H would have been better off
moving on the south side here.
12. F3 V keeps the sure thing to the north.
F7 H is now connected from the right out to F7/E9.
13. C9 Once again, V gets a link and plans to fight for connection in
the middle.
D5! A very sneaky threat. If V plays a knee-jerk E5, H plays D9,
and forces V to choose which side of C9 to play defense on.
If north, H attacks south at B11, with some north ladder help
at D5, and east ladder help at G10. If south, C8 wins for H.
14. C6! But V sees right through all that! This move strengthens ties
to C9, and allows V to stop H even if H makes the E5 link.
G1 H tries to throw some doubt in V's ability to stop H from
connecting from D4 to the left.
15. F2 F1 V forces two ladder steps, which restores ability to stop
16. E2 E1 H after H's threat of E5.
17. H1 Now this is safe for V.
C8 H's last gasp at a win. Inexact play by V could lead to a
ladder east then north to H's link to the east edge.
18. E7 The only win-preserving move in the area.
D8 Forced.
19. E8 Threatens to connect at D9 or F8; H has run out of tricks.
H resigns.