 here is a small
number of old traditional abstract games that still catch the attention of millions of people around the world.
The best known of these are Checkers, Mancala, Chess, and Go. The first two refer more to a family than a single game. There are many old variants based on the same ideas that have spread around the world, Mancala in Africa and Checkers in the West and Arab world. But Chess and Go refer to specific games.
Chess has undergone an historical
evolution since its beginnings in India and China around the sixth century, through the Islamic world,
and finally into the checkered boards of Medieval Europe. Now, at the beginning of the 21st century,
Chess has been regulated by FIDE for about 150 years. However, any curious reader knows that there exist
many variants of Chess: Giveaway Chess, Progressive Chess, Capablanca Chess, and so on.
The 1994 Encyclopedia of Chess Variants by D. B. Pritchard describes hundreds of variants.
The definitive, but never finished, Chess Variants website (at www.chessvariants.com) contains thousands
of variants!
Go has been played for almost three millennia.
It is older than Chess, and has suffered less change throughout its history. Also, if the same curious reader
stries to find information about Go variants, he will not be overwhelmed by countless games and themes.
Moreover, of the few variants of Go that exist, probably less than 50, many of them are not playable—they
are more proposals for games than actual, fun games. Why is this so?
Some people insist that Go is less
historically contingent, more structural or mathematical, meaning that it would be easier to find similar
games in different cultures. In fact, this is not so, while checkers, race games and n-in-a-row games do seem to have appeared independently in many cultures. Chess has more elaborate rules, which include a piece-capturing sub-goal. This might be irrelevant, but it might indicate more scope for the imagination.
The aim of this article is not to
compare strengths and weaknesses of these two great games, but to present some playable variants of Go,
which in our opinion are very hard to find. We have chosen a small set of games, leaving the remaining
few behind, with the justification that is easier to pick a game to play from a small number of
good options than from a greater number of average choices. Some good games were left out
because they have already been presented in Abstract Games, such as Anchor (AG5) or Gonnect (AG6).
The latter is a very good alternative Go variant, giving a tactical goal that can be used to
increase the drama and interest in the opening stage, as well as a "cold" post-endgame stage, adding extra layers to Go.
Linear Go, or Alak
This is pseudo-Go played on a line. A. K. Dewdney proposed this idea in his book The Planiverse, which is a
science fiction book about a two-dimensional universe. In 2001 Alan Baljeu perfected the game.
Black and White alternate in placing stones on a line of n cells. If placing a stone thereby removes all the Go liberties of any group of stones of the opposite color, those stones are immediately removed. However, it is legitimate (and usually very beneficial!) to play a move that leaves a group of your own stones without liberties, whereupon they stay on the board. It is illegal to place a stone where one was removed immediately before. Placing a stone is compulsory when legal, and the game ends when the player having the move cannot legally place a stone. The winner is the player with the most stones on the board at the end of the game.
Since Alak is one dimensional,
an entire game can be represented with a sequence of lines. Here is a sample game:
Black resigns, since after any black stone drop, White protects his related group by dropping on the other empty cell. Therefore, White wins 6-5.
It seems as if it is a bad move to play on the fourth point from the edge of an empty end, as the opponent can hop under it:
It is bad now for Black to play on either of the rightmost points for the same reason that White won the sample game.
Here is a long game ending in a tie.
As well as a game ending in a tie, it is theoretically possible to have a draw by endless repetition on boards of length seven or more. We have never seen this happen, however.
In endgames, if you have half or more of the cells occupied from one end, and safe, you should win. Here is an example:
There is almost no way Black can force White to take him off, except as the last move, so White is bound to win here, whatever else is to the left.
Here is another sample game:
Black wins by capturing all the white stones!
As a final note,
naturally one might play this game on any length board. There is a tendency to think that for
sufficiently long boards it would always be drawn by endless repetition, as it is so easy to remove pieces.
However this seems not to be the case, and indeed we think we may be able to prove a theorem that either
player may force the game to end if he chooses. Naturally this would not prove that optimal play would
always result in a terminated game, but it is highly suggestive.
Progressive Atari Go
This game is Go with the progressive 1234... game mutator. This means that on the 1st move Black plays one stone; on the 2nd move White plays two stones; on the third move Black plays three stones; and so on. Passing is still permissible.
To improve the game, an extra
rule is added: "When an atari occurs, the sequence stops." These simple additional rules create a very nice game full of new threats and tactics. Here is an example position after move 4.A3 B3 C3 D3:
Another position is presented below. At turn 11, Black wasted a huge number of moves to make a small group (despite the fact that it was inside White's territory). A careful turn 12 for White settled the game for a White win.
1.M12, 2.B3 C3, 3.B11 C11 L3, 4.D3 L11 M11 L12, 5.H3 J3 K3 D11 E11, 6.L7 L8 L9 L10 M6 N6, 7.G2 M3 C7 B12 G12 G13 F11, 8.D2 L6 K11 H11 J11 H12 H13 M13, 9.A5 B5 C5 C6 C8 C9 B10 G11 M2, 10.F5 F6 F7 F8 F9 G10 G5 H5 J5 K5, 11.G7 G6 H6 J6 J7 K7 H8 K8 H9 J9 K9, 12.A3 E3 F2 F4 E1 G1 H1 J1 K1 L1 M1 M5.
A complete game sample follows. Black starts with a handicap stone at G7.
1.G7 L11, 2.C3 C11, 3.C5 C7 C9, 4.D3 E3 D11 E11, 5.G3 G4 G10 G11 E5, 6.F2 G2 H2 J2 K2 L2, 7.H3 J3 K3 L3 D5 F5 E9, 8.A3 B3 B2 M2 M3 M4 M5 M6, 9.L4 L5 L6 L7 M7 N7 B5 G12 G13, 10.F3 N6 K10 L10 M10 N10 K11 K12 K13 M12, 11.A5 B9 D9 K9 L9 E10 F10 H10 J10 K6 L8, 12.A10 B11 B12 B13 H12 H13 J11 M9 N8 F11 F12 F13, 13.C6 E8 J6 B10 C10 D10 A4 B4 C4 D4 E4 F4 A9, 14.M8 A11 H11.
White wins 85-84. Notice that on move 13, J6 is necessary, for otherwise White would be able to create a group with two eyes inside Black's area. It is this extra move that reduces Black's count by one and allows White to win! It is surprising how often the game result is very close, in spite of the large numbers of placements in the final stages.
Although we have not tested them, many
variations are possible:
Different progressive sequences, such as 1222..., 1357..., etc.
The restriction that none of the stones of the same series may be dropped to join the same connected group (including each other).
Progressive HexGo
HexGo, while mathematically appealing, tends not to make an interesting game,
because of the lack of cuts and cross-cuts, and because move sequences tend to
be more like that of Hex than Go. However, the progressive transformer turns
this into quite a playable game. It could also be played "atari" style (see above),
but this seems less compelling than at square progressive Go, perhaps because it takes more moves to surround and capture groups in a short move series. Here are two sample games.
1.F10 2.F9 G9, 3.E10 E9 F8, 4. G8 G7 E7 F7, 5.D8 E8 D7 E6 F6, 6.G6 H5 I4 J3 K2 G10, 7.F11 C6 G5 H4 I3 J2 K1, 8.B8 C7 D6 D5 D4 J6 J5 J4, 9.A10 B9 C8 D3 E5 E4 E3 F2 G2, 10.C4 A9 C5 B6 B7. Black wins 48-43
1. F6, 2.C9 F9, 3.C6 D6 E6, 4.D8 E7 F7 G6, 5.A8 B7 G5 H5 H6, 6.A9 B9 F3 G3 H3, F8, 7.H9 H8 H7 J3 J2 J1 I4, 8.D3 E3 I2 I1 C10 E10 G10 G9, 9.C4 D4 E4 E5 I7 J6 F2 G2 G1!, 10.Resigns. Black's cunning placement in move 9 had been quite overlooked by white!
HexGonnect
Another way to play Go on a hexagonal board is to use the Gonnect rules, making HexGonnect. Here is a position where Black is able to create a safe structure under White's area of influence.
White's move 14 has three purposes: keep the initiative, squash Black's group, and kill D9. Black's move 15 is the winning move. It was very tempting to move C5 first, but that would have been disastrous as Black cannot make another eye down there even with the move. White's A8 reply would have killed off the invasion.
In the real game White also attempted an invasion of Black's territory on the right, but unsuccessfully. It is much harder to invade and make life in HexGo, because of the difficulty of surrounding single points for eyes, and the lack of cuts to gain traction. Black was very lucky to succeed on the left!
Dagger Go
This is a variant of handicap Go described by Henry Segerman. Black has a stronger handicap
option in that he may play his handicap stones later in the game rather than at the start.
It has been generally agreed in the past that such "daggers" are far too powerful—worth far more than two regular handicap stones due to their ability to kill otherwise perfectly sound groups.
A more reasonable
handicap, worth perhaps closer to two standard handicap stones, and making a
more natural game, might perhaps be called "blunt daggers". These are extra free moves, playable any
time except that the two stones played simultaneously must not orthogonally touch any other stone on the board, including each other. This means regular live groups are usually still alive, so the handicapped player does not need to be watching his back all the time! We have not played Blunt Dagger Go, but suspect it would be a very playable game.
Simultaneous Capture Go
This is a very interesting "serious" Go variant. If a stone is placed making a capture, but in doing
so its own group's liberties are thus removed, then all groups without liberties, of either color,
are removed simultaneously. This makes for a very playable game, rather similar to regular Go for
the most part, but intriguingly different. There are no normal ko's, for example, but similar
repetitive situations can arise. It is also a very "natural" variant—maybe even more natural than the original!
Rosette
If we use a tessellation of hexagons and play Go on the intersections, we get a three-liberty Go game.
This game tends to be much less strategic and more tactical. The number of liberties of each piece is
less, so an attack on any individual piece or small group is more urgent. Three moves are enough to
capture one isolated piece. A stone in atari cannot escape that easily, since making
an extension provides that piece with only one extra liberty, not two as in Go, so the opponent
can maintain the threat. Atari races are very common. Indeed, it is possible for either player to ladder the other whenever two stones are in contact, and in a moderately sized space this acts as its own ladder breaker! Go played in this way is a very unstable game.
After 1.H9 I9 Black can capture the white stone!
A black stone at 'a' wins this circular capturing race! Perhaps "ladders" should be called "spiral staircases" in this game!
Because of this, it seems that in general stones can be further apart than at regular Go, yet still effectively connected. For example:
As long as there are no enemy stones in the immediate vicinity, each pair of neighboring black stones is unbreakably linked. From this one can see it might be a very fast-moving game, but also highly tactical, as the exact placement of an enemy stone could be vital in maintaining these connections.
A game called Rosette, invented by
Mark Berger in 1975, is based on this concept, but with an attempt to reduce the excessively
unstable nature of the game. He defined a rosette to be a ring of six stones of the same color surrounding a hexagon. A rosette is deemed to have two eyes implicitly. This dilutes the excessively tactical character of three-liberty Go. Another game based on this concept is Freeling's Medusa, in which it is also possible to move stones.
Since Rosette is still a tactical game, boards should not be too big, or interest might be difficult to keep in the early stages. As rosettes to some extent counteract the tactical nature of pure three-liberty Go, however, maybe it is not so vital to play on small boards. Here is an example endgame on a small board:
1.E3 C4, 2.E5 D5, 3.E7 D3, 4.C6 F2, 5.F4 B4, 6.H3 C2, 7.G4 D1, 8.G2 E1, 9.F6 A5, 10.D7.
This position is a bit tricky for White. B6 would be a loss, as would G6 or H5, too. White should play 10....A3, with the assurance that Black has the same problem, meaning that Black must reply 11.G6, then 11....B2, 12.H5 B6 and the game is a tie: 12-12!
This feature may
be named "Race to Rosette." As the rosette nullifies a seki, it becomes important
to make one before the opponent—at least in these small games.
Here is a true seki. Both players have played 11 stones. Neither dares to move:
This is not a seki, though superficially like one:
(A White stone was captured). Black will win whoever has the move—White cannot play at either empty point, but Black can play at E5. Black has won the "Race to Rosette."
Conclusion
These seven games show some different playable approaches to the game of Go. Chess, Checkers, and Mancala became extended families of games as a result of centuries of conscious innovation or as a result of accumulated errors in communicating the rules as the games spread.
In fact, little has changed. Nowadays, information can still be miscommunicated, and players will still try to improve existing games. This process of game evolution will continue to enlarge the Chess, Checkers, and Mancala families, and perhaps the small Go family will yet prove to be prolific.
Website References
Variations on Go: http://www.di.fc.ul.pt/~jpn/gv/gv.htm.
Medusa: http://www.mindsports.net/Arena/CompleteGames/Territory/Medusa.html.
Note: The games in this article are scored with Chinese rules.
In other words, a player's point count is the total of territory plus stones on the
board at the end.
Captured pieces are ignored. |
