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Medusa
General
I'll presume that the reader is familiar with the rules and some basic concepts of Go.
In 1975 Mark Berger invented "Rosette", a Go variant played on the intersections
(triple contacts) of a hexagonal board. His first idea was to simply apply the rules of Go and
see how it worked out. As it turned out, regular concepts like 'ko' and 'seki' remained intact,
but there was a big difference when a group was in 'atari', that is: when it had just one liberty
left, like the white stone below.
In Go a point has four liberties and extending from a group in atari may increase the number of its
liberties by 2. In Rosette an extension increases that number at most by 1, and this one (or the other)
is consequently taken to keep the group in atari. The attacker has the choice of direction and may lead
the head of the 'escaping' group towards the edge or even around towards its own tail, to die.
Of course things were balanced by the fact that both players suffer or enjoy this to the same extent, but Mark
concluded rightly that it gave rise to too much tactical involvement to leave much room for any long term strategy.
So he invented a safety mechanism up and above the implicit safety mechanism of having two 'eyes', and
called it a rosette.
A rosette is formed by six stones of one color, occupying a small hexagon. A group containing a rosette
lives unconditionally. This turned out to be a great improvement and I made it a key idea in shaping Medusa
and
.
Thanx Mark, wherever you are!
Capture by Enclosure
Medusa employs Go-like enclosure with a touch of Othello: captured pieces are reversed to show
the opponent's color. The introduction of the rosette as the sole (explicit) safety mechanism in Medusa
follows the same reasoning as above: a group atari cannot escape without outside support. Of course implicit
safety mechanisms such as a group having (a clear option on) two eyes remain.
The difference
The difference between Medusa and all other Go variants is the option to actually move stones.
By the nature of the concept the actual amount of movement is limited.
There is no movement in the early stages where stones are wide apart, claiming their initial influences.
In fact up to the middle game a stone should be so efficient as to need no movement.
By the time tactical involvement becomes more dominant, moving to escape or to attack becomes part
of the considerations. Towards the end smaller claims may be established with it.
Programming Medusa
The tree of Medusa has an exploding branch density when the movement options become manifest.
Humans are not affected by this because they 'see' with such nice tools as plan, focus and pattern
recognition. They may take a glance at a position and see whether things appear efficient as they are
or whether movement may be needed. In an actual game a player also knows the situation
and anticipates the spots where movement may be needed. The computer faces a totally different situation.
From the early middle game on, literally thousands of options may be at hand in the first ply alone,
millions in the second, billions in the third. The option to move any or all of the groups
creates so many combinations that I deem it impossible to write a program. Given I'm right, this should
at least bear some relation to the peculiarities of this human phenomenon of pattern recognition.
With the computer eating away at the classics, it's nice to know there are at least a couple of
games where humans will remain superior for much longer, if not indefinitely.
Medusa and its support-act
are featured in
R. Wayne Schmittberger's "New Rules for Classic Games" (John Wiley & Sons, Inc. New York;
ISBN 0-471-53621-0).
Rules
- The game starts on an empty board. Play is on the hexagons. Only the lighter colored cells are
part of the board, thus a cell in the center has four neighbours, one on the edge has three and a corner has two
- Each player has enough bi-colored stones - black one side, white the other
- Off the board, players use a 19-point track marked in the center. Between evenly balanced players,
the marker is placed 3 points towards the player who has white. This is the game's komi
Komi is a way of settling the first player's advantage. Many high level games would be needed to
establish a reliable number. Nobody ever objected to three though.
Indicating komi is not the marker's primary function - it is there because refraining from
putting a stone on the board at one's turn earns a point, indicated by moving the marker.
Although the track has 19 points, its unusual for it to move more than a few points either way.
Options
- Black moves first after which turns alternate. On his turn a player has two options:
- He may place a stone on any vacant cell
- He may move any or all of his groups
- He may use either or both. If he uses both, placing a stone must precede movement.
If he drops the first option he may move the marker one point towards his side
Movement
For movement purposes a group is defined as two or more connected stones of the same color.
- Moving a group means taking one of its stones and moving it in a staight line over any number of
friendly stones in an unbroken row, to land on the first vacant cell beyond
- No group may move more than once in a turn
- By movement groups may split or join
- If a group moves to contact a friendly group that has not yet moved itself,
the latter therewith loses its right to move in that turn. The implication is that the order of moving
groups may make a difference
Two adjacent stones make the smallest group: it can crawl along a line, one step per turn. A compact triangle
of three stones has a maximum of six options for movement and can, given enough turns, literally crawl
its way to anywhere on the board.
Life & Death
- A group lives unconditionally if it contains a 'rosette' - six stones around one of the board's
61 dark-colored cells
- For capturing purposes a single stone is, by definition, also a group.
A group without a rosette lives as long as it has at least one 'liberty', that is: one adjacent vacant cell.
A group that is down to one liberty, and thus under immediate threat of being captured, is said to be 'in atari'
- Assuming none of the groups involved is protected by a rosette, a group that loses its last liberty
is captured and reversed immediately to show the opponent's color
- Capture may result from placement or movement or both. If a capture is the result of placement only,
the stones are reversed before the movement phase. Thus the group resulting from the capture has the
right to move in the same turn. Groups captured by movement contain at least one stone that has moved,
and may not move in the same turn
- If placement results in one or more opponent's groups losing their
last liberty, they are captured whether or not the stone placed has any liberties itself at the time
of placement
- If placement results in losing one's own last liberty without killing any opponent's group,
the placement is suicidal and the player's own stone or group is reversed before the movement phase.
Suicide is legal
Object
- The game ends by one player's resignation or if both pass completely on successive turns.
In the latter case dead stones are reversed
- The winner is now the player with the most territory.
Territory consists of a player's number of stones on the board
plus the number of cells totally surrounded by his stones plus - for the player whose side it is on -
the number of points indicated by the marker
- Seki may occur: empty points not totally surrounded by either player count for neither
Examples
At the top black is safe. A white placement at A is suicidal and gives black a rosette,
making movement at B (qs15) useless. Of course if white plays at B, black must answer by
completing a rosette at A himself on the next turn.
At the bottom black threatens to connect by capturing the group on the bottom left side.
It's white's turn however and the four black stones at the bottom are killed by a suicide placement at C,
creating a five stone black group with two liberties, followed by two movements (ec1 & ec3).
The next diagram shows a seki: neither player can occupy A or B without having his stones killed.
Strategy
Invasions in Medusa, including those unlikely to succeed, don't harm as long as the opponent must answer
by placement. Failure only makes that the opponent gets some dead stones on cells that would have been
part of his territory anyway, while the invader doesn't lose anything in trying. However, if the invading
stone is so weak as to require no answer by placement, the invader loses a marker point. The same holds for
overdefensiveness: 'killing' already dead stones doesn't so much change the division of territory,
but it gives the opponent the opportunity to refrain from placement and move the marker.
Notation
Signs used in notation are:
| ! | Good move |
| !! | Very good move |
| ? | Bad move |
| ?? | Blunder |
| !? | Doubtful |
| ?! | Risky |
| = | Equal position, draw |
| + | Won |
| - | Lost |
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