Haiku

At each game's end, a
dialog full of untried
possibilities.

Chinese and Japanese Go rules

The following Go example shows a safe set of stones with two eyes:

   . . . . . .
   . . o o . .
   . o o . o .
   . o . o o .
   . . o o . .
   . . . . . .

Would this set be called a single group even though it is composed of two disconnected halves?

Most players would call it a single group. In area rules it doesn't matter what you call it. In territory rules it could conceivably matter what you call it, (though it doesn't in practice), because territory rules, in all their artificial absurdity, have to refer to groups from time to time in order to define what is considered "dead" and what is considered "alive".

In territory rules, this matters(!). In area rules, it doesn't matter - if there is any dispute you just play it out (and with no cost) until a group or groups is removed from the board.

Logically speaking, you should call the above two separate groups, each helping to keep the other alive. But people never speak so precisely in practice.

There is even a worse situation. The following group has only one true "eye"; the other one, in the NW corner, is a so-called "false eye", and can eventually be filled and the whole lot captured.

   . x x . o .
   x o o o o o
   x x x x o .
   x . x x o o
   x x x x o .

Territory rules actually have to define the concept of eyes, false eyes, and the rest. It is lunacy. (Area rules define nothing - you just play it out to the grim end if necessary). Territory rules, with their defined false eyes, come to grief in this famous sort of position:

   . x x x x x
   x o o o o x
   x o o . o x
   x o . o o x
   x o o o o x
   x x x x x .

Here, black has TWO false eyes, and not a single true one! And yet, both separate groups, or parts of a group, are keeping one another alive; rather like your above example. And even the Japanese admit that black is alive, in spite of what their rule books say!

Basically, territory rules are an abortion. Computers cannot handle them because they are essentially logically flawed. [Bill Taylor]

A progressive game of Y

Here follows a Y game with a 1222 progressive mutator and the following restriction: both drops must be on non-adjacent groups.

   1          .
   2         . .
   3        . . .
   4       . . . .
   5      . . . . .
   6     . . . . . .
   7    . . . . . . .
   8   . . . . . . . .
   9  . . . . . . . . .
     /       /       /
    a b c d e f g h i

         X       O
    1. c5      c7 e8
    2. d7 f8   c6 e7
    3. d6 f6   d8 g8
    4. f7 d4   f9 e5
    5. e6 h8   g9 i9
    6. a5 b7   b5 a6
    7. b6 a4   g7 a4
    8. h9 a3   b6 b3
    9. resigns

Final position:

   1          .
   2         . .
   3        O X .
   4       X . . X
   5      X . X . O
   6     O X O X X X
   7    . X O X O X X
   8   . . . O O X O X
   9  . . . . . O O O O
     /       /       /
    a b c d e f g h i

'O' cannot play both b4 and b5 (the two drops would belong to the same group). So 'X' make occupy one of those cells plus another below to connect the bottom edge.

Progressive Mutators

One of most general mutators is [Progressive] - players get an increasing set of moves per turn. The most common forms are 1234... and 1222... Most games do quite well with 1234... but most have to be restricted in some way to keep the flavour of the original game as much as possible, and prevent it becoming a mere bludgeoning race: Chess retains check-stop; Go has atari-stop; 1222 Hex is often played by dropping non-adjacent stones, and so on.

Similarities

In the main desert of Konn'ex homeworld I found a bonding game. The rules are: "In a hexagonal board (of size 5 per edge), 11 stones for each player are placed in the two initial rows (players stand on opposite sides). For each moved stone, the player must also move another friendly stone in the same direction and an enemy stone in the opposite direction (e.g., if you move northwest, the enemy moves southeast). Captures are by replacement and mandatory (with a max-capture rule). Wins the player that stalemates the adversary."

The natives explained me that in the desert, strong bonds (be friend or foe) are essential as water, and so their games reflect that concern. How alike are we all... [T.Sagme, Travels]

Non-reversible moves

In the Orion sector, a traveller showed me a book of games concerning reversible and non-reversible moves. In most of these games, pieces were judged by the notion of piece gradient. For example, a stone could move thru a friend if it was moving forward, but it could not jump again backwards. Transparent in one side, opaque in the other.

Earth has games with piece gradient (like Chess and its pawns) and games without gradient (like Go). I personally like games without gradient but it was fascinating to find a complete family of games using this specific concept. [T.Sagme, Travels]

Further biographical remarks about our patron saint, Trabsact Sagme.

Trabsact Sagme was a mystic and game player of the late BC years, Tibetan. Widely regarded as the mother of abstract games, and in particular Go. She had an affinity with Parrots, Snails and Spiders (qv). Her writings on abstract games were preserved for posterity by Megas Bactras, (or Bacttras), a central Asian of mixed Bactrian/Greek, who transmitted them to the West soon after Alexander's conquests. Though eventually lost sight of, they were rediscovered by Bart MacStages, a British adventurer of late C19, (who incidentally helped Col Younghusband's expedition to Tibet).

Trabsact Sagme was the Earth's 1st serious ExoLudologist. She was born around Ulan Bator, in 2293.

Yes; widely regarded as being the same Sagme!

The mystics and physicists at both ends of this great journey, as well as we here in the middle, have all para-simultaneously been groping toward this same conclusion. Trabsact Sagme of BC 454 and Tabsact Sagme of AD 2293 are in fact THE SAME ONE. Apparently this can be achieved by some sort of Quantum gravity effect involving trivalent logic, snail-shell spiral symmetry, and other physico-mystical effects. I'm a bit hazy on the details; it's the sort of thing you chaps would know more about than me anyway. I gather it has something to do with the timelessness and non-locality of abstract games in particular and the abstract world in general; (OC, as a mathie I am more familiar with these concepts.)

The fact that we play almost all our games with o and x symbols these days is in honour of Sagme's fondness for snails and spiders. That she was also fond of parrots is not so much reflected in our games, though we often quote from the Book of Parrots, one of Sagme's most popular!

"The novice squawks loudly, but the wise parrot plays her eggs silently on the board." - The Book of Parrots (Trabsact Annals)

Sente/Gote

It is difficult to balance offense/defense. Many games are flawed because offensive or defense is too strong. The initiative cannot always be good or always be bad. It must depend on the context created by the best player. [T.Sagme, Meditations]

Initio

Trabsact Sagme was (will be) the Earth's first Exoludologist. She was born around Ulan Bator in 2293. Since her infancy, she was very interested by all knowledge created and gathered in the 20th and 21st centuries about abstract board games, a subject almost forgotten on those exciting days. Alien civilizations were found across the big black sky, and Humanity finally read Encyclopedia Galactica. After collecting the most important games on Earth, she decided that her life goal would be to study games from alien civilizations. She was one of the few people with the right to enter into some alien homeworlds. It was no coincidence the ones allowing her to enter were exactly the ones which had more respect about abstract board games. Some of the civilizations she visited:

• Civ-3: They use trilogic as a foundation for all mathematical activities, i.e., instead of true/false logic, they use true/false/unknown.
• Konn'ex: They see all objects and concepts as connections of others, and their games reflect these way of seeing things.
• Zet: Everything is a part of something. Their games, usually create complex pieces from atomic ones.

She found many resemblances with Human games, especially in connection and pattern games, namely, Hex and Gomoku were found in almost all home worlds (however in different board sizes and move equalizers). Curiously, no game similar to Chess was ever found!