BIVERSI

On a 10x10 toroidal board, with two reversi start patterns (one crossed and one parallel) set up antipodal to each other. Play mechanics and game object as at Reversi, but 1222 transformer. The two moves per turn must be played one in each section as long as they remain disjoint; after which moves may be played anywhere legal.

a b c d e f g h i j        O's      X's
                         ================
o o . . x . . . . .   1.  .  c4    d4  g9
. o x x . . . . . .   2. d3  f10   i8  d2
o o o x . . . . . .   3. a1  g6    e1J b4
. o o x . . . . . .   4. b4  i7    j7  a5
x x x x o . . . x x   5. a7  e5    f6  j0
. o . . . o o . o o   6. j8  i9    b6  b1
o . . . . . o o o o   7. b3  b0    j6  i0
. . . . . . o o o o   8. j5  c5    d5  i5
. . . . . . x o x .   9. h9  i6    
. o . . . x . . x o   0.

Rules and other rules

There is a difference between "rules of the game" vs "rules about playing the game". "Rules of the game" are purely logical ones - all that is needed to play (or referee) by a computer. i.e. The board and piece powers, the actual moves, prohibitions and priorities. "Rules about playing the game" are specifically for humans; they are physical rather than logical. i.e. playing time, what to do about irregularities or illegal moves, whether things like "check" have to be said out loud, fast scoring methods, blowing smoke in your opponent's face, etc.

In three player games, it seems a good rule to say "it is illegal to leave a next-player immediate win, if preventable". Also, if player A wants to make sure the next opponent plays to block the 3rd opponent from an immediate win, he must say, "B, C is about to win, please stop him which you can do by playing this". Then B is physically obliged to stop C, and A gets the proper reward for his forethought. But if both A and B overlook that C has a win coming up, A will say nothing, B will fail to prevent it, and C will duly win, without (a legally required) takeback, and profit from HIS own alertness. This is a good compromise that does not affect the purity of the rules of the game and makes it the responsibility of the previous previous player to warn that danger is at hand. This is fair since it's the previous previous player who benefits from all this anyway.

The PIE rule

The more long-term the goal is, the smaller the relevance of the PIE rule. There is a strong temptation to think this way, but I am in some doubt. For example in Go, it turns out that once the board size is past a small minimum, the komi is remarkably constant. It seems to be about 7 for all board sizes greater than 5x5. This suggests that the long-termness of the goal (at least of some games) is irrelevant - the PIEness is always about the same; though of course it diminishes in PROPORTIONAL importance to the other moves.

Another reason is that the initial advantage can be built up with good play to its final conclusion. The PIE rule is a tool for the placing player to reduce it to a value very near zero. Ideally, a perfect use of PI implies that only a perfect player can use that setup to achieve victory

p.s. For some reason I'm reminded of a pair of comments about playing against GOD (Game Optimization Device) and the DEVIL (DEVice of ILegitimacy)

* GOD always makes the optimal game-theoretic move; but
* DEVIL always makes the best move given what your overwhelmingly likely response is to be.

If GOD plays a perfect game; DEVIL may play even better (!) because it exploits your weaknesses.

Little Go change

I found many reflexes of Go on my voyages. One of those were a game with the same rules of our Go but with a different fix for KO positions. They had an extra movement: a push move when a player has three stones surrounding one:

  . . . . . . . .        . . . . . . . .
  . . . . . . . .        . . . . . . . .
  . . . . . . . .        . . . . . . . .
  . . o x . . . .        . . o x . . . .
  . o . o x . . .   =>   . o o x<- . . .
  . . o x . . . .        . . o x . . . .
  . . . . . . . .        . . . . . . . .
  . . . . . . . .        . . . . . . . .

This solves KOs and make group structures much weaker. [T.Sagme, Travels]

Defeat

The weight of defeat is lightened by learning. [T.Sagme, Meditations]

SEND IT

On each turn, the player may drop up to 4 pieces on empty cells. Such cells must be on an orthogonal line of sight of a friendly piece already on board (the cells in between being empty). Drops are sequential, not simultaneous.

None of the new stones may be part of the same group

Groups with no liberty are captured (as in Go).

When both pass, the winner is whoever has more area plus pieces
(Chinese Go scoring).

Pie rule: 13444 mutator.
==============================

Initial moves on a square board:

a b c d e f g h i j k l m       XX            OO
                               =====================
. . . . . . . . . . . . .   1  i3             cgk7
. . . . . . . . . . . . .   2  bg3 g11 b7     il7 i11 l12
. x x . . . x . x . o . .   3
. . . . . . . . . . . . .   4
. . . . . . . . . . . . .   5
. . . . . . . . . . . . .   6
. x o . . . o . O . o O .   7
. . . . . . . . . . . . .   8
. . . . . . . . . . . . .   9
. . . . . . . . . . . . .  10
. . o . . . x . O . x . .  11
. . . . . . . . . . . O .  12
. . . . . . . . . . . . .  13

Blockdance

On each turn, the mover must identify a block of connected men of his own; name one as pivot; and rotate the block any multiple of 60º around the pivot, provided all the landing places are either empty, opponent stones, or one of his own cells that the move is just vacating.

Any opponent stones landed on are captured and removed. Passing is legal, and compulsory if no moves are legal. Winner is whoever kills all of his opponent's stones.

abcdefghijklmnopqrstuvwxyzABC   Player Y     Player O

       . . . o o . . .        1 v5.2 xz5wy6  w8.3 v9
      . . . o o o . . .       2 t7.4 not(s6) w12.2 x11
     . . . . o o . . . .      3
    y y . . . . . . . . .     4
   y y y . . . . . . . . .    5
  . y y . . y . . y . . . .   6
 . . . . . . y y y y . . . .  7
. . . . . . . . y . . . . . . 8
 . . . . . . . . . . . o . .  9
  . o o . . . . . . . o o .  10
   o o o . . . . . . . , o   11
    o o . . . . . . . o o    12
     . . . . y y . . . o     13
      . . . y y y . . .      14
       . . . y y . . .       15

abcdefghijklmnopqrstuvwxyzABC

[notation: the post-dot-number is the clockwise angle moved in units of 60]

This game from Bill Taylor was inspired after playing Karl Scherer's Squaredance.

The PIE Rule

In games with forced draw, the PIE rule is useless, unless... the cutter gambles! He can make a position that seems to win for one side, and wins for the other!! That's another advantage of PIE, it may be able to reborn a drawish game.

Rythmomachia

Here is a blog about the medieval abstract game Rythmomachia.

Silence

Good4both

A bit of asymmetry is no bad thing, if it is the same for both players. [T.Sagme, Book of Parrots]

Fun first

The most important feature of a game is to be a intellectual challenge for regular humans, which brings pleasure to both. A good game continues to be fun and challenging for increasing committed players. [T.Sagme, Meditations]

Balancing starts

[...]It is a triviality that the usual method of playing games where there is an obvious first-move advantage, is unfair to the second player. "First" is clearly an average of half a move ahead of "Second", e.g. at random times. A typical attempted rectification of this, in abstract-game-playing circles, is the 1 2 2 2 2 ... move transformer, whereby after the first move, each player plays two moves consecutively. Though inappropriate for most games if used directly, it may have its uses if some further restrictions are added.

It has the Cesaro-propery of "evening-out" the starting advantage, (though
for VERY short games a further integration to 1 3 4 4 4 4 may be suitable),
and it is nice to see the sum of 1-2+2-... coming to 0 by almost every method.

Now, another move transformer often used is the "Progressive" transformer, whereby the moves are taken in series of 1,2,3,4,5 etc. It makes for fun games, if hardly very serious ones; and e.g. Progressive Chess already has quite a long history. But it often struck me that even so, there was a very slight advantage to First. (e.g. His number of moves ahead is successively 1 -1 2 -2 3 -3... so that First is always first to get to a new number of moves ahead, rather than Second.) And so it now appears this advantage is real! There is an advantage to 1/4 of a move to First!

So one way I have considered for some while of rectifying the Progressive transformer was to make it an "Odd-Progressive" transformer. This has move series of 1,3,5,7... , which gives the number of moves First is ahead each time as being 1 -2 3 -4... , which is clearly fairer than the above.

ps: A later idea about progressive games is the "slowing-down" mutator 443322111... which is excellent for slow starting games!

Rules

Every good rule is a Pandora box where is hard to see all consequences. If it is easy, the rule may be useless. [T.Sagme, Meditations]

Active and Passive Games

Games can be seen as "active" or "passive"; perhaps "violent" and "sluggish" would be better terms. In active games the pressure is on to get out and make things happen, before your opponent does. In passive, it tends to be better to wait or at least movement is so slow that one cannot get too active.
 
Chess is a bit of both, though I feel the passive tendency dominates a little. Go is finely balanced. Most chess variants tend to be very active, (e.g. Handgrenade and Progressive); indeed most progressives are very active. Connection games tend to be sluggish.
 
(Handgrenade Chess: No direct take allowed. In a move, all opposite pieces at King distance are captured. The one who captures the King wins)

Fractional Hex

[From Edward Jackman conversations] Speaking of Hex, here's another idea to address it's first-player advantage that may not have been explored much. I found it in the Mudcrack Y and Poly Y book, but it applies to Hex as well. The first player draws a line connecting the midpoints of the opposite sides of one cell, dividing it half, creating two 5 sided cells. She plays her opening move to one of the two halves. The fewer sides a cell has, the weaker a move there is. You might even require that the line divides the cell into a 4 and a 6 sided cell and the move goes in the smaller cell -- that would be a very weak move, even in the center of the board.

Standard move, filling entire cell:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +---+       +
 \     /xxxxx\     /
  +---+xxxxxxx+---+
 /     \xxxxx/     \ 
+       +---+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

Half move:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +-+-+       +
 \     /  |xx\     /
  +---+   |xxx+---+
 /     \  |xx/     \ 
+       +-+-+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

One third move:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +---+       +
 \     /    ,+     /
  +---+    /xx+---+
 /     \  |xx/     \ 
+       +-+-+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

Loss

Every loss should always teach a new lesson. [T.Sagme, Meditations]

Game Sources

These are useful sources to find new games:

• Mixing known concepts in strange ways (i.e., applying game mutators).
• Choose a good word and squeeze its content into a game.
• Get a board, some stones (of one or more types) and a position that pleases you, and hear the story they have to tell.

Perfection

"We achieve perfection only with a perfect use of imperfect actions" [T.Sagme, Meditations]

The Waves of Fortune

Talking with an old friend, we noticed that if there were no mistakes in some games we were playing, the moves would be always the same, i.e., the perfect match. That remark stayed inside my mind because it annoyed me the feeling that, in perfect information games (i.e., no luck and no hidden information), two players devoting enough time and skill so that eventually are able to completely master the game they love, will destroy it! The game collapses to a single and fixed contest - always win, always lose, always draw...

In games where the random factor exists this does not happen! I'm not talking of 100% random procedures (they are not games) like the Roulette or the Lottery, but something like Backgammon (a game with luck) or Stratego (a game with hidden information). If the balance of randomness is finely tuned, a good player will consistently beat any worse player. Facing two perfect players in a game like that, the final outcome is not decided at all! Using a fair random generator, each will have a certain percentage of chance to win. A statistical average of wins/loses will still apply but not for an individual game - the actual game being played. And if that average is near 50%, the joy cannot be destroyed by sufficient skill or dedication.

The Ocean of Abstract Games it is an area of flat water, where nothing random or secret appears to disturb the surface. With algorithmic evolution (not just speed, speed is useless for Go), this part of the Ocean will continuously grow smaller and smaller. I wonder if, sometime, most of these games will have the need for the Waves of Fortune...

Balance

"Let your mind be open, but not so open or it will fly away." [T.Sagme, The Book of Parrots]

BI-POD

BIPOD (c) 2004 Bill Taylor

It is played on a trapezium-shaped hex board, with two cells on the long side occupied by different coloured pieces, so that the colour-colour and colour-corner empty-cell numbers are equal:
_______________________________
. . . . . @ . . . . Q . . . . . 1
 . . . . . . . . . . . . . . .  2
  . . . . . . . . . . . . . .   3
   . . . . . . . . . . . . .    4
    . . . . . . . . . . . .     5
     . . . . . . . . . . .      6
=`abcdefghijklmnopqrstuvwxyz-';

The two players alternate in placing a single(*) blocking stone in any empty cell.  On any turn, a player may elect instead to "adopt" the running option.  The other player then becomes the Blocker, and continues playing single blocks on each turn. The Runner now plays single stones of whichever starting colour he chooses for that turn.

Runner wins if he can create two paths, one from each of his start cells, in the appropriate colours, to any points on any of the three short sides. Blocker wins if Runner has failed in his goal when all the cells are filled.

(*) It is recommended that for email play, the players agree to play any number of stones they like, between one and (say) three inclusive.

*************

Sample Game:

1. e13f2   su3
2. a3c3   adopt

Move 3 does not have impact in the position, so in fact it is a pass to see if Second places another stone. But Second adopts.
_______________________________
      x . @ . . . . Q . . . . . 1
       x . . . . . . . . . . .  2
  x x x . . . . . . x x . . .   3
   . . . . . . . . . . . . .    4
    . . . . . . . . . . . .     5
     . . . . . . . . . . .      6
=`abcdefghijklmnopqrstuvwxyz-';

3. v2 o    j4

While First saves the right position, Second tries to block the left sector.
_______________________________
      x . @ . . . . Q . . . . . 1
       x . . . . . . . o . . .  2
  x x x . . . . . . x x . . .   3
   . . . . x . . . . . . . .    4
    . . . . . . . . . . . .     5
     . . . . . . . . . . .      6
=`abcdefghijklmnopqrstuvwxyz-';

4. g3 o    h2
5. j2 o    i3
6. m3 o

First then makes a threat at g3, which provides extra space.
_______________________________
      x . @ . . . . Q . . . . . 1
       x x o . . . . . O . . .  2
  x x x o x . o . . x x . . .   3
   . . . . x . . . . . . . .    4
    . . . . . . . . . . . .     5
     . . . . . . . . . . .      6
=`abcdefghijklmnopqrstuvwxyz-';

 6...     m5
 7. p4 o  y3
 8. w3 O  x4
 9. v4 O  w5
10. u5 O  v6
11. t6 O  p6
12. resigns  

But even that extension is not enough because Second uses the right white pieces to block part of the way of the left white pieces.
_______________________________
      x . @ . . . . Q . . . . .  
       x x o . . . . . O . . .  
  x x x o x . o . . x x O x .    
   . . . . x . . o . . O x .    
    . . . . . x . . . O x .      
     . . . . . . x . O x .      
=`abcdefghijklmnopqrstuvwxyz-';

Players

Even if there are many types of games, there are two main types of serious players: generalist and specialist gamers. Specialists dedicate most of their free time to one game (even if they know and play other games) and dedicate large amounts of time learning openings, tactics and strategies about it. Generalists are meta-gamers curious with new rules, different ideas. Sometimes the former define the later as "people who failed to become good at one game", but this is an unfair critic. Most player are not generalists and so are bound to tradition and mainstream culture, playing games that society (sometimes just by historic reasons) maintains. In a sense, the same happen with religion, scientific models (at some extent), music... But it would be better for many obscure and excellent games if that was not so.

A generalist analysis a scenario with much less prejudice (and much less depth) than a specialist. Specialists are more uncomfortable with the unfamiliar. They like the assurance that practice and study provide. Even with enough intellectual skills, the generalist do not have the patience for the learning required. Performance is not the main goal. What matters are delight and surprise by unusual new thought processes.

There are two opposing problems. A specialist would think: "Why should I lose all my investment in game A to look at game B?". A generalist would think: "Why should I invest time in game A? Why not game B?". These questions do not have easy, general answers. I'm still not able to answer mine. [T.Sagme, Meditations]

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!