Trabsact Sagme Diaries

Jun 17, 2008

A Progressive moku

Played on a Go board. Black drops one stone, White then drops two stones, Black drops three, and so on...

A player wins if he makes a 5 in-a-row but he must just drop one stone in his last turn.

CHERRY

Cherry is a Alak variant. First the rules of Alak:

This game is played on a 1-D line. Black and white alternate in placing single stones on a line of n points. If placing a stone thereby removes all the go-liberties of any group of stones of the opposite color, those stones are immediately removed. It is illegal to place a stone where one was just removed. Placing is compulsory if legal, and the game ends when the player having the move cannot legally place anywhere. The winner is the player with the most stones on the board at game end.

Cherry (invented by Bill Taylor, 2008) is played on a semi-infinite line segment where the first cell is marked (*):

* . . . . . . . . . . . . . ...

Wins the player the occupies the first cell with a friendly piece that cannot be captured by the adversary in the next move.

A sample game:


* . . . . . . . . . . . . . ...
* . x . . . . . . . . . . . ...
* o x . . . . . . . . . . . ...
x . x . . . . . . . . . . . ...

X wins because O cannot drop into the 2nd cell right now.

PUSH WOOD

(by Richard Nowakowski, 2003)

Play on a line of N dots (this is an 1D game) each player has M pieces on the line extremes. For e.g., if N=9 and M=3:

x x x . . . o o o

On each turn, each player may:
* move forward a friendly stone to any empty cell or move out of the board (jumps are allowed).
* push a friendly stone backwards if it is backward adjacent to an enemy stone. Every stone in that group is pushed backwards any number of cells until it finds another stone. If there are no more stones, the player may even push out the group or part of the group over the line extreme.
* There is a KO rule: a player cannot repeat the previous position (variant: the player cannot push back any stone that was pushed back in the previous move).

Wins the last player that has a legal move.

A sample:


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

x resigns

Trabsact Sagme Diaries

A game, when moved, usually travels with its own social context. For e.g., a game from the Trok planet, in the island of Mag, is played only by children with lemur-like and duck-like animals. Some centuries ago, the game went to a neighbor island, Dag, and, even if the rules changed a bit, the ducks and lemurs are also thrown by the Dag children. [T.Sagme, Travels]

Jun 16, 2008

GO-6-MOKU

Rules of 9x9 Go, except that there is no passing and the winner is
whoever gets a 6-in-a-row. Suicide is illegal, except that a 6-row
may be completed in an otherwise liberty-less position. 1st-move swap.

a b c d e f g h i _oo__xx_ . . . . . . . . . 1. b2 d4 . o o o . O . . . 2. d3 e4 . . x o o x . . . 3. e3 f3 . x . x x o o . . 4. c4 c5 . . x . x x . . . 5. f4 c3 . . . . . . . . . 6. c2 b4: . . . . . . . . . 7. d2 f5 . . . . . . . . . 8. g4 e5 . . . . . . . . . 9. f2 resign

Jun 4, 2008

FREE Y

Swap option exists.
Winner is whoever makes a connected group that either
   (a) includes two nearly-opposite edge-points; or
   (b) includes three edge-points whose inter-point distances
                     are all less than half the circumference.

abcdefghijklmnopqrs     _oo_ _xx_  (after swap)     . . o x . .      1.  g3   j6    . . o x . . .     2.  k5   l6   . . o x . . . .    3.  m5   n6 . . . . . . . . .   4.  o5   p6 . . . o x o o o . .  5.  h6   i5 . . . o x x x x .   6.  g5   i3   . . . o . . . .    7.  i7   l8    . . . . x . .     8.  h2   j2     . . O . . .      9.  i1   k1?      . . . . .      10.  i9   resign abcdefghijklmnopqrs

Mar 11, 2008

Card Chess

photo by Alexander Dzhantimirov
Imagination solves almost all
(the coordinates are wrong, but who needs perfection?)

Feb 13, 2008

PROGRESSIVE FENCES

Cul-de-sac with L-shaped walls allowed.
Walls may be placed along edges, but not beyond them.
Win by crossing over the target edge.

The turns are progressively 1 2 2 3 4 4 5 6 6... moves, with a move being
one orthogonal step by the player's stone, or one length of 2-wall placement.
A player may distribute his available moves as he pleases (so placing a wall
costs two moves), subject to not being permitted to completely wall off
his opponent from his target.

Sample game (notation: Xy* means that a wall was placed at coordinate Xy with a certain shape given by symbol *. If * is 1,2,3 or 4 it means a L-shaped wall on the 1st, 2nd, 3rd or 4th quadrants; if * is - means a horizontal wall with center Xy; and if * is | means a vertical wall with center Xy): 1. S (Bottom) 1 2. NN 2 3. SS 2 4. N Fi- 3 5. Fh4 Hh3 4 6. Fd| Ge2 4 7. NES Hj2 5 8. He2 Hc| Fb3 6 9. Fj4 Ej| Gb2 6 10 Ib| Jc| Id- E 7 11. NNNESSEN 8 12. Kb3 Kd4 Je- Hk| 8 13. NEESSWSWW 9 14. If2 Gf- Ef1 Ed| Dc1 10 15. SWWWNNNWNW 10 16. SWWSSWN Bk- Dk- 11 17. SSSSSE Bg- Dg- Dj- 12 18. WWNNNEEE Fg1 Hg4 12 19. Eh1 E2E Df- Bf1 Bd- Ce1 13 20. Bb| Cc- NWWW Jg2 Kg3 Ki- 14 21. Bottom resigns Final Position Top's goal A B C D E F G H I J K L a + - - - - - - - - - - - - - - - - - - - - - + : | | | | b : | + + +---.---' + | +---. : : | | | | | | | : c : +-------`---+ + + | + | + : : | | | | : d :-------+ + | | + +-------+ ,---: : | | | | | | : e : + +---+ + +---'---' +-------+ : : | | | : f : +---+-------`---+-------+---' + + : : T | | : g :-------+-------+ `---+ ,---+---'---. : : | B | | : h : + + + +---,---+---. + + + : : | | : i : + + + +-------+ + + +-------: : | | : j : + +-------| ,---+---' + + + : : | | | : k :-------+-------+ + + | + + + : : | : l + - - - - - - - - - - - - - - - - - - - - - + A B C D E F G H I J K L Bottom's goal

Dec 17, 2007

QUADRAPHAGES

Startup:

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

In each turn a player (a) moves his stones rookwise, the previous # of cells;
                      (b) announces a new number (between 1 and 8);
                      (c) moves his stones the new number of cells.

When a stone leaves a cell, it marks it with its own colour.
A stone may not land on a marked or occupied cell, or leave the board.
Given a number, stone must move if it can; if not, it remains stationary.
If possible, a player must choose a number that allows at least one stone
to move.

Intervening own-pieces or marks of either type do not block a move,
but opponent pieces do.  The first turn begins with operation (b) & (c) only.

The game stops when all four stones in succession fail to move; then...
the winner is whoever has the most marked cells.
"""""""""""""""""""""""""""""""""""""""""""""""

Game Sample               _xx_                         _oo_ 1.  ....  ....  1  a7a8  i3i2    c1c2  g9g8  3  c2f2  g8d8 2.  a8a5  i2i5  3  a5a2  i5i8    f2f5  d2d5  2  d5b5  f5f7 3.  a2a4  i8i6  7  i6b6  a4h4    ----  ----  3  b5e5  f7f4 4.  i6i9  a4a1  8  a1i1  i9a9    ----  ----  4  e5e1  f4f8 5.  ----  a9e9  6  i1i7  e9e3    ----  ----  3  e1h1  f8c8 6.  e3h3  i7i4  1  i4h4  h3h2    h1g1  c8c7  5  c7h7  g1b1 7.  ----  h4c4  4  h2h6  c4g4    h7d7  b1f1  5  f1f6  d7d2 8.  ----  g4b4  1  h6g6  b4b3    d2d3  f6e6  2  d3f3  e6c6 9.  ----  ----  4  g6g2  b3b7    ----  ----  3  f3c3  c6c9 10. g2g5  b7e7  1  e7e8  g5h5    c9d9  ----  2  c3a3  d9f9 11. ----  ----  6  ----  e8e2    a3g3  ----  4  g3g7  f9b9 12. ----  h5h9  2  ----  e2e4    ----  ----  1  b9b8  ---- 13. h9h8  e4d4  3  ----  d4d6  and wins 40-39

Final Position:

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

This game can also be played on a hex-board. It has less
possible directions, so it's easier for a player to control
where the adversary may go, when the board starts to get full.

HEXAPHAGE
========= (numbers up to 6)  Rules as for quadraphage.

               _oo_                         _xx_ 1.  ....  ....     ....  ....    ....  ....  1  j5h5  d3e4 2.  g2f3  g6f5  1  f5d5  f3g4    h5i4  e4c4  3  c4f1  i4f7 3.  ----  g4m4  4  d5l5  m4j1    f7b3  f1b5  4  ----  b3j3 4.  ----  ----  3  j1d1  ----    ----  b5e2  1  e2c2  j3k4 5.  ----  l5k6  3  k6e6  d1a4    k4h1  c2i2  5  ----  h1c6 6.  ----  ----  2  ----  e6i6    ----  ----  1  c6d7  i2k2 7.  resign

Final Position:

abcdefghijklm       o x x o    1    x x o x X   2   x x o . x .  3 O x x o x x o 4   x o o x x o  5    x o o O o   6     X x . .    7 abcdefghijklm

Nov 30, 2007

AbGamers

When we talk about abstract board gamers there is a relevant distinction. On one hand, there are people that don't mind giving lots of time and attention to abgames and, on the other, people that try an abgame or two from time to time. The first ones are hard to find and the net, like in r.g.a, is a perfect way for these guys (well, we) to meet and discuss and play abgames. It's difficult, if not impossible, to replace the net in this.

The second ones are much more common. There are thousands and thousands that like to play abgames. I live in Portugal, a country with no social history of abgames except for Chess and Checkers. From my experience, me and some local friends were able to promote abgames events alongside with hundreds of schools, where the finals alone gathered 500+ young people (we are preparing the 4th edition). We also made a set of 10 small books, discussing historical puzzles and games, that sold thousands for each copy. And Portugal only has a population of 10 million. I guess that from all these tens of thousands, some got interested and started reading and playing a bit more than before (I know that that happened at least in some cases). This is another way to contribute to the abgames future community.

[this blog has been too quiet, just like the main website, the World of Abstract Games. In these last months I didn't had much time to process new games (but I'm still collecting them) so be patient and check or recheck the 500+ pure abstract games already posted]

May 23, 2007

Sagme's Diaries

With falling stones
many battles rage, but
the game is one.
[From Sagme's Haiku]

May 17, 2007

1222 UNRESTRICTED 6-MOKU

Sample Game:
XXXX OOOO 00. --- o25 n24 n26 01. p24 p25 p26 o23 02. m25 n25 q25 l11 03. o26 o27 q24 p27 04. o28 q26 n23 o29 05. l23 m24 k22 p23 06. q23 r22 s21 o22 07. m22 m23 m20 m26 08. n21 o20 p19 k24 09. j23 k23 i23 n19 10. l21 j24 o19 q19 11. m19 r19 p18 r20 12. o17 t22 q17 n20 13. r16 j22? p16 p17 14. resign Final Position: g h i j k l m n o p q r s t u . . . . . . . . . . . . . . . 14 . . . . . . . . . . . . . . . 15 . . . . . . . . . O . x . . . 16 . . . . . . . . x O o . . . . 17 . . . . . . . . . o . . . . . 18 . . . . . . x o o o o x . . . 19 . . . . . . o o x . . o . . . 20 . . . . . x . x . . . . o . . 21 . . . x o . x . o . . x . x . 22 . . o x x x x o o o x . . . . 23 . . . x o . x o . x o . . . . 24 . . . . . o x x x x o . . . . 25 . . . . . . o o x o x . . . . 26 . . . . . . . . x o . . . . . 27 . . . . . . . . x . . . . . . 28 . . . . . . . . o . . . . . . 29 . . . . . . . . . . . . . . . 30 . . . . . . . . . . . . . . . 31

HIXT

Rules:
* On his turn a player drop a friendly stones in an empty cell, and
connects it, via a bridge, with any friendly stone (at diamond's distance)
* Stones connect via adjacency or using a bridge
* PIE rule for the second player's first move
* The player connecting two opposite edges or making a Y connecting
three non-adjacent edges, wins the game

Sample Game:

XXX === OOO j13 o8 h7 i10 l9 o10 l11 l7 k8 o12 j5 i6 g6 f7 d7 l5 m4 s4 q4 p3 p5 s6 p15 o14 m14 r15 c10 i12 g12 b9 c8 f9 d11 m2 g2 i4 j3 j1 h1 1-0 Final position: |a b c d e f g h i j k l m n o p q r s t u v w x y z A B C | x o__ . . . . . . 1 | \__ | x__ . . o__ . . . . . 2 | \__ \__ | . . x__ . . o__ . . . . 3 | \__ \__ | . . o . __x__ . x o . . . 4 | __/ \__ | | . . . __x __o . x . | . . . . 5 | __/ __/ | | . . __x __o__ . . . . o . . . . 6 | __/ __/ \__ | . x o x__ . o__ . . . . . . . . 7 | | \__ \__ |. x . | . . x . o . . . . . . . 8 | | | | | o | . o__ . . x . | . . . . . . . 9 | | \__ | | | x . . o . | . o . . . . . . 10 | | | | | x__ . . | . x . | . . . . . . 11 | \__ | | | . x__ o . . o . . . . . 12 | \__ | | . . x__ . . | . . . . . 13 | \__ | | . . . x__ o__ . . . . 14 | \__ \__ | . . . . x o . . 15 |a b c d e f g h i j k l m n o p q r s t u v w x y z A B C

Hixt is a hex variant of Twixt with some different connenction criteria. The board should be large enough so that the drama of a single bad move could not determine the match outcome. Probably, a hex board with edges of size 10 should already provide a nice battle.

May 2, 2007

A multiplication game

This game is focused for young people when learning multiplication.
Let's consider multiplications x*y with values ranging from 1 to 9.

First, one player picks one pair, say x1*y1. The second player chooses another pair x2*y2. Then the second player takes the modulus of the difference , i.e., |x1*y1 - x2*y2| and takes that difference as his points. Then, the second player must choose a pair x2*y3 or x3*y2 (i.e., he must keep one of the numbers from his last picked pair). This is the first turn. Then this is repeated (now the first player starts choosing a pair, makes the difference and choose a related pair, and so on...). Pairs can never be choosed twice.

The game ends when one player cannot continue (there are no similar pairs to choose since all were selected already). The player with less points wins the game.

It's possible to speed things up but restricting to pairs x*y where x<y.

An initial example:
____ Player1 ____________ Player2 ____ --- (--------) 3x5 | 4x4 (1 points) 4x9 --> |3x5-4x4|=1 6x6 (0 points) 6x9 | 7x8 (2 points) 7x9 8x8 (1 points) 8x9 | 9x9 (9 points) 5x9 6x7 (3 points) 6x8 | 7x7 (1 points) 5x7 4x8 (3 points) 5x8 (and so on...)

May 1, 2007

Board Games Studies 2007 (part 3: The Spielmuseum)

The game museum, near Vienna, is a project from Dagmar de Cassan and her husband. Nowadays, it consists of thousands of games that are being archived and cataloged in a digital database. Let's hope they can solve the space problem so that people can consult and play many of these board games.

Board Games Studies 2007 (part 2: The Talks)

There were several talks at the Colloquium ranging from psychology, history (we heard, for instance, about the history of Draughts, Go and Liubo), regional games (some films in India and Zanzibar where game masters play Bao) and math (the connections between math theories and chess).

Here are some pictures of one talk that defends that the Ashtapada board was not used to play any specific race game and how the round board found in the Kurna temple does not represent any game:

Another talk presented a study from Alex de Voogt about the tactical similarities and differences between beginners and masters in the complex mancala game of Bao.

The next talk showed some boards and regional designs of an old race(?) game called Liubo from China (the rules, seemingly, are lost).

Apr 30, 2007

Board Games Studies 2007 (part 1: The Games)

Last week at St. Pölten, a small city near Vienna, it took place the 10th Board Games Studies Colloquium. It is a chance to meet several different people around board games (historians, inventors, collectors...). Here are some games that I found out there:

These first two are two games rescued from the Netherlands's patent office in the 80's by Fred Horn (a prolific game inventor, a jazz musician and a great guy). The first game (for 2 or 4 players) uses a Go-like rule to capture every group that's unable to move. The second uses hidden-information so that the special stone can move into the farthest cell (jumps over enemy stones flip them and make them friendly pieces).

This is an old Stratego-like game:

This is a new edition of a card set designed by Descartes himself (!):

A geometrical game where players have an equal set of pieces all with the same volume (48 units) and each piece cannot be adjacent to another piece of the same height or color and identical pieces must be placed differently (the picture shows an invalid position, both yellow pieces are placed in the same position).

This next one is a connection game called ConHex by Michail Antonow:

Apr 19, 2007

Patterns @ Conimbriga

Conimbriga is an archeologic site of an ancient Roman villa at the center of Portugal. Here are some photos and some of its interesting floor tilings.

Apr 2, 2007

CHOSEN CHESS

[by João Neto] In normal Chess you choose a piece, then you move it. In Chosen Chess, when it's your turn, you move the (previously chosen) piece, then you choose another piece (for the next move).

In the first move White choose a (movable) piece, then Black do the same.
In the subsequent moves players move the chosen piece (if possible), then choose a different piece.
No Check, checkmate or en-passant.
Castling is a King move.
The player that captures the adversary King wins the game.

Mar 30, 2007

BEAT IT OR EAT IT

[Bill Taylor 1993 post @ r.g.a] Though this games is played with cards, and is (very vaguely) one of the trick-taking family of games, it still belongs here in rec.games.abstract. It is as much a strategy game as sprouts, chess and Go, being a 2-player game of complete information with no element of chance (apart from the starting layout, and even this is symmetric between the players).

Long ago, I played a (more complex) version of this game, for a while. The original game was a 4-suit game, each player having his own trump suit. However this 2-suit version seems just as skillful, as much fun, and "cleaner". It is even possible to play a one-suit version !!  No other changes in the rules are needed, except that the starting layout can no longer be symmetric. But the two-suit version seems neatest.

I post it here because...

(i) it deserves to be far better known than it is;
(ii) it seems to be essentially unique of its kind;
(iii) I would eventually be keen to start an email game or two.

The game has been around a fair while, but doesn't seem to have a name of its own. It was first introduced to me as "Besicovitch's game", but such a name is hardly descriptive. We sometimes used to call it "Finchley Central" as a small in-joke, indicative of the hair-trigger timing needed to decide when to strike your main blow. The game usually see-saws one way then the other, as every advance tends to leave one weaker. Thus it might fairly be called "See-Saw" or "Negative Feedback".  Until a concensus is reached, I shall call it "Beat It Or Eat It"; being descriptive of the mechanics of play.

One nice thing about the game is its almost complete freedom from *arbitrary* rules, once the basic logic of play is set. The main exception is the length of the suits.  13 is the obvious length, and feels about right. Shorter would be good for practice games, and longer (up to 26) would be possible, with one "red" suit and one "black" suit.

The core idea of the play is:- taking the lead in turns, one player leads and the other follows, until someone gets rid of all his cards, thus winning.

--------------------------------------
"BEAT IT OR EAT IT"  (Full rules)

1. Two players play with a deck of 13 hearts and 13 spades. Aces count high.

2. The initial layout is symmetric, and obtained thus:-  One player shuffles, and deals 13 cards to the other, who keeps only the red cards. The blacks are returned to the undealt cards, and the dealer gives himself black cards identical to his opponent's reds. Then each gets the remainder of the other color. The "leader", (player of the 1st card), is chosen at random.

3. The leader plays any card onto the table. The follower EITHER picks it up,  OR (if he can, & wishes to), beats it by playing a higher card of the same suit. These cards stay on the table, and the follower becomes the leader for the next play.   Continue with (3) again.

4. On any play, the follower may, if he desires, (& must, if unable to beat the card led), pick up all the cards on the table, and add them to his hand. The leader then remains as leader for the next play.  Continue with (3).

5. Whoever first plays the last card left in his hand, is the winner.
  (It is immaterial whether this occurs as a lead or a follow.)
-------------------------------------

So, the idea is to get rid of all your cards. But it is essential along the way to sometimes (voluntarily) pick up all the tabled cards, to get some of the high ones there, (even though this hinders your main goal, of course).

And often, (especially if the opponent is close to winning, or has too few low cards for comfort), you will have to lead a high card that he CAN'T beat, forcing him to pick up all the junk on the table.

Remember, all played cards, leaders and beaters, stay on the table (face up), until one player chooses to or is forced to "eat" them, i.e. pick them all up, and suffer being follower again for the start of the next series of plays. As long as no-one "eats" the stuff on the table, the lead alternates.

So there it is. It is a great game; and as I say, one of complete information. In fact it is standard for both players to keep their hands face up on the table in front of them, for convenience; (these hands are only on the physical table of course, not the "logical" table).  If you try it out, you will quickly notice the negative feedback element mentioned above.

It is usually an advantage to start, but by no means always; it depends on the nature of the starting layout, and perhaps on the parity of the suit length.

I warmly recommend everyone to give it a try.

To indicate the nature of the play, here is a sample game, with a 7-suit pack.

Initial layout: (LEFT has the opening lead)

LEFT: hearts A Q T 9 8      RIGHT: hearts K J       spades K J                   spades A Q T 9 8 8h, Jh. 8s, Js. 9h, Kh. 9s, LEFT eats all (by choice). Layout now:  (RIGHT is on lead) LEFT: hearts A K Q J T 9 8     RIGHT: hearts -       spades K J 9 8                  spades A Q T Ts, Js. 8h, RIGHT must eat. 9h (R must eat). Th (R must eat). Layout now:  (LEFT is still on lead) LEFT: hearts A K Q J      RIGHT: hearts T 9 8       spades K 9 8               spades A Q J T 8s, Ts. 8h, Jh. 9s, Js. 9h, Qh. Kh, RIGHT must eat all. Layout now:  (LEFT is still on lead) LEFT: hearts A       RIGHT: hearts K Q J T 9 8       spades K              spades A Q J T 9 8 Ah (right must eat);  Ks and LEFT WINS.

This game hardly showed much ability on either part.   RIGHT should have
struggled more actively in the last phase of play, e.g. when he led the 9h, which led to an immediate simple forced loss. But it was probably too late by then anyway. There was a very clear-cut error earlier. When RIGHT led the ten from his 3-card hand of AQT hearts, it would clearly have been uniformly better to lead the queen. (However he was probably lost anyway.)

LEFT also made a blunder in the very first round; he could have beaten the 9s with the Ks, led back the Th (compulsory eat), the Ah (ditto) & Qh (winning). (Suit length of 7 is not really enough to give the full flavor of the game.)

Mar 24, 2007

FANO NIM

[bill Taylor, 2005] Here's a cute little mathematical game. I'm surprised it hasn't been around the abstract game world before. It's only the second game I know of that's based on the Fano plane - the smallest possible 2D Projective Geometry.

Here it is - it has vertices THEY WAR, and lines YEA WHY TRY HER RAW WET HAT,
neatly compiled into a triangle with three altitudes, and an incircle which
is also a "line"...
Y /|\ / | \ / | \ / | \ / | \ / _.-"|"-._ \ /.' | `.\ H. | .E /: "-. | .-' :\ / | ";-T-:" | \ / : _-' | `-_ : \ / \' | `/ \ / ,-' `. | .' `-. \ /_-' `-..|..-' `-_\ W--------------R--------------A

Note there are no interior intersections between the altitudes and
the circle, only at the tangent points where they triply intersect
with the sides as well.

Anyway, the game is a form of Nim.

The diagram starts with a small integer at each of the seven vertices,
the number of "seeds" at that vertex, preferably a different one for each.
(These can be decided on in one of several standard ways.)

On each turn, the player to move must remove THE SAME number of seeds from
any three vertices in a line, (remembering that the circle is also a line).

Last person to make a legal move wins. (This is the standard
winning condition for CGT games. There is also the "misere" version OC.)

I will leave it as a fun exercise for fans to compile a list,
hopefully exhaustive, of all the "N positions" (Next player wins),
and all the "P positions" (Previous player wins).

And note, too, that if one too quickly learns the correct optimal play,
(though it is not as straightforward as regular Nim), one can easily
extend it to larger projective geometries; (the next one has 13 lines
comprising four vertices each and meeting four at a vertex.)

It can, OC, be played on any geometry at all; but the projective
nature of the game ensures that the winning condition is equivalent
to producing a line of zeros, which is a nice target to aim for!

BESIEGE

[by João Neto] Start with the NxN board full of stones. Then, alternating moves,
each player removes a stone (that stone is not captured) When a player makes a
square, he captures all the stones inside that square (no diagonal squares).

E.g.

x x x x x 5 x . x x . 4 x x x x x 3 x x . . x 2 x . x x x 1 a b c d e

If a player removes stone e1, he will capture stones c3 and d3

When there are no capturable stones left on the board, wins the player
with more captured stones.

Area vs Territory Go Rules

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

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

Games Operators, aka, Mutators

[Posts@rec.games.abstract ~ Dec 99, Jan 2k]

[Douglas Zare] Here are five examples of operators on games:

1) Misere: The object of the new game is to lose while playing the old game.
2) Move and switch: After the first move, the second player can choose to switch sides rather than respond.
3) Bad advice, as in Fred Galvin's "Compromise Chess": A player offers two possible moves to the opponent, who advises the player which to play. If there is only one legal move then this is simply made.
4) Use a doubling cube, as in backgammon. I have heard that this is a nice addition to speed chess, and would guess that this would make spectator sports more interesting.
5) Bughouse: Instead of playing, you can drop in a piece your partner has captured on a parallel color-reversed board. The partnership of the first winner wins.This doesn't do much for go or pente, but how does it affect checkers?

All of these take in games and produce new games, though there may be a few choices to make in the implementation. In my experience, understanding the original game carries over to some level of understanding in the new game, although there are substantial differences. Interestingly, the first three are close to involutions, i.e., applying the operator twice may produce the original game. The first three also produce legal games, albeit strange ones, and can be played on many internet game servers to the confusion of kibitzers. (I'm always willing to play backgammon misere unrated as zare_10027 on Yahoo.)

I am curious what other interesting operators have been tried, particularly those which are simple, preserve some of the structures of the original game, and are fun. I would also appreciate any pointers to annotated games or the theory of hex misere and backgammon misere. (Are there videos of grandmasters playing bughouse?) On the other hand, I would like to know how much the endgame theory of bad advice go resembles that of ordinary go.

[Tim Chow] John Conway has suggested "Whim," which is Nim except that at any point in the game a player may say "Whim" instead of moving; this decree alters the game from normal to misere. The whim may be invoked only once per game (*not* once per player per game). It turns out that Whim is just Nim with an extra "invisible" pile of counters (I forget of what size) representing the whim, but the same operator will surely have more interesting effects on other games.

[David Bush] Misere doesn't work well for chess and related games. Selfmate puzzles notwithstanding, it's usually impossible to force your opponent to checkmate you. Misere Go sounds like a disaster. Checkers might be interesting, with cumpulsory captures. Maybe Misere suicide chess, where captures are compulsory and the King is just another piece, but the last player to move WINS...? Speaking of which, suicide might be an applicable operator to battle games. There are tons of fairy chess rulesets which might apply to battle games (chess, checkers, etc.) For example, unambiguous chess requires all moves to be representable unambiguously with 3 symbols in descriptive notation, where the dash - doesn't count, but the x for captures does. E.g. you couldn't play QR-K1 if KR-K1 is also possible. Maybe some games have move notation which could be adapted for this. Or, salt shaker chess starts the game with a salt shaker on a central square. The shaker moves in the same direction & distance as whatever piece is moving (king when castling.) You may not move the shaker off the board with your move. The issue of what2do if the shaker would land on an occupied square, could be dealt with in several ways. Then there's nuclear chess, where each piece adjacent to a capture, friend or foe, is removed from the board (except the capturing piece.) Or protean chess, where each piece (except possibly the king) takes on the powers of movement of whatever piece it captures. Or et cetera...

[Fred Galvin] Here are some references on misere hex (and other variants):

Ronald Evans, A winning opening in Reverse Hex, J. Recreational Math., Vol. 7, No. 3 (Summer, 1974), 188-192.
Ronald Evans, Some variants of Hex, J. Recreational Math. Vol. 8(2) (1975-1976), 120-122.
Jeffrey Lagarias and Danny Sleator, Who wins Misere Hex?, in: Scott Kim, ed., Articles in Tribute to Martin Gardner (Atlanta International Museum of Art and Design, January 16, 1993), 146-148.

[anonymous] you can pre-give an amount of -say- money to each player. Whenever such a predefined condition occurs , both players bet from their money , whether they want the condition to be valid or cancelled , and the highest bet decides. Of course this bet-amount is substracted from the higher-bet-player's money. This usually increases (and sometimes completely changes) the structure of the game. As an example consider betting tic-tac-toe , where always the player moves , who bets most. Or betting go : after move 3n , the n-th free square is filled with a piece from the player whith the higher bet. Or betting football : all 10minutes a player is removed from the team whith the lower bet. A handicap for good-players can be applied by allowing different initial amounts of money.

[Andy Tepper] How about a HoardMoves(G,n) operator? At any time instead of moving you may delay up to n moves and then make them all at once in the future. For instance, in HoardMoves(Go,1) you could skip a turn and then play the two moves in parallel on some future turn. A group would have to have 3 eyes to be alive. (Assuming moves were made in parallel. You could always say that the two moves must be made in sequence which keep the 2 eyes rule.)

[Gerry Quinn] Sounds a bit horrid in Chess. Both players will hoard at the start, with White hoping to declare mate in (say) ten, and Black having to scramble for some tactics to prevent it. But then Black will be further behind, and White will win when he has hoarded a couple more. As Alekhine said (or was it Nimzowich) "In Chess, the threat is stronger than the execution!" Hoarding a _partial_ move might be interesting in Chess, though. Pass a move twice, and you have a free one in hand. This might be fairly balanced.

Mar 23, 2007

Nice Chess Sites

About the Origins of Chess

http://www.mynetcologne.de/~nc-jostenge
http://www.samsloan.com/origin.htm

About Tournament Chess

http://www.mark-weeks.com/chess/55571wix.htm
http://www.chesscafe.com/

Curiosities

http://www.xs4all.nl/~timkr/chess/chess.html