Card Chess

photo by Alexander Dzhantimirov

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

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

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

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]

Sagme's Diaries

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

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.

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...)


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).

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:

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.

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.

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.)

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.

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

Go and the 'Three Games'

Go and the 'Three Games' -- A text by William Pinckard

Games-playing is one of the oldest and most enduring human traits. Disparate pieces of evidence such as dice discovered at Sumer, game-boards depicted on Egyptian frescoes, Viking chess pieces, and ball parks constructed by ancient empires deep in the Andes link up directly with contemporary phenomena such as Saturday night poker games in Kansas City and the annual go title matches in Tokyo.

Games are undeniably a concomitant of civilization and even in their most primitive forms presuppose some degree of sophistication. Most of all, they require the ability to think in abstractions and to manipulate ideas in logical terms, thereby giving form to what is formless and creating small, recognizable patterns in the shadow of great mysteries.

From ancient times in Japan the so-called 'Three Games' were backgammon, chess and go. Chess probably comes from India, backgammon from the Near or Middle East, and go from pre-Han China. Backgammon is a gambling game which, using dice, gives luck or chance the preponderant role. Chess in one of its earlier forms also used dice, but takes its present shape from the structure of a royal society and from war maneuvers. Go is the most abstract and 'open' of the three; and with its freedom from complicated rules, its simplicity of form, its fluidity and spaciousness, it comes remarkably close to being an ideal mirror for reflecting basic processes of mentation.

Go is played with black and white 'stones' all of exactly the same value, thus somewhat resembling the binary mathematics which is the basis of the computer. The stones are played onto the board and are left as they stand throughout the game, so that the game itself takes shape as a visible record of the thinking that went into it. About three hundred years ago an eminent Chinese monk came to Japan on a visit and was shown the diagram of a game of go which a master of that time had recently played. Without knowing anything of the game save the sketchy description they gave him at the time (this was after go had more or less died out in China), the monk studied the moves as shown on the record and after a few moments remarked with much admiration and respect that the player must have been a man who had become enlightened -- which was indeed the case. (It is interesting to note that this story is told on the one hand by go players to illustrate the quality of the game and on the other hand by Buddhists to show the acuity of the monk from China.)

The great 17th century Japanese playwright Chikamatsu, in a famous passage, compares the four quarters of the go board to the four seasons, the black and white stones to night and day, the 361 intersections of the board to the days of the year, and the center point on the board to the Pole Star. It would be easy to erect a tower of fanciful theory along these lines, but that would only obscure the obvious point. In this striking analogy Chikamatsu is describing a feeling of hugeness and all-inclusiveness -- the board conceived as a complete world system in potential form. The board and pieces can be thought of as limitless: any number of lines and an endless supply of stones to play with, the game itself being the life of the players. (In Chikamatsu's play a young man becomes old and grows a long beard while watching a single game.) Only because we are human and must put practical limits to our activities, do we use just a small part of the infinite board. But this field of nineteen by nineteen is large enough to contain everything we are able to put into it. The number of possible games playable on this board has been reckoned to be more than the number of molecules in the universe.

An anonymous go player has written: 'The board is a mirror of the mind of the player as the moments pass. When a master studies the record of a game he can tell at what point greed overtook the pupil, when he became tired, when he fell into stupidity, and when the maid came by with the tea.'

Contrary to the opinion of many people, go has nothing to do with Buddhism. Because it is a valid system in itself, it offers nothing contradictory to other systems, but in fact go is an older inhabitant on this planet than is Buddhism. In China it became one of the Four Accomplishments, the others being poetry, painting and music. It reached Japan around the 6th century and for a long time remained the exclusive property of a leisured noble class. Then during the 16th century all this changed. The many great families and clans which had warred happily against each other for a thousand years were gradually brought under the hegemony of the Tokugawa Shogunate. It was during the subsequent period of the Tokugawa era (roughly from 1600 to 1868) that go, along with haiku, kendo, tea ceremony and so on, was most actively cultivated as a way of constructively channeling the mental energies of the people during the long years of peace. One formal word for go in Japanese is Kido. Ki is the old Chinese word for go, and -do is the Chinese word for Tao, which means Way -- or, more specifically, a Way to enlightenment.

All games channel mental energies, whether they lead to enlightenment or the reverse, but it is suggestive to consider the 'Three Games' in their social context because then we can see how each of them reflects certain basic characteristics of a general or regional type.

Chess, for example, the great historical game of the West, involves monarchs, armies, slaughter, and the eventual destruction of one king by another. The game appears to be entirely directed along the lines of the great myths of the West from the Mahabharata to the Song of Roland -- the overthrow of a hero and the crowning of a new hero. The pieces, from king down to pawn (peon), give a picture of a heirarchical and pyramidal society with powers strictly defined and limited.

Backgammon, the favorite game of the Near and Middle East, is preoccupied with the question of Chance and Fate (Kismet). All play is governed by the roll of dice over which the player has no control whatever. The players are matched against each other, but each tries to capture a wave of luck and ride it to victory. The loser curses his misfortune and tries again, but the individual is helpless in the grip of superior forces.

Go, the game of ancient China and modern Japan (and now popular throughout the world), is unique in that every piece is of equal value and can be played anywhere on the board. The aim is not to destroy but to build territory. Single stones become groups, and groups become organic structures which live or die. A stone's power depends on its location and the moment. Over the entire board there occur transformations of growth and decay, movement and stasis, small defeats and temporary victories. The stronger player is the teacher, the weaker is the learner, and even today the polite way to ask for a game is to say 'Please teach me.'

Things are different now, but in earlier times, when go was so much admired by painters and poets, generals and monks, the point of the game was not so much for one player to overcome another but for both to engage in a kind of cooperative dialogue ('hand conversation', they used to call it) with the aim of overcoming a common enemy. The common enemy was, of course, as it always is, human weaknesses: greed, anger and stupidity.

Every year in March department stores all over Japan present elaborate displays in connection with the Doll Festival. If one looks carefully at the miniature weapons, musical instruments and furniture of a really complete display one will find a tiny backgammon board, a Japanese chess (shogi) board and a go board.

The 'Three Games' is a useful classification because taken together they make up a coherent world view. Most of philosophy boils down to speculation centered around the three basic relationships of the human species. The first is man in his relationship to the remote gods and the mysterious forces of the universe. The second is man in the society he builds up around him. The third is man in his own self. Or, to put it another way, man the backgammon-player, man the chess-player, and man the go-player.

That we have these three shows that they answer basic needs in the human spirit. People everywhere are preoccupied with social structures, position and status; and everyone who is capable of reflection must sometimes speculate on his private relationship to fortune and fate.

But go is the one game which turns all preoccupations and speculations back on their source. It says, in effect, that everyone starts out equal, that everyone begins with an empty board and with no limitations, and that what happens thereafter is not fate or wealth or social position but only the quality of your own mind.

Seo's unknown game

[Seo Sanghyeon mathmaniac@hanmail.net] This game (name and author unknown) is played on square grid board of odd size. But don't choose smaller than 3x3. It's trivial. 5x5 with two players is interesting enough, but 7x7 is more strategic, I think.

EQUIPMENT: I strongly recommend to play by paper and pencil. It's hard to play with board and stones. Since there is no capture, no need for eraser.

INITIAL POSITION: Each player chooses start position, and drop his stone there.

DROP: On each turn, each player drops a stone on an empty cell adjacent, orthogonally or diagonally, to his last dropped stone. And board wraps, i.e. first row is adjacent to last row, etc. And draw (this is why paper and pencil is recommended) a link from his last dropped stone to his newly dropped stone. When playing diagonally adjacent cell, this link should not be crossed.

. . . .
. o 1 .
. x , .
. . . .

If 'x' plays '1', a link from 'x' to '1' is drawn, and since it cannot be crossed, 'o' cannot play ','.

.. o2 o3 o4
.. o1 ,, o5
.. x. o7 o6
.. .. .. ..

On the other hand, if 'o1'-'o7' is played in that order, there is no link from 'o1' to 'o7', so 'x' can play ','. So that's why playing with board and stones is ambiguous.

A variant

.. .. .. ..
.. x1 x3 ..
.. ,, x2 ..
.. .. .. ..

According to the rule described above, now 'x' cannot play ',', because 'x1' to 'x2' link will be crossed. But there's a variant that allows crossing of his own link. And it seems this leads to more interesting game on 7x7.

EXAMPLE GAME:

'x0', 'o0' is initial position, i.e. diagonally opposite corner. Since board wraps, there's no difference between corner and center. But wrapping moves are harder to read. 'x' plays first.

x0 .. x5 o5 o6
o7 .. x4 x6 x7
x8 .. x3 .. **
.. x2 o2 o1 ..
.. x1 o3 o4 o0

(o8: resign)

COMMENT:

x2-x3 prevents white to move toward upper left corner. x5 is of same line, preventing o4-x5 wrap move. And notice that, after o7, o cannot play marked ** cell, since it will cross x7-x8 link.

. . / . . . .
\ x . x o o .
\ o . x x x \
. x . x . . \
. . x o o . .
. . x o o o .
. / . . | . .

If you draw board this way, It's not that hard to see. (It can be done on TwixT board, too.) So, white has at most three cells to play, but black has five.

. . / . . . .
\ x 5 x o o .
\ o 3 x x x \
. x 1 x . . \
\ 2 x o o 6 .
. 4 x o o o \
. / . . | . .

Also notice that

x0 ** x5 o5 o6
o7 :: x4 x6 x7
x8 .. x3 .. ..
.. x2 o2 o1 ..
## x1 o3 o4 o0

o cannot play o7-**-## line, since it crosses x0-x1 link. Therefore
:: as a reply to ** is a mating move.

RingGo 80% Go 20% Hex

[(C) 2001 William I. Chang] RingGo is a variant of Go played on a hexagonal lattice with 127 points, 18 of which are removed from play in order to strike a balance between how easy or hard it is to make a group of stones live. The board inherits from Rosette, Medusa, and especially a conversation with Greg Van Patten. Most points have 4 liberties.  While it is harder to make two eyes, it is easier to connect groups so the network may have two eyes.  In this sense, I think the game achieves its goal of combining Go's intricate eye-making tactical play with the connection-making strategy of Hex (though perhaps not enough of the latter).  I'm sure it can be refined and improved if more people tried it.  The board is generalizable to odd-order lattices by repeating the Medusa pattern, although there are lots of other beautiful patterns to choose from.

           . . . . . . .                  . . . . . . . . .
          . . . . . . . .                . . . . . . . . . .
         . . . o . o . . .              . . . o . o . o . . .
        . . o . . . . o . .            . . o . . . . . . o . .
       . . . . . o . . . . .          . . . . . o . o . . . . .
      . . o . o . . o . o . .        . . o . o . . . . o . o . .
     . . . . . . . . . . . . .      . . . . . . . o . . . . . . .
      . . o . o . . o . o . .      . . o . o . o . . o . o . o . .
       . . . . . o . . . . .      . . . . . . . . . . . . . . . . .
        . . o . . . . o . .        . . o . o . o . . o . o . o . .
         . . . o . o . . .          . . . . . . . o . . . . . . .
          . . . . . . . .            . . o . o . . . . o . o . .
           . . . . . . .              . . . . . o . o . . . . .
                                       . . o . . . . . . o . .
             . . . . .                  . . . o . o . o . . .
            . . . . . .                  . . . . . . . . . .
           . . . o . . .                  . . . . . . . . .
          . . o . . o . .
         . . . . . . . . .
          . . o . . o . .     RingGo boards of order 5/7/9, with 55/109/193
           . . . o . . .      points.  The order-11 board has 301 points.
            . . . . . .
             . . . . .

One might play RingGo on a Go board if one can envision dividing each
square into two triangles with a diagonal line drawn top-left/bottom-right.
(There actually was a commercial version of Hex done this way!)  Or, have
the players sit adjacent and both look toward the *.

   . . . . . . .           *
   . . . . . . . .
   . . . o . o . . .
   . . o . . . . o . .
   . . . . . o . . . . .
   . . o . o . . o . o . .
W   . . . . . . . . . . . . .
     . . o . o . . o . o . .
       . . . . . o . . . . .
         . . o . . . . o . .
           . . . o . o . . .
             . . . . . . . .
               . . . . . . .

               B

This game should play very differently from other hexagonal Go variants.
I tried and liked it :-)  Any suggestions or comments will be greatly
appreciated!

William Chang   Los Gatos, California   18 April 2001
email: wchang@acm.org, williamichang@hotmail.com
(C) 2001 William I. Chang

---

Other Boards:

Rings board

          o o   o o   o o
         o   o o   o o   o
          o o   o o   o o
       o o   o o   o o   o o
      o   o o   o o   o o   o
       o o   o o   o o   o o
    o o   o o   o o   o o   o o
   o   o o   o o   o o   o o   o
    o o   o o   o o   o o   o o
       o o   o o   o o   o o
      o   o o   o o   o o   o
       o o   o o   o o   o o
          o o   o o   o o
         o   o o   o o   o
          o o   o o   o o

Medusa board

          o o o o o o o o
         o   o   o   o   o
        o o o o o o o o o o
       o   o   o   o   o   o
      o o o o o o o o o o o o
     o   o   o   o   o   o   o
    o o o o o o o o o o o o o o
   o   o   o   o   o   o   o   o
    o o o o o o o o o o o o o o
     o   o   o   o   o   o   o
      o o o o o o o o o o o o
       o   o   o   o   o   o
        o o o o o o o o o o
         o   o   o   o   o
          o o o o o o o o

Revolving Games

Finding ways to spin your games
or
The stable King and his revolving servants

[December 2000] We (Bill Taylor and Joao Neto) have invented and started to play some games wth a common rule theme: if some condition is met, the moved piece changes its powers. Like a game with rotating officials.

This, if done well, can result in very dynamic games, where some pieces lead very wild lies.

Joao invented a game based on a simple idea: depending whether the turn number is even/odd, the moved piece is promoted/demoted. This basic change makes (in Joao's opinion) a very good chess variant, called Promotions and Demotions, or just ProDem.

But, is this the only possible way to use this dynamic idea?

Revolving Games

There is an old chess variant, named Revolving Chess (whose origins we don't know), whose rules are:

REVOLVING CHESS

1. Same as FIDE, except:
2. Each moved non-king piece, changes its status in the following order:
  2.1. Knight to Bishop,
  2.2. Bishop to Rook
  2.3. Rook to Queen
  2.4. Queen to Knight

--------------------------------------------------
The original game was fully "royal", but we play with stalemate
= win for stalemater, though still with castling (R changing to Q).
--------------------------------------------------

Game Sample

1. d4      d5      
2. c4      d:c4    
3. Nc3(B)  b5      
4. a4      c6      
5. a:b5    c:b5    
6. b3      a5      
7. b:c4    b:c4    
8. e3      R:a6(Q)
9. Ne2(B)  e5      
10 B:c4(R) Bd6(R)  
11 R:c8(Q)  Qa:c8(N)
12 B:a5(R)  e:d4    
13 Rb5(Q)+  Nc6(B)  
14 Q:c6(N)  R:c6(Q)
15 Q:d4(N)  Q:d4(N)
16 e:d4     Nf6(B)  
17 Bf4(R)   O-O(Q)  
18 Ra6(Q)   Qc2(N)+
19 Kd2      N:d4(B)
20 R:f6(Q)  B:f6(R)
21 Q:f6(N)+ g:f6
22 Ba6(R)   Kg7
23 Rha1(Q)  Qe8(N)
24 Ke3      Ncd6(B)
25 R:d6(Q)  N:d6(B)
26 h3       Be5(R)+
27 Q:e5(N)  f:e5
28 Ke4      f3
29 Kf5      Kf7
30 g4  1-0 [if Ke7 or Kf7 then h4]

Final Position:

. . . . . . . .
. . . . . k . p
. . . . . p . .
. . . . p K . .
. . . . . . O .
. . . . . . . O
. . . . . O . .
. . . . . . . .

--------------------------------------------------

Since it's the older game, we may think of it as the standard revolving positional game in this text, despite the fact that Promotions and Demotions was an independent discovery. In fact, ProDem was the first game we played, and it was then that many different and yet related ideas appeared.

Firstly, the rules of ProDem:
-----------------------------------------------------
PROMOTIONS & DEMOTIONS [aka "even-up, odd-down"]

1. The FIDE rules apply except in the following:
2. On even turns, a moved (non king) man is promoted after move completion.
3. On odd turns, a moved (non king) man is demoted after move completion.
4. The Promotion/Demotion system has this ordering: P < N or B < R < Q.
5. Pawns on the 1st rank may move 1 or 2 squares.
6. Pawns on the 8th rank cannot move, but may be captured.
7. There is no En-Passant, Mate, Check or Castling.
8. The winner is whoever first captures the opponent's King.
9. White does not play on turn 1.

notes:

* A Pawn can promote to Bishop or Knight at the mover's choice.
* A Rook can demote to Bishop or Knight at the mover's choice.
* Queens cannot be promoted, so they cannot move on even turns.
* Pawns cannot be demoted, so they cannot move on odd turns.
* Since every pawn promotes when moving, there is no FIDE promotion.
* Black must start, with a Knight's demotion.
(helps neutralize 1st move advantage).
----------------------------------------------------

Here goes two sample games:

1.   --     Nf6(P)
2.   c4(B)   e6(B)
3. B:e6(P)  Qe7(R)
4. e:f7(B)  R:B(Q)
5.  Qc2(R)  Nc6(P)
6.   g3(B)   h5(N)
7.  Bg2(P) N:g3(P)
8. f:g3(B)   d6(B)
9. B:d6(P) B:d6(P)
10  Nf3(R)   d5(B)
11.  Rc5(B)  Rh4(N)
12.  Nc3(R) N:g2(R)
13.  Rb1(B) B:a2(P)
14.  Bh7(R)  Bc6(R)
15. Rhf1(B)  Rg6(N)
16.  Bg2(R)   a6(N)
17. R:g6(B) Q:g6(R)
18. Rh8(Q)+  Kf7
19. Qxa8(R) Nxc5(P)
20.   b3(B)   b5(B)
21. B:e6(p)+  Kd7
22. R:c5(Q)+  K:e6
23. Rf5(B)+   Kf7
24. Rf8(Q)+   1-0

Final Position:
. . . . . Q . .
. . p . . k p .
. . p . . p r .
. b Q . . B . .
. . . . . . . .
. . . . . . . .
p . . O O . . O
. . B . K . . .

[note: even if these games have non royal Kings, we still use the + symbol which means some piece is attacking the King]

1. --        Nc3(P)      
2. b3(B)     d5(B)      
3. Bb2(P)    Bf5(P)      
4. c4(B)     e6(B)        
5. Ne3(P)    Bc4:B(P)    
6. h4(B)     c4:B(B)    
7. Bh4:Q(P)  Bb3:Q(P)    
8. Nc3(R)    Ra8:P(Q)    
9. Rb1(B)    g6(B)      
10.Bb1xB(P)  Be6:P(P)    
11. g6:f7(B)+  K:f7        
12. Rh5(B)+    Ke7          
13. d3(N)      a5(B)        
14. Kd2        Ba:Rc3(P)+  
15. b2:c3(B)   Nf6(R)      
16. Ke1        Rg8(B)
17. g4(N)      Rf5(Q)
18. Bf6(P)+    Qxf6(R)
19. Ne5(R)+    Re6(Q)
20. R:Qe6(N)   K:e6
21. Be8(R)+    Kd7
22. Re8e5(N)+  Ke6
23. Bh3(R)     a1(B)
24. Kf1        B:e5(P)
25. resigns    0-1

Final Position:

. . . q . b b .
. p p . . . . p
. . p . k . . .
. . . . p . . .
. . . . . p N .
. . . . . O . R
. . . . O O . .
. . . p . K . .

Other remarks:

* The Rook is probably the strongest piece. It may move any turn, and still transforms into a strong piece.
* A (possibly good) method of play would be to always move your king on odd moves, so your piece strength constantly went up and never down. Hwever, this would waste so much time it probably wouldn't pay off anyway, since a player doing that increases his army, but slows by half its efficiency.
* Of course, making the other player moves his King on a even turn, makes him lose a promoting turn.
* A pawn on the last rank cannot move. That is especially bad, since the other player can use it as a protecting wall.

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

Well, taking different behavior given a turn number is one possibility, others exist:

which colour square the piece is on
which colour square the piece goes to
whether the piece changes square colour when it moves
whether the piece moves forward or back (allowing no promotion for sideways)
whether the piece has any immediate neighbours or not
whether the piece is making a capture or not

These options can be divided into two groups, where the game is completely defined by presenting:
a) merely the board and the next player
b) the board and the next player and some extra information (like the turn number as in ProDem)

Notice that in this classification, FIDE Chess belongs to group b), as it may be necessary to state that a King is moved (for castling) or if some pawn was moved (to make en passant capturing). We both feel that group a) games are more elegant, (but that does not mean dropping the others!! :)

With that last point as motivation, Bill invented the next game:

------------------
MOVE UP, TAKE DOWN
~~~~~~~~~~~~~~~~~~
1. All men move as in chess, except there is no castling or en passant.

2. Movement is compulsory, and once his king is captured a player loses.

3. Once a move is made, that piece immediately changes into the next one up this cycle -  P to N to B to R to Q to P; except if it was a capture,
then the order is the opposite.

4. A pawn on the 1st rank may move 1 or 2 spaces if not capturing.
  A pawn on the 8th rank may never move again, but can be captured.

5. If there are no pawns on the board before a move is to be made,
  the order changes to N B R Q N, (or its reverse for captures).
------------------

We would like you to specially notice rule 5. Its motivation was to ensure that a board with no pawns would no longer require knowledge of its *orientation*, similar to the "no-external-info" mentioned above. However, it has resulted in a new idea:- that when a certain condition is true (no pawns), the game dynamics changes. This is not a common feature in Chess Variants, but may be an excellent concept to extend.

And here goes a sample game

1. g4(N)   d5(N)  
2. e3(N)   f6(N)  
3. Ne:N(P) Q:d5(R)
4. b4(N)   b6(N)  
5. c4(N)   a6(N)  
6. N:f6(P) e:f6(Q)
7. N:b6(P) c:b6(Q)
8. Be2(R)+ Be7(R)
9. N:d5(P) Q:a1(R)
10 Nc3(B)  Nf6(B)
11 B:a1(N) B:a1(N)
12 R:e7(B) K:e7    
13 Ba3(R)  Bd7(R)  
14 Nf3(B)  Rd6(Q)  
15 Rd3(Q)  Nc5(B)  
16 Be4(R)+ Kd8    
17 Rh4(Q)+ Kc7    
18 Q:a1(R) B:f2(N)
19 Q:f2(R) Q:f2(R)
20 K:f2    Ra7(Q)+
21 Ke2     Re8(Q)+
22 Kd1     Na6(B)  
23 Rf1(Q)  B:d3(N)
24 Q:d3(R) g5(N)  
25 h4(N)   Ne4(B)  
26 Rc3(Q)+ Kd8    
27 Nf3(B)  B:d5(N)
28 B:d5(N) Q:d5(R)
29 a3(N)   h6(N)
30 Nc4(B)  Q:a1(R)+
31 Q:a1(R) Ng4(B)+
32 Kc2     R:d2(B)
33 K:d2    Qe4(N)+
34 Kd3     Nd6(B)?
35 Bg8(R)+ Bf8(R)
36 R:g4(B) Rf6(Q)
37 Ra5(Q)+ 1-0

Final Position:

. . . k . . . .
. . . . . . . .
. . . . . q . .
Q . . . . . . .
. . . . . . B .
. . . K . . . .
. . . . . . . .
. . . . . . . .

SloPro LISBON

Winner is who first makes a connected group touching three non-adjacent
sides; or one touching two opposite sides; or closed circuit surrounding at least one space or opponent stone.      122234445666... moving with different-group restriction. Corners belong to both sides.    

Sample Game:

OOO starts
 1. p7
 2. m6 m8
 3. n7 n9
 4. l9 q8
 5. p5 o8 n11
 6. o6 r7 m10 q10
 7. j7 p3 k12 o10
 8. m4 j5 q6  s10
 9. g4 g6 k7 h10 q12
10. h3 k4 f5 j11 t11 t13
11. h5 j3 k6  m2 n5  r9
12. f2 k2 o2 v13 l5  t9
13. u8 i4 n3 v11 p9 s12 k10
14. h1 l3 h7 l11 v7 u12 v15 x9
15. n1 r5 u4 k14 u6 q14  s8 y8
16. j1 s2 i8 t15 z7 p11  z9 m12
17. c6 i6 w6 w10 A8 s14 A10 w14 A6
18. e4 t5 f7 t7  B7  a8  d9  B9 g10 o12
19. b9 j9 o4 t3  w8  y6 x11 e10 h11 u14
20. s4 e6 x7 c8 i10 y10 d11 g12 y12 j13
21. C8 d7 f9 r3  y4 e12 i12 i14 n13 n15 x13
22. f3 x3 v5 z5 c10 z11 f13 l13 o14 h15 l15 r15
23. e8 v9 h13 p15 & resign

Final position:

abcdefghijklmnopqrstuvwxyzABC    
       x x . o . . . .           1
      x . x o x . x . .          2
     x x o x o o o o . x         3
    x o o x x o . x o . o        4
   . x o x x o o o x x . x       5
  o x o o o x x x . o o o o      6
 . o x x o o o o x x x x x x     7
x x o . x : x o x o o o o o o    8
 o x o o o x o o o x o x x x     9
  x o x x o x o x x . o x o     10
   x . o x x o x . x o o x      11
    o x o o x x o o x - x       12
     x o x x o . . x x o        13
      . o o - x o o o o         14
       x . x oo x x x          15
abcdefghijklmnopqrstuvwxyzABC

XXX wins at k8 and then either f11/m14 next turn

DISPATCH GAMES

Dispatch is a game, or set of games, where starting with a stone on board, the player orthogonally dispatches a seed to another empty cell and then grows a pattern (usually a mino, like a tetrominoe or a pentominoe). Check the rules here.

Here are two games:

TETROMINOE DISPATCH

       XXX              OOO
  1. c3-h1234        c9-j8h8910
  2. h4-h567,g78     j3-j4567
  3. g8-g9,10,11,f11 c9-b234c4
  4. h5-d4bcd5       c9-de9e1011
  5. g8-cdef8        c9-b789a7
  6. c8-abc6c7       j3-j12kl1
  7. c3-abc1c2       j8-k891011
  8. a1-a2345        resigns

   a b c d e f g h j k l
1  x x x . . . . x o o o
2  x o x . . . . x o . .
3  x o x . . . . x o . .
4  x o o x . . . x o . .  
5  x x x x . . . x o . .
6  x x x . . . . x o . .
7  o o x . . . x x o . .
8  . o x x x x x o o o .
9  . o o o o . x o x o .
10 . . . . o . x o . o .
11 . . . . o x x . . o .
   a b c d e f g h j k l

PENTOMINOE DISPATCH

       XXX              OOO
  1. c3-l12345      m3-m456kl6
  2. l5-jk5j6jk7    c13-l13,lmno12
  3. c3-abcde12     l12-cdef11f12
  4. k7-lmn7n56     c11-bd3bcd4
  5. c3-cde2e34     f11-e5f2345
  6. e2-efg1g23     f5-f6789,f10
  7. b12-b7891011   f4-g4,h1234
  8. c2-a2345       b4-a678b56
  9. l1:m1mn2n34    c11-c10,9876
10. k7-k11121314l1 f10-jklm10m9
11. k11-hj11h8910  f12-gh12h131415
12. e12-efg13g1415 f6-gh5gh6h7
13. h9-jklmn9      o12-no10o98p8
14. h8-jklmn8      l12-l1415m14n1314
15. n4-o4567p7     c13-d13def14f15
16. b12-b1314c1415d15   h4-j4k1234
     draw 30-30 (!)

  a b c d e f g h j k l m n o p
1  . . . . x x x o . o x x . . .
2  x x x x x o x o . o x x x . .
3  x o x o x o x o . o x . x . .
4  x o o o x o o o o o x . x x .
5  x o . . o o o o x x x . x x .
6  o o o . . o o o x . . . x x .
7  o x o . . o . o x x x x x x x
8  o x o . . o . x x x x x x o o
9  . x o . . o . x x x x x x o .
10 . x o . . o . x o o o o o o .
11 . x o o o o . x x x x o . . .
12 x x x x x o o o . x o o o o .
13 . x o o x x x o . x o . o . .
14 . x x o o o x o . x o o o . .
15 . . x x . o x o . . o . . . .
   a b c d e f g h j k l m n o p