Neutral Mutator (part III)

Another game that fits nicely with this mutator is Y. The complexity of this game on even quite small boards is amazing:

     abcdefghi    --x---?----o---?--
5       ?          e1  f4   e4  h2
4      x ?         c1  c3   f2  e5
3     x o ?        g1  d4   a1  i1
2    x . o o       b2  g3  h2i1 a1
1   ? x x ? o     c3d4 g1  resigns

'o' must swap (as there is only one empty cell), and though momentarily creating a winning path, must immediately destroy it by exchanging one of his vital stones. But in doing that, 'o' provides a winning path for 'x'.

Neu-Reversi can be played in two ways.

(a) NeuVersi: a neutral stone can be dropped anywhere on the board;
(b) AdNeuVersi: it must be adjacent to some stone(s) of some player(s).

In both games, the playing of a genuine stone must follow reversi rules, and neutral stones can be turned over to the player's colour as if they were opponent stones; and if two neutrals are flipped, both must be legal reversi moves in the order played.  As always, if a player cannot make a legal move he is obliged to pass, and if both are thus obliged to pass the game ends and the count is done.  Note, there is no need for the extra game-end placement default-option rules in these games.

The discoverers have tried both versions, and found them both to have their own intriguing characters, which are noticeably (though not overwhelmingly) different from the parent game.  In general, as with all Neu-games, there tend to appear more strategic plans and tactical resources than with parent games, for the same-sized boards.

Here is an example for NeuVersi :

    --x---?-----o---?--
1.  e3  g7    f3  c4
2.  f4  f6    b3  h8
3.  c5  b4    a4  g4
4.  a2  h4

. . . . . . . .  1
x . . . . . . .  2
. x . . x o . .  3
o o x x x x ? ?  4
. . x x x . . .  5
. . . . . ? . .  6
. . . . . . ? .  7
. . . . . . . ?  8
a b c d e f g h

'x' tries to get the h8 corner in the next turn. However, 'o' moves 4... h4 a8, with the following result:

. . . . . . . .  1
x . . . . . . .  2
. x . . x o . .  3
o o o o o o o o  4
. . x x x . . .  5
. . . . . ? . .  6
. . . . . . ? .  7
? . . . . . . ?  8
a b c d e f g h

if 'x' swaps h8, there will be only one neutral left (a8) which provides no captures. So, the move is illegal and 'x' cannot take the corner. [cont.]

Neutral Mutator (part II)

In these neu-games, the instances of two game plans being executed quite independently of each other, is much more common than in regular games. The neutral structures serve to undermine enemy positions and to create optional paths to the game's goal. It is a very flexible tool.

I realized that this mutator could be used in many more games. But before continuing, as Bill Taylor noted, the rules would not be totally specified unless we say what happens when the board is almost full:

1) When there is 1 space and no neutrals left: player to move fills the space;
2) when there is 1 neutral and no spaces: mover converts the neutral to his own;
3) when 1 of each: mover fills the space, then opponent converts neutral.

As a default option, these end-game rules always apply.

A second experiment was Gomoku. We were surprised to see what a remarkable game was discovered. The complexity and balance of Neumoku seems extraordinary.

NEUMOKU: On a unlimited square board, each player may:
       * Drop a friendly stone plus a neutral stone
       * Flip two neutral stones into friendly stones and then flip another friendly stone into a neutral stone
       The goal is like Gomoku.
       PIE RULE: After the third move, the second player may swap sides.

A sample game:

   --x----?-----o----?--
1.  n3  m5     o2   n4
2.  l6  q2     o3   p2
3.  o4  p5     m2   q1
4.  n2  n6    n4p2  o2
5. q1o2 n2     p4   q5
6. n2q5 n3     p3   m3
7. n3p5 q5     p1   q3
8.  p0  q6    q5q6  p3
9.  l4  k5    m3q3  p2
10. p2q2 q1     r2   r3

Actual Board:

j k l m n o p q r s
. . . . . . . . . .  -1
. . . . . . x . . .   0
. . . . . . o ? . .   1
. . . o x x x x o .   2
. . . o x o ? o ? .   3
. . x . o x o . . .   4
. ? . ? . . x o . .   5
. . x . ? . . o . .   6
. . . . . . . . . .   7

Here, 'o' has a winning sequence:

   --x---?-----o---?--
11.  o5  l5    r7  s1
12.  s7  l3    q4  t0

j k l m n o p q r s t u
. . . . . . . . . . . . -1
. . . . . . x . . . ? .  0
. . . . . . o ? . ? . .  1
. . ? o x x x x o . . .  2
. . . o x o ? o ? . . .  3
. . x . o x o o . . . .  4
. ? ? ? . x x o . . . .  5
. . x . ? . . o o . . .  6
. . . . . . . . . x . .  7
. . . . . . . . . . . .  8

Next turn, 'o' wins at column 'q' or the diagonal from p4 to t0. [cont.]

Neutral Mutator (part I)

Joao Neto has found a most promising new game mutator which seems applicable to a number of games. It is most applicable to games which begin with an empty board and continue with players adding a piece per turn. Obvious examples are: almost all connection games, Go, Go-moku, Reversi. Initially, this idea was meant to create a Hex variant, called Nex (or Neux):

NEX: On a Hex board, at each turn, the player must do one of:
       * Drop a friendly stone plus a neutral stone;
       * Flip two neutral stones into friendly stones and then
          flip a different friendly stone into a neutral stone.
The goal is as for Hex, with a connecting path including no neutrals.  

Here is a sample game:

    Vertical   Horizontal                      
  --v-----?-----h------?--                          
 1. b11   f6    d7     b8
 2. e7    g5    h3     f4
 3. i3    g3    g6     e6
 4. f6g5  a11   d10    h4
 5. f9    d9    g3h4   d7
 6. e4    f3    f4e6   d10
 7. i4    d6    h5     e3
 8. d6d7  g5    e3f3   f4
 9. i5    c4    h7     f8
10. h6    d3    g7     c10
11. d3c4  f6    f8d9   g3
12. i7    b10   i6     b9
13. b9b10 h6    c10b8  f3
14. c8    k5    d5     b11
15. e5    e9    a11b11 b8
16. e9k5  b9    e8     k2
17. j7    k7    j6     j2
18. k6    g4    j5     i2
19. k4    k1    k3     j3
20. j4    g8    i2j2   d5
21. Resign

Final Position:

  a b c d e f g h i j k
1  . . . . . . . . . . ?
2   . . . . . . . . h h ?
3    . . . v h ? ? h v ? h
4     . . v . v ? ? h v v v
5      . . . ? v . ? h v h v
6       . . . v h ? h ? h h v
7        . . . v v . h h v v ?
8         . ? v . h h ? . . . .
9          . ? . h v v . . . . .
10          . v h ? . . . . . . .
11           h h . . . . . . . . .
              a b c d e f g h i j k

These games are full of tactical subtleties. An interesting feature is that no piece is totally useless, because it can always be used to swap two neutrals. Swap battles tend to occur after some critical mass of neutrals is achieved. Forcing moves, (i.e. where the player forces the opponent to drop a piece of their own colour) are a key to success in this game,   as that is the only sure way to stop him flipping two '?'s next turn.

[cont.]

A new tiling for board games?

Anybody seen this pattern used on board games? There is a mix of cells with different connections, some with four connections and others with six. Also, its dual (if you play in the intersections) has three and four connections. This may be a good playing field for games exploiting the compromise between square and hexagonal boards.

Trabsact Sagme Diaries

There's art between the keeping and the releasing. When we talk about desires, this is called wisdom. When we talk about games, this is called mastery. [T.Sagme, Meditations]

Hop Chess

0. Same as FIDE except:
1. On each turn, each player must do both the following actions:
   1.1. Move a friendly chess piece; then
   1.2. Move his hopper to any empty square
2. If a chess piece moves onto a hopper (of either color),
    it must move  again (it's invalid to return to the initial square).
   2.1. Kings cannot move onto a hopper, nor castle across one.
   2.2. If the piece cannot move after the hopper, the move is invalid.
   2.3. If a queen lands on a hopper, it continues with the same type of
    movement that it used to get there (ie, both orthogonal or
    both diagonal moves).
   2.4. En-passant is still possible, but not if either pawn moves twice
3. Initially, the hoppers start off-board.
   White's first move is restricted to a piece move only.
  
Notes
  
* When moving the hopper, the player may place it where it was.
  He does not have to change the place of his hopper every turn.
* Pieces may move over hoppers.
* A piece may execute two hops, if it moves from one hopper to another.
* A hopper extends the moving/capturing range of pieces,
  so a King may be under check via one or both hoppers.
* It is not possible to capture more than one piece per move,
  since hoppers are always on empty squares.
* A pawn may promote onto a hopper and then the player must move
  the promoted piece.

Example   (@ white hopper, # black hopper)

r . b q k b n r    Some valid moves:
p p . . p p p p     Bc8-f5-e4
. . n p . . . .     d2-d4:c5
. . p . . # . .     Nc6-d4-f5:g3
. . . @ . . . .
. . . . . . O .
O O O O O O B O
R N B Q K . N R

A game:

HOP-CHESS
=========
 1. e4         Nf6  d5
 2. d4   d3    e6   b4+  
 3. Nc3  g5    Be7  b4  
 4. B:f6 e5    e:d4 b4    
 5. Q:d4 e5    g:f6 b4    
 6. e:f6 e4    Na6  c5    
 7. f:e7 d5    c:d4 b4    
 8. e:Q+ f3    K:Q  e8+
 9. Nce2 f3    d3   b4    
10. c:d3 c1    Nd4+ e8    
11. Kd2  h3    N:b2 c4+
12. Kc2  a4    Na3+ e6
13. Kb3  c1    Re5  a5
14. Ne4  c6+   Ke8  e3+
15. N:e5 c6    a5   a4+
16. K:a3 b1    b5   b4+
17. B:b5 e1    resign

r . b . k . . .
. . . p . p . p
. . . . . . . .
p B . . N . . .
. # . . . . . .
K . . . . . . .
O . . . . O O O
R . . . @ . N R

Even though the existence of hoppers makes the opening and middle game much more attack-oriented, and also the distant endgame, it dies NOT seem to be the case for most K & P endgames, even with a minor piece or two.  The reason is, that the weaker side can use his hopper to stop the stronger king from ever making a breakthrough into the enemy area, as usually happens in endgames.  So there are SOME games at least that are harder to win in the hopper version. But not many.

Trabsact Sagme Diaries

The way to one's goal often lies in the opposite direction. [T.Sagme, Meditations]

Ataxx

Ataxx & Hexxagon are very interesting games but there doesn't seem to be any strategic element, merely tactics. However, on much bigger boards, there might be some strategy. This variant is a very large game of Hexxagon with a restricted progressive mutator (which speeds and adds depth to the game) and with a more mixed-up start (to allow more flexibility of directions).

===
1344 HEXXAGON

Every move must be from stones already on the board at the start of the turn
===
  abcdefghijklmnopqrstuvwxyzABCDEFG      XXX    OOO
          x . . . x . . . o          1.  v4  n6,m5p4,f6
         . . . . . . . . . .         2.    
        . . . . . . . . . . .        3.    
       . . . . . o . . x . . .       4.      
      o . . . . . . . x . . . o      5.      
     . o . . . o . . . . . . . .     6.        
    . . . . . . . . . . . . . . .    7.        
   . . . . . . . . . . . . . . . .   8.        
  o . . . x . . . . . . . o . . . x  9.  
   . . . . . . . . . . . . . . . .  10.          
    . . . . . . . . . . . . . . .   11.        
     . . . . . . . . . . . . . .    12.        
      x . . . o . . . x . . . x     13.      
       . . . . . . . . . . . .      14.      
        . . . . . . . . . . .       15.    
         . . . . . . . . . .        16.    
          x . . . o . . . o         17.  

Trabsact Sagme Diaries

Let the players be silent, Let the pieces talk. [T.Sagme, Proverbs 3,2]

13(4) progressive mutator

Amazons is another example of a game using the progressive 13(4) mutator. So, the first player makes one move, then the second player makes three moves, and then, on every remaining turn, both players make four moves. There is a restriction (we should always attach restrictions to progressive mutators): a piece can only move once per turn. Here is a board after 7 moves:

a b c d e f g h i j k l m n o p q r s
. . . # y # . . . . . y . . . o . . . 1
. . . . # # . # . . . . . . . y . . . 2
y . . . # . # . . . . . . . . . . . . 3
. # # # # . # . . . . . . . . . . . . 4
. # . . # . . . . o . . . . . . . . . 5
# # . . . . . . . . . . . . . . . . . 6
# . . . . o # . . . . . . . . . . . . 7
. . . # . . . . . . . . . . . . . . o 8
. . . y . . . . . . . . . . . . . . . 9
. . . . . . . . . . . . . . . . . . . 10
. . . . # o . . . . . o . . . . . . . 11
. . . . y . . . . . . . . . . . . . . 12
. . . y . . . . . . . . . . . . . . . 13
. . . . # . . . . . . . . . . . . . . 14
. . . # . . . . . . . . . . . . . . . 15
. . . y o . . . . . . . . . . . . . o 16
. . . # . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . 18
. . . . . . . . # . . . . . . . . . . 19
a b c d e f g h i j k l m n o p q r s

Moves: Y vs O

1. s4d4/b4
1... a7d7/g4 d19g16/g7 l19l16/i19
2. a8a5/b5 d1d2/d1 d4d3/d4 h19c14/c4
2... h1g2/e2 d7e6/e3 l16l11/e4 a12b11/b6
3. a5a9/e5 d3a3/a7 d2e1/g3 p19p2/h2
3... g2j5/f1 e6f7/f2 b11f11/a6 g16e16/e14
4. a16d16/d17 c14d13/d15 a9d9/d8 s12e12/e11


A Quoridor variant

FOUR-WAY WALLS
==============
* One player has stones n s e w, the other N S E W.
* Each stone must try to cross the boundary furthest in its name-direction.
* With 13444 equalizer, in each turn each of a player's stones, (move order at the mover's discretion), must move one orthogonal step; then a wall is played (but not on the boundary); all as in Corridor.
* If any stones are adjacent to the moving stone in its chosen direction, it may jump them to the next vacant cell. If a wall blocks this direction part-way through such a jump, either unblocked right-angle may be turned.
* The winner is the first player to get three stones off the board.


  A   B   C   D   E   F   G   H   I   J   K
a + - - - - - - - - - - - - - - - - - - - +
  :                                       :
b :   +   +   +   +   +   +   +   +   +   :
  :             s                         :
c :   +   +   +   +-------+-------+   +   :
  :                     W                 :
d :   +   +   +-------+   +   +   +   +   :
  :         S |     e |                   :
e :   +   +   +   +   |   +   +   +   +   :
  :         E |       |                   :
f :   +   +   +   +   +   +   +   +   +   :
  :       |                 N |           :
g :   +   +   +   +   +   +   |   +   +   :
  :       |         n         |           :
h :   +   +   +   +   +   +   +   +   +   :
  :                             w         :
i :   +   +   +   +   +   +   +   +   +   :
  :                   |                   :
j :   +   +-------+   |   +   +   +   +   :
  :                   |                   :
k + - - - - - - - - - - - - - - - - - - - +

   N E S W    wall    n e s w    WALL
   """""""""""""""""""""""""""""
1. - - - W    CEj     e e s -    Fik
2. N E S W    GIc     n e w w    Cfh
3. N N S W    EGc     n e w w    DFd
4. N N W W    Hhf     n e w s    Ddf  
5. N E S N    Fdf

This is a very fun game. Both player must, at each turn, decide which enemy player they want to delay, while advancing their own as far as possible.

Trabsact Sagme Diaries

Let complexity emerge - do not seek it out. [T.Sagme, Proverbs 2, 14].

Self-limitation

We, email game inventors (not many I know), tend to create (and play) games that are ascii-friendly. The same happened with the appearance of Zillions. Many new games are Zillions-friendly, especially Chess Variants submitted at CVP's contests (there are nearly one thousand CV's for Zillions). I'm not saying it is bad, but it is always important to notice our self-imposed limitations.

Trabsact Sagme Diaries

Defeat may be victory, below the surface of shallow facts. [T.Sagme, Meditations]

BIQALA

Here is an idea for a double Mancala game played with two concentric rings:

 3 3 3 3 3 3   A's outer board (3 p/cell)  K J I H G F
3  4 4 4 4  3  A's inner board (4 p/cell) L  D C B A  E
3  4 4 4 4  3  B's inner board            e  a b c d  l
 3 3 3 3 3 3   B's outer board             f g h i j k

0. The rules of Wari are used, except:
1. The movement is around the board of the emptying cell only.
2. For his move, a player may transfer any number of stones of a friendly cell to one or more adjacent friendly cells of the other board. If this move is made, the player must pick and transfer one of those stones to the opponent as a captured stone.

Still about a little Go change

[check previous] What should happen around the edges? Should pushes be allowed? The rule can be restated as: "If an isolated piece is in atari, the other player may push it into that empty cell."

This means that the next move would be possible:

  . . . .       . . . .
  . x o .       . x o .
  x . x o       x x o <
  [edge]        [edge]

This rule still has the effect of eventually create new eyes and more KO problems. One way to solve that is to state the rule like this: "If an isolated piece is in atari, the other player may push it into that empty cell, placing a new stone on that cell".

The previous move would result on the next position:

  . . . . .
  . x o .
  x x o o
  [edge]


Cost

Victory is nothing if defeat is nothing. [T.Sagme, Meditations]

BIVERSI

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

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

Rules and other rules

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

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

The PIE rule

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

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

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

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

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

Little Go change

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

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

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

Defeat

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

SEND IT

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

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

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

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

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

Initial moves on a square board:

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

Blockdance

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

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

abcdefghijklmnopqrstuvwxyzABC   Player Y     Player O

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

abcdefghijklmnopqrstuvwxyzABC

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

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

The PIE Rule

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