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]