Trabsact Sagme Diaries

Mar 23, 2007

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 . . . .
. . . . . . . .
. . . . . . . .

Mar 22, 2007

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

Mar 20, 2007

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

Sacrifice Mutator

Sacrifice Reversi (by Patrick Duff) is a Reversi variant with an extra rule: Instead of making a regular Reversi move, a player can choose to flip one of his own stones on board. There's also a KO rule to avoid repetitions.

This idea is a game mutator, it can be extended to modify many other games. Reversi Draughts or Reversi Chess could make a difference in some positions. Other games, like Moku or Hex would not produce interesting variants, since there's no position where an enemy piece is better than your own stones. I'm not sure about Reversi Go. Could it be possible to make a position where an enemy stone is better than a friendly one?

Meta-Game

Nick Bentley sent me an idea for a meta-game with an automatic balacing mechanism, which is called Mind Ninja:

Take any boad which begins empty. The game proceeds in 5 steps

Player 1 decides three things, which he must convey to player 2:

what the pattern will be;
whether the builder or blocker will receive free moves in step 3;
how many free moves that player will receive.

Then, player 2 decides which player is the builder, and which is the blocker.
Either the builder or blocker takes free moves as specified in step 1.
Starting with the builder, the players alternate moves.
The game ends either when the board is completely full or the pattern has been built. If the pattern has been built, the builder wins. Otherwise, the blocker wins.

Mar 16, 2007

More hex-mokus

M u l t i m o k u Go Moku on a 3.4.6.4. tiling There are 6 rows through each hexagon, 4 through each square and 3 through each triangle. The ratio of Hexagons:Squares:Triangles = 1:3:2, so the average number of rows through a cell is 4 as in standard Go Moku. (The 4.6.12 tiling gives the identical game as the 3.4.6.4. tiling. Each dodecagon has 6 rows, hexagons have 3 rows, squares have 4. The topology of the game is the same.) In this ascii representation, 'H' is the center of a hexagon, 'S' is the center of a square and 'T' is the center of a triangle: . . . . . . . . . . . . . . . . . H T . . . . . S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of rows --> Each hexagon 6 rows through it: . 1 . . . . . 6 1 2 . . 5 6 2 3 . 5 6 1 2 3 . . 5 3 . 4 4 4 H 4 4 4 . 3 5 . . 3 2 1 6 5 . 3 2 6 5 . . 2 1 6 . . . . . 1 . Each square has 4 rows through it: . . 2 1 . . . . 2 . 3 . 4 1 3 . . 4 2 3 . . . . S . . . 3 2 4 . . . 3 1 4 . . 2 . . . 4 . . 1 . 4 2 . . . . . . 1 . . . . Each triangle has 3 rows through it: . . 2 . . . . 1 2 . . . . 1 . . 2 2 T 2 2 2 2 . 2 . . . . 2 1 . . . . . . . . 2 . . 1 . . . . 1 . 2 . . . 1 . . . . . . . The 4.6.12 tiling gives the identical game as the 3.4.6.4. tiling. Each dodecagon has 6 rows, hexagons have 3 rows, squares have 4. The topology of the game is the same. Proposed board for Multi-Moku Three move equalization No 3-3 or other placement restrictions abc d efg h ijk l mno p qrs t uvw x yzA B CDE 1 . . . 2 . . 1)l13 p15 3 . . . . . . . 2)t17 swap or play 4 . . . . 5 . . . . . . . . . . . 6 . . . . . . 7 . . . . . . . . . . . . . . . 8 . . . . . . . . 9 . . . . . . . . . . . . . . . 10 . . . . . . . . 11 . . . . . . . . . . . . . . . 12 . . . . . . . . 13 . . . . . X . . . . . . . . . 14 . . . . . . . . 15 . . . . . . . O . . . . . . . 16 . . . . . . . . 17 . . . . . . . . . X . . . . . 18 . . . . . . . . 11 . . . . . . . . . . . . . . . 20 . . . . . . . . 21 . . . . . . . . . . . . . . . 22 . . . . . . . . 23 . . . . . . . . . . . . . . . 24 . . . . . . 25 . . . . . . . . . . . 26 . . . . 27 . . . . . . . 28 . . 29 . . .

Hex-mokus

Moku games (ie, achieve n in-a-row pattern to win) are usually played on square boards with four directions (horizontal, vertical and two diagonals). When translating to a hex board there are one problem, hex tillings only have three directions, which is too few, so the direct translation of hex-moku is a very drawish game, since there are no space to create winning positions with multiple threats. One way to prevent this is to use six directions to win, extending the types of lines inside the board. Here are some possible examples with sample games, including a standard three directions (which ended in a not so surprinsing draw):

Triangular Go Moku on the vertices of a hexagonal grid. Winning rows in six directions. AB CD EF GH IJ KL MN OP QR ST UV WX YZ ab 1 . . 2 . . . . 3 . . . . . . 4 . . . . . . . . 5 . . . . . . . . . O 6 . . . . . . . . . . . . 7 . . . . . . . . . . X . . . 8 . . . . . . . O . . X . . . 9 . . . . . . . . X O O . . . 10 . . . . . . O . X X . . . . 11 . . . . . . O X X X X O . . 12 . . . . X . X X O . . X . . 13 . . . . . O X O O . . . O . 14 . . . . X O O O . . . . . . 15 . . . . . O . O . . . . . . 16 . . . . X . . . O . . . . . 17 . . . . . . . . X X . . . . 18 . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . 22 . . . . . . . . . . . . 23 . . . . . . . . . . 24 . . . . . . . . 25 . . . . . . 26 . . . . 27 . . "O" won with a row at M10, N11, O13, P14, Q16 HEX Go Moku I (winning rows in 3 directions) Sample Game: XXX OOO 1. i9 j10 2. i10 j11 3. j9 k9 4. i8 i7 5. i11 i12 6. h7 k10 7. g6 f5 8. h8 j12 9. h9 j13 10. j14 h6 11. j8 g8 12. k8 l8 (f) 13. f9 g9 (f) 14. h11 h10(f) 15. h12 i13 16. k13 i5 17. g5 g3 18. j6 i3 19. i4 f6 20. f4 k5 21. j5 j7 (forced) 22. j4 n10 Draw . . . . . . . . . 1 . . . . . . . . . . 2 . . . . . . O . O . . 3 . . . . . X . . X X . . 4 . . . . . O X . O X O . . 5 . . . . . O X O . X . . . . 6 . . . . . . . X O O . . . . . 7 . . . . . . O X X X X O . . . . 8 . . . . . X O X X X O . . . . . . 9 . . . . . . O X O O . . O . . . 10 a . . . . . X X O . . . . . . . 11 b / . . . . X O O . . . . . . . 12 c . . . . O O X . . . . . . 13 d / . . . . X . . . . . . . 14 e . . . . . . . . . . . 15 f . . . . . . . . . . 16 g . . . . . . . . . 17 h / / / i j k l m n o p q HEX Go Moku II with 3 move equalization (winning rows in 6 directions) Sample Game: XXXX OOOO 1 g11 m9 2 s7 m7 3 m11 j8 4 p10 p6 5 g9 n8 6 l10 o7 7 q5 (f) k7 wins in 3 8 i7 or q7 l8 (double 3) abcdefghijklmnopqrstuvwxy - 1 - - - - 2 - - - - - - - 3 - - - - - - - - - - 4 - - - - - - - - X - - - - 5 - - - - - - - O - - - - 6 - - - - -(O)O O - X - - - 7 - - - - O - O - - - - - 8 - - - X - - O - - - - - - 9 - - - - - X - X - - - - 10 - - - X - - X - - - - - - 11 - - - - - - - - - - - - 12 - - - - - - - - - - - - - 13 - - - - - - - - - - 14 - - - - - - - 15 - - - - 16 - 17 I see now that 5) ... n8 wins in 4 always ending the same double three at l8. Since 5) g9 (or s5) was forced, the 4) ... p6 wins in 5. The first two 'X' moves I suggested didn't even slow 'O' down.

More information at http://www.di.fc.ul.pt/~jpn/gv/hexgomoku.htm.

SCALA

Scala is a little-known abstract game published in 1986 by Skill Games.
It has features reminiscent of Halma, Camelot, and Lines of Action.

RULES. The game is played with the following setup:

14           [o] 13          . . . 12       . . . . . 11      . . . . . . . 10    . . . X X X . . . 09  . . X X X X X X X . . 08  . . X X       X X . . 07  . . O O       O O . . 06  . . O O O O O O O . . 05    . . . O O O . . . 04      . . . . . . . 03        . . . . . 02          . . . 01           [x]    a b c d e f g h i j k

* GROUP - A set of connected (orthogonally or diagonally) stones.
* TURN - On each turn, each player moves or jumps one stone.
  + MOVE - A stone may move to any adjacent (orthogonal
           and diagonal) empty cell.
  + JUMP - A stone may also jump over any stone (friend or foe)
           landing on the opposite empty cell (it must be empty).
           A player may make on the same turn, multiple jumps with
           the same stone, and may change direction after each jump.
  + It is not valid to move or jump to its own first cell.
* CONNECTION - After each move or jump, any stones not connected
              (orthogonally or diagonally) to another stone of the
               group is captured.
* CAPTURE - If, after a move or jump, the group is divided, the
            larger of the remaining groups containing pieces of both
            colors survives.
           The smaller group, or the group containing pieces of a
            single color are removed from the board.
           There is only one connected group on the board, after
           each move.
           Some other restrictions:  It's not valid
           to produce two groups with the same number of stones,
           if both groups have stones of both colors.
           It's not valid to separate the two colors completely.
* GOAL - Wins the player who advances one stone into the opponent's
        first cell (the cell marked in the first diagram with a
         color dot).

More information at http://www.di.fc.ul.pt/~jpn/gv/scala.htm

Game Sample       Final Position 14          [O]             1. f5-h5-j7       d9-b7-d5-f5 13         . O .            2. d7-d9-f11      f9-d9-d7-d5 12       . O X . .          3. d6-b8-d10      f10-h10-j8-j6 11     . . . O . . .        4. h6-j8-h10-f10  d8-b6-d6-f4 10   . . . X O . . . .      5. f6-d6-b6-d8    c9-c8 09 . . . . X . O X . . .    6. c7-c9-e11      g10-h10 08 . . . .       O O . O    7. f10-g10        h10-f10-f12 07 . . . .       . O O .    8. d8-f10(:bc8)   g9-h10 06 . . . . . . . O X . .    9. g5-h6          h10-j8 05   . . . O . X X . .     10. i7-g9          i9-i7-g5 04     . . . X . . .       11. g6-i8          f5-h5 03       . . X X .         12. h6-i7          j8-h6 02         . X .           13. e6-e4-g4-g6    d5-f5-f3(:c6) 01          [o]            14. g10-e12        h6-h4   a b c d e f g h i j k    15. d10-d11        h4-h3                            16. i6-k8          j6-i6                            17. g6-h6          h8-j6                            18. h7-h8          j6-i5                            19. e11-e13        i5-h4                            20. d11-f13        h4-h2                            21. e13-f14        resigns, 1-0

SCORING HEX-MOKU

Played on a 8 sided hex board, each player gets 1 point for each 4 in-a-row made. The player that gets 7 points or a 5 in-a-row wins the game. Initially, one player drops 3 stones (2 blacks and 1 white) and the adversary decides color (black starts the game).

Sample Game: XXX OOO 1) k2 o8 2) m2 q8 3) o2 q2 4) i2+ g 5) k5 s8 6) m8 u8+ 7) w8 k4 8) m4 n3 9) n5 l3 10) j5 p5 11) h5 f5 12) k6 l7 13) j7 i8 14) i6 g4 15) k8 l9 16) g6 e6 17) i4 j3 (forced) 18) f7 e8 (forced) 19) m6 o6 (forced) 20) h3 & wins 7-1 Final Position: abcdefghijklmnopqrstuvwxyzABC 1 . . . . . . . . 2 O X X X X O . . . 3 . x o O O . . . . . 4 . O x O X . . . . . . 5 . O X X X X O . . . . . 6 . O X X X x o . . . . . . 7 . . x . X O . . . . . . . . 8 . . o . O X X O O O O X . . . 9 . . . . . O . . . . . . . . 10 . . . . . . . . . . . . . 11 . . . . . . . . . . . . 12 . . . . . . . . . . . 13 . . . . . . . . . . 14 . . . . . . . . . 15 . . . . . . . .

Projective Hex

[Bill Taylor: This article is chiefly for rec.games.abstract; but I cross-post to sci.math for the possible interest in tilings of Projective Planes]

One of the great blessings of connection games like Hex and Bridgit is, that victory is certain for one or other side, AND the structure of the game ensures that a victory for one is *automatically* a defeat for the other, with no special rule needed to say so.  So there is no element of a mere "race" to do something first, where both players might achieve this goal almost simultaneously.

Although there is no "social" defect in such races, (e.g. even chess can be so viewed - a race to capture the opponent's king before he captures yours), it is mathematically and game-theoretically slightly unaesthetic, compared to the Hexlike feature of   [win = not(loss)]   by structure.

Hex and Bridgit both suffer from another slight unaestheticity though, to wit, that the two players have (slightly) different tasks; one must make a North/South connection, and the other an East/West one.   Indeed, in Bridgit they even play on different points!  Again, this is no barrier to playing the game or to its being a jolly good game, but again it seems a very slight aesthetic defect.

One game that achieves both goals, i.e. (1) complementary winning conditions and (2) identical tasks; is the excellent "Y" version of Hex, which really deserves to be better known.  However, I introduce yet a new variant here.

------

Some while ago, Dan Hoey and myself jointly invented a game we called PROJECTIVE HEX, invented in this newsgroup, in fact.

It was Dan who, partly inspired by "Y", first ventured onto Projective Planar boards for Hex-like games, but couldn't find a nice winning condition, surprisingly. My contribution was to observe that the condition of making a GLOBAL LOOP, (i.e. a closed path that crossed the boundary an odd number of times) was "THE ONE" - and that it stood out "like a sore thumb". Dan agreed about the sore thumb, and kicked himself for not having seen it before. Dan also constructed a program to print out beautiful Hex-like boards based on the Projective Plane, and thus having 6 pentagons amongst a variable number of hexagons.

My latest contribution has been to change the pattern of the boards slightly, to make them more homogeneous-looking (though not fully homogeneous in fact), and thereby arrange it so that games can easily be played at the keyboard, i.e. by email etc.

For the new Projective Hex, now probably the best abstract board game in the world (ha-ha!), the boards are similar to this as follows...

   A B C        As you see I've had to insert a 27th alphabet letter!   D E F G       Interior cells and interior-edge cells each have 6 H I J K L      neighbours, as in Hex; but the 6 corner cells have 5. M N O # P Q R S T U V      The side dimensions are always n and n+1.   Each edge   W X Y Z       is flipped end-to-end and laid alongside its opposite.

In this 3-&-4-sided board, there are 15 edge cells which thus connect to their opposite cells via Projective connections as shown here...

   z_y_x_w   z/A B C\w     Each of the original edge/corner cells "re-appears" v/D E F G\r    on the opposite side, in lower case letters. q/H I J K L\m q|M N O # P Q|m Each corner still has 5 neighbors. l\R S T U V/h g\W X Y Z/d   c~c~b~a~a

So on the original board, cell  H  is connected to D I N M Q V (in order). Whereas  M  is connected only to  N R L Q H.

The whole collection of 21 hexagons and 6 pentagons makes up a "standard" tiling of the Projective Plane.

To play the game, "Projective Hex", one merely plays as at Hex, filling any one cell your own colour on your turn; and whoever makes a global loop of adjacent cells of their own colour, is the winner.  And, as mentioned above, it is only possible for ONE colour to do so, and at least one of them must always do so, by the time all cells have been coloured. So complementary winning conditions, and equal tasking have both been achieved.

Example: here is a completed game, with both having played 7 moves, and the 2nd player (white) has won, despite his opening disadvantage.

   . X O   . . X O . . O O . . X O X . . X O X . .   X O . .

The loop might be more visible if "ghost" edge cells are entered as well...

    ___o_x    /. X O\x   /. . X O\x /. . O O .\ <. X O X . .> \X O X . ./ o\X O . ./   o~o~x~~~

For actually playing the game, naturally, as always, the first player has an enormous advantage; a sure win, in fact, by the usual strategy stealing argument.  But beyond the very smallest boards it is very hard to find.

This advantage can be left as is, giving the weaker player first move; or (say for more formal games), one of the usual equalizing methods can be used.  Probably the simplest is the "cut-and-choose" method of 3-move equalization (mentioned on another thread recently), whereby one player plays 3 opening moves, black-white-black, then the other player chooses which colour to be.  It is also conceivable that even 2-move or 1-move equalization would be suitable, as e.g. the corner cells are not quite so valuable as the central ones, so an opening move there might well be a losing one, but only just, making 1-move
equalization a viable option.

Play Hex in different boards

[from here] Here are some alternate boards to play Hex on. This first one I call "Pex11" because the cells are all pentagons, and the tiling is number 11 on the list of all known classes of pentagon that tile the plane. The complete list can be found here (Check also the Penrose tilings).

Of all the classes given, only two of them, 11 and 14, meet these criteria:
* nowhere do more than three pentagons meet in a point.
* the pattern is topologically distinct from a hexagonal grid.

In a normal hex grid, each interior cell is adjacent to six other cells.
In the type 11 pattern, half the interior cells are adjacent to five neighbors.
and the other half are adjacent to seven. The pentagons are colored accordingly.

Chili Sandwich Chess

1. The FIDE rules apply, except in the following.
2. Whenever a piece or pawn moves, all pieces and pawns between it and
another piece of the same type (on a row or column), are taken.
3. There is no FIDE capture.

Eg, Rg6 would take Be6 and pawn g5
. . . . . . . . . . . . . . . . . . r . b . . R . . . . . . p . . . . . . . . . . . . . . . . . . . . . . . R . . . . . . . . .

variant 1: change "are taken" to "change color"
variant 2: change "are taken" to "change to color of player"
variant 3: change "type" for "color"
variant 4: add diagonal captures
variant 5: delete rule 3.

Delegating Chess

1. Like FIDE Chess, except:
2. Non royal pieces move (capture) like one of the friendly pieces that can move (capture) to its square. In the case of Pawns, they give their diagonal forward capture to friendly pieces in the squares they could capture to, and their forward non-capturing move to a friendly piece right in front of them on the square they could otherwise move to.
3. There is no castling.
4. There is no Pawn double-move or en-passant capture.

Notes:

* A non royal piece which is not in the moving (capturing) range of another piece of the same color, cannot move (capture).
* The King moves and captures like the FIDE King.
* There is still Pawn promotion on last rank.

SampleQ c . k . . . p . . . . . . . . n . . b . . . . . . . . . . . . . q . . . . . . . N . . . . . . . . . . . . . . . . . . . . p . O . . . . . . . . . . . . R . C K . . Q 1. b3-e5+ (since Cc1 can move to b3, the pawn may move like the Cardinal) 1... Nc10-d8 (to protect the King, he also could move like the Cardinal at b12) Q c . k . . . p . . . . . . . . . . . b . . . . . . . . . . . n . q . . . . . . . N . . . . . . . . . . . . . . . . . O . . p . . . . . . . . . . . . . . R . C K . . Q 2. Kd2 (freeing the Cardinal to move like the Queen at g1) 2... Q:g7 (it also uses the power of Cb12) Q c . k . . . p . . . . . . . . . . . b . . . . . . . . . . . n . . . . . . . . . q . . . . . . . . . . . . . . . . . O . . p . . . . . . . . . . K . . . R . C . . . Q 3. d4:g4 (attacking the Queen at g7 with the power of Qg1) 3... Qe9+ (the check is because of the Knight) Q c . k . . . p . . . . . . . . . . . b . . . . . q . . . . . n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O . . . . . . . . . . K . . . R . C . . . Q 4. g4-e4 4... C:a12 (capturing the useless Queen) c . . k . . . p . . . . . . . . . . . b . . . . . q . . . . . n . . . . . . . . . . . . . . . . . . . . . . . . . . . O . . . . . . . . . . . . . K . . . R . C . . . Q 5. Cc2 (giving Rook powers to the Queen, and C+Q powers to the Rook). and so on...

Clues for a Conceptual Toolbox for the Game Designer

Abstract Games are very curious mathematical objects. They tend to be are deprived of any significant cultural context to present what – in principle – really matters to another curious thing called a game player. This act of cultural removal is rather subjective, but anybody can sense it, when we see several people around the world play the same game and enjoying it the same way. Many games, like Go or Chess are played on several dozens countries at this very moment. Not even conjectural prohibitions based on Religion, Law or by political reasons, manage to destroy the memory of the rules that define those persistent and rather illusionary things…

Here in, an abstract game is: (a) A game for 2 players; (b) with no luck element and no hidden information; (c) where each game turn (except perhaps the first and the last one) consists of a move by the 1st player and another by the 2nd player; and (d) the set of rules agreed by both players do not leave any space to ambiguity.

This, in a way, restricts the field of study, but leaves an endless Ocean of possibilities and magical wonders! We can say, with no hesitation, that Humanity only scratched the surface of such great Sea of Games. Herein, the goal is to present a set of conceptual tools for those who like to design and test new abstract games, to inform people how to avoid common errors and pitfalls and so, in conclusion, to create better games.

There are two concepts that I find most relevant! The first one is Depth, or strategic complexity, meaning the capability of a certain game to have a certain number of degrees of skillfulness. The exact number of different skills is never exactly known, even because no one reached an precise definition of what is a degree of skill. A possible way is to say that a player is one skill above the another if he wins 2 out of 3 games. Even saying that, skill levels of different players are not disjoint, since the concept is not transitive. Different ways of playing work better on certain players than others. Just like Soccer! The more skill levels a game has the better, it means that a person can continuously learn about the game for a long time (even more than a single life or an entire civilization). A deep game also gives the players more chances to recover from crises (i.e., bad moves), or stating differently, if a player on a relatively bad position is replaced by a better player, this one may still be able to balance the game.

The other condition is Clarity. Clarity means that most board positions should be as close as possible to the way the Human mind sees things. This concept will surely be very different for a Martian, but since no ET was found yet, let’s stick to this human-centered vision. Tic-Tac-Toe and Hex are exceptionally clear. There is not, however, a direct correlation between clarity and the description of the rule set. Some simple games to describe tend to mess a lot when an actual game is played, but a difficult game to describe will possibly have some clarity problems as well. For instance, many Chess Variant designers find on clarity a merciless judge. People are used to the way a Knight moves, but some similar fairy pieces (with the same right to existence as any other) create a problem of lack of clarity that prevents players to be interested on such opaque game.

The joint combination of this two features give a glimpse on the quality of the game. Tic Tac Toe suffers due to limited strategic possibilities, Go scores highly but is penalized by subtle rules, Hex scores very highly (I dare to say that 19x19 Hex would approach Go in depth, while retaining a much better clarity). A computational approach of this subject would say that given a game tree with N nodes, complexity would be the total nodes required to formulate sensible strategies, and clarity would be the ability to search deeply inside the game tree in order to achieve them.

Well, but this are just general concerns that you should have in mind. What about the real and objective game´s ruleset? The next section will talk about some basic game mutators. That is, modular concepts that can be applied to almost any game, creating new games (not necessarily better ones).

Basic Mutators

As we all found by experience, there are many good ideas out there hidden on obscure games. The next list is not intended to be complete, but it tries to dissect as many basic concepts as possible, in order to provoke people to mix them in some strange, new and hopefully also in skillful ways.

Let’s state some extra principles to those already stated on the initial Abstract Game definition. The game may have a board, consisting of cells linked together in some specific ways (a square tiling, an hexagonal tiling, a rhombus, …). Each player has, at least, one set of stones of a certain color (let’s say, black stones for the first player, white stones for the second), where the possible playing options are stated by the rules defining the game.

Each mutator must be seen as a rule, or part of a rule, that needs some preconditions before execution (i.e., may only works on certain game states/positions), and may create, when executed, events that enables other mutators to work (even on the same player´s turn). On the following list, some mutators have glimpses of possible preconditions and events.

Pass A player does not affect the game state. It is the null mutator.

Drop This is, probably, the most applied rule on abstract games. A piece may be dropped into a certain board cell. The drop restrictions can be various. The most common is that the cell must be empty. Other options would restrict it to a certain area (e.g., must enter into the players initial zone), on local conditions (e.g., must be near a friendly stone), or global ones (e.g., the board must not have more than x stones).

Move The move mutator is also very widely used. A stone already on the board, can move from a cell A to a cell B. This movement may be subject to certain restrictions, like intrinsic ones (e.g., it can just move to an adjacent cell, to orthogonal/diagonal cells, …), contextual ones (e.g., it can move to an empty cell, a cell not attacked by the opponent, only moves if it has x adjacent friends, …), or global ones (e.g., the total number of stones define how each stone can move).

Capture A set of stones, either friendly and/or unfriendly, are removed from the board and those cells become empty. This usually is an action caused by the execution of another mutator (most cases, this is a consequence of moving). Capturing can be a consequence of a certain pattern, like custodian capture (like Hasami Shogi), simple jumping (Checkers), cannon capturing (like in Xiang-Qi), bombing (all adjacent enemy stones are captured). Capturing may provoke several lateral effects, like Suicide (the captured piece is destroyed like in The Way of Go), or Protean capturing (the piece inherits the captured stones abilities, like in Cannibal Chess).

Jump A jump is simply using another stone to move to another cell not in range otherwise. This not include the Chess Knight, since it does not need another stone or piece to make its move.

Merge Two or more stones occupying the same cell are transformed into a different piece. Bashke, Laska and Focus use this concept in the Checkers game world.

Pivot The pivot mutator is a generalization of the Jump mutator. Usually a jump uses the intermediate stone as the pivot to move on a straight line. General pivot moves have much more liberty. Other kinds of pivot moving are scaling (check Scalus for use of that concept), and rotation (check Kefren or Twirls of Action) also known as Twirls, named by Claude Chaunier. These are just two possible ways to explore Pivot moves.

Swap A stone (the swapper) can swap position with another stone (the swapped). Possibly, the swapper will be on moving range from the swapped.

Shift Shift also means push a set of stones into a specific direction (e.g., check Epaminondas or Abalone). This shifting may produce other events, like single or group capturing.

Pile Piling inserts an extra dimension to bidimensional boards. There are several ways to pile, namely Staking (the new stone is placed on the top) and Queuing (is placed on the bottom).
This may provoke a change event, meaning that the new stone merged the piled piece. This also implies possibly a splitting mechanism.

Change This means changing the stone status. After the application of such mutator, a stone acts and reacts differently to the same conditions. Some examples include: stone promotion (increase its power) and demotion (decrease it), freezing (cannot move), stoning (cannot move or be captured), make royal/unroyal, …

Local Interactions After a move is done, the actual cell interacts it some local neighbors (the adjacent stones, the nearest orthogonal neighbors, …) and affects them. For instance, there are gravity forces (attracts all by one or more cells), and magnetic forces (attracts opposite color, repels equal ones). Some games where this is applied are Magnetic Go and Magnetic Chess.

Momentum A momentum mutator creates multi move games. It works like this: A previous moved stone will repeat its behavior on the following turns while it’s valid. Until now, from our knowledge, this was only used on Chess Variants.

Progressive This mutator affects the way turns are defined. The typical progressive mutator adds an extra movement for each player’s new move (one move for Black, two for White, three for Black, …). Other progressions are possible, softer ones (1, 2, 2, 3, 3, 4, 4, …) and wilder ones (1, 3, 5, 7, …). This obviously reduces the game length, and for some games it is a nice way to play a fast variant (give it a try with 9x9 Go). The set of movements could be sequential or simultaneous, it depends on the context where it is applied.

Save It’s a kind of active passing. The player gives the turn to the other player, but it saves the move for later use, i.e., next turn it can move twice in a row. This is a very strong mutator, and should be used with extra restrictions, in order to keep the game interest.

The produced events can activate more than one mutator. For example, a multiple move/capture is an application of a certain capture mutator within itself.

Improving the Spark

There is no magical formula for making an abstract game with depth and clarity. That implies a little of luck, insight or something else that creates the ‘spark’. I will speak of the something else, and also about the fact that the spark, if not treated right, may be lost, transformed into a poor game that lacked the basic care of any newborn.

Let’s start on the initial setup. First, the game designer should decide what shape will define the board and if it begins empty or not, if there is still the possibility to drop stones afterwards. A related point is to decide the total number of stones. A good rule is to see how stones are capable of moving (if they move at all). Board density (i.e., the average number of stones per cell) is relevant on this decision. A game with moving stones and growing density may face ‘traffic’ problems on the endgames. Usually if stone mobility is high, then density should be low, and vice versa.

If the designer chooses an initial setup, he must see if that setup does not go through another global pattern before the game really begins (i.e., both players found that to attack or defend, they should position their stones into a certain tactical pattern). In those cases, the designer should change the initial setup to that intermediate one. It will speed the initial phase, without decreasing its depth (this of course, may be risky, if the designer or the game testers are not able to see other potential good openings, on those cases, the game depth will suffer).

The number of moves of a typical game is an essential thing to note. Very short games are not very interesting, except for children, very long games take much time to be played and tend to be rather tedious. Perhaps if Go was presented today, it would suffer from this fate, many people would not be interested because it takes too long to finish a game, and they would miss its remarkable depth. Ralf Gering marks 20 turns (i.e., 20 moves for each player) has a minimal mark for a average game score, in order to have some interest. Of course, this also depends on the number of moving options, but too many options reduce clarity! This is a tight business! For maximal turns, an original game that takes more than 100–120 turns will need a good marketing!

An important subject is to avoid mirror tactics. This happens when one player can mimic the other, in order to achieve a draw (like in Halma) or even victory (like in Hip on even square boards). This can be done by using odd boards (that is with a center cell, usually called Tengen), allowing captures, or asymmetrical positions (i.e., that after a certain move, the other player cannot mimic it).

Two more things about the initial phase, Handicaps and Equalizers. Handicaps are always a good way for two players with different skills still manage to get some fun paying (ups, I mean playing) the game. This is done by creating a better position for the weaker player, by giving him some extra moves, extra material or easier winning goals.

Equalizing means to balance first (or even second) player’s advantage. This can be done, using an Handicap system; or by using the N-move equalizer: After N moves, the player on disadvantage may choose which side to play. When N is 2, this rule is also known has the PIE rule (i.e., you cut, I choose). There are other ways, like giving two moves per player, except for the first game move, but these are less general and may not work everywhere.

Besides the beginning, there is also the end! How the game should stop? What will be the winning goal? There are several classical concepts:

1. Territorial – wins the player with more controlled cells
2. Pattern – wins the player that first achieves a certain pattern of stones or cells: n-in-a-row, n-in-a-group, n-enclosed
3. Connecting – link two or more edges, link two or more special cells, link all friendly stones
4. Capturing – capture x enemy stones, capture some key stones (i.e., royal stones)
5. Reaching – reach a set of key cells, surround a certain stone or cell area

The designer should take special attention on one thing. On a typical endgame, the winning player has enough power to win? Is he able to decide the final outcome of the game? In Chess, we know that King + Bishop vs. King is a draw. If almost all Chess games would end on this position, then another winning rule would be needed (e.g., the Bare King rule – a player looses all other pieces are captured).

After the rule set is defined, the designer should look into each single rule and ask some questions: Is this rule necessary? Why is it so? Is it a logical consequence of some other rule(s)? If so, it should be placed on the notes section, not among the rules! Does the rule interacts with the other rules to create some more tactical possibilities? Or is it totally independent? If so, and if the rule decreases clarity without giving some to the game as an whole, then the designer should rethink about keeping the rule.

Combinatorial Game Theory talks about game temperature. A hot game state is one where the player has the advantage to move. Otherwise a cold game is one where the player does not want to move (in that sense, a game with a pass rule is never cold, since players may pass their turns). Some samples: Hex is hot and gets hotter. An extra move never hurts the player and usually puts them in a winning position, more so towards the end of the game. Go starts medium hot then cools down to lukewarm. Towards the end of the game moves become less effective until they are not worth making. Gonnect starts hot then suddenly turns freezing cold at the end. An extra move is good during the early and middle games, but can become a game-loser in the endgame. This does not give the designer a way to determine a level of quality, but can give him insights about how his own game reacts from the opening until the endgame.

Final Words

A really nice thought is to imagine that maybe some games invented in this century will be played in the year 3002 (perhaps one of your own games), where Hollywood, Microsoft, Intel, the Computer Game Industry, and so many other powerful businesses would already entered into oblivion…

PROGRESSIVE POKER

With a normal deck of 52 cards:

Player 1 takes one card from the face-up deck, then player 2 takes 2,
then 3, then both players take 4 at a time till they have 25 each.

As soon as they are chosen, the player must add the cards as he chooses
to one of his 5 poker hands face-up on the table, (all starting empty).

When the 50 cards have all been played, all the poker hands are compared,
each against each, 25 comparisons in all.  Whoever records the greatest
number of wins, wins the game.

* Poker hands are in order:

Straight flush,
4 of a kind,    (i.e. same rank)
full house,     (a 3 of a kind and a pair)
flush,          (all same suit)
straight,       (5 in number sequence, A high or low but not both)
3 of a kind,
2 pairs,
1 pair,         (2 of same rank)
nothing.

Sample Game:      Player-1                           Player-2 Ah.1                               As.2  Ks.2 Ad.3  Qs.2  Ac.4                   Js.1  2s.2  Kc.3  td.4 Kh.1  Qh.1  Jh.1  th.1             9d.4  8d.4  7d.4  6d.4 5h.3  5s.3  5d.3  5c.3             Qc.3  Jc.3  tc.3  9c.3 4c.5  4d.5  4h.5  4s.5             6s.5  7s.5  8s.5  3s.2 3h.2  3d.2  2s.4  ts.5             9s.2  3c.1  Qd.1  8c.1 Ah  Kh  Qh  Jh  th        1        Js  3c  Qd  8c  .. Qs  3h  3d  ..  ..        2        As  Ks  3s  2s  9s Ad  5h  5s  5d  5c        3        Kc  Qc  Jc  tc  9c Ac  2c  ..  ..  ..        4        td  9d  8d  7d  6d 4c  4d  4h  4s  ts        5        6s  7s  8s  ..  .. CARDS LEFT: c : . . . . . . . 7 6 . . . . d : . K . J . . . . . . . . 2 h : . . . . . 9 8 7 6 . . . 2 s : . . . . . . . . . . . . .

Cycle: a game that needs improvement

[This is a bit of a challenge. The original rules follows but they do not provide a good dynamics, the game needs, if possible, improvement]

Played on a square board with orthogonal bridge connections.

On each turn, each player may:

1) Pass, or
2) Drop a friendly stone on an empty cell, or
3) Connect two orthogonally adjacent friendly colors with a bridge, or
4) Capture a stone in custodian capture (both friendly stones must have
been played in previous turns, so it takes a turn just to capture)
* A corner stone may be captured if both adjacent cells are occupied
by enemy stones
* KO rule - not the same board position in two consecutive turns.

After two consecutive passes, wins the player with the largest cycle
concerning friendly bridges.

Egs:

White has a cycle of size 4 (the smallest possible)
while black as a maximum cycle of size 12
. . . . . . . . . . o--o . . . . | | . . o--o . . . . . x . . x--x--x . | | | | . x--x--x--x x--x . | | . . x--x--x--x . . . . . . . . . .
Capture, since it wastes a move, may not be executed
at once, leaving a lot of potential threats in the board

Should White capture the black stone or just continue to extend
his groups? If Black plays at d2 it forces the capture at d4
and gains one tempo sacrificing one stone (it should then play d1)
. . . . . . . . . . . x x . . . . . o--o x . . . . . . x . . . . . . o o x . . . . . . . . . . . . . . . . . . .
I'm not sure if it's easy to make larger cycles, so probably the game score
could be the sum of all the max cycles on each group (probably the sum
of the squares of all max cycle sizes - in order to players to take risks in
achieving larger cycles)

The game does not provide tactical richness and thus is dull. If you can work out a better variant, please send your proposal.