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.

Rythmomachia

Here is a blog about the medieval abstract game Rythmomachia.

Silence

Good4both

A bit of asymmetry is no bad thing, if it is the same for both players. [T.Sagme, Book of Parrots]

Fun first

The most important feature of a game is to be a intellectual challenge for regular humans, which brings pleasure to both. A good game continues to be fun and challenging for increasing committed players. [T.Sagme, Meditations]

Balancing starts

[...]It is a triviality that the usual method of playing games where there is an obvious first-move advantage, is unfair to the second player. "First" is clearly an average of half a move ahead of "Second", e.g. at random times. A typical attempted rectification of this, in abstract-game-playing circles, is the 1 2 2 2 2 ... move transformer, whereby after the first move, each player plays two moves consecutively. Though inappropriate for most games if used directly, it may have its uses if some further restrictions are added.

It has the Cesaro-propery of "evening-out" the starting advantage, (though
for VERY short games a further integration to 1 3 4 4 4 4 may be suitable),
and it is nice to see the sum of 1-2+2-... coming to 0 by almost every method.

Now, another move transformer often used is the "Progressive" transformer, whereby the moves are taken in series of 1,2,3,4,5 etc. It makes for fun games, if hardly very serious ones; and e.g. Progressive Chess already has quite a long history. But it often struck me that even so, there was a very slight advantage to First. (e.g. His number of moves ahead is successively 1 -1 2 -2 3 -3... so that First is always first to get to a new number of moves ahead, rather than Second.) And so it now appears this advantage is real! There is an advantage to 1/4 of a move to First!

So one way I have considered for some while of rectifying the Progressive transformer was to make it an "Odd-Progressive" transformer. This has move series of 1,3,5,7... , which gives the number of moves First is ahead each time as being 1 -2 3 -4... , which is clearly fairer than the above.

ps: A later idea about progressive games is the "slowing-down" mutator 443322111... which is excellent for slow starting games!

Rules

Every good rule is a Pandora box where is hard to see all consequences. If it is easy, the rule may be useless. [T.Sagme, Meditations]

Active and Passive Games

Games can be seen as "active" or "passive"; perhaps "violent" and "sluggish" would be better terms. In active games the pressure is on to get out and make things happen, before your opponent does. In passive, it tends to be better to wait or at least movement is so slow that one cannot get too active.
 
Chess is a bit of both, though I feel the passive tendency dominates a little. Go is finely balanced. Most chess variants tend to be very active, (e.g. Handgrenade and Progressive); indeed most progressives are very active. Connection games tend to be sluggish.
 
(Handgrenade Chess: No direct take allowed. In a move, all opposite pieces at King distance are captured. The one who captures the King wins)

Fractional Hex

[From Edward Jackman conversations] Speaking of Hex, here's another idea to address it's first-player advantage that may not have been explored much. I found it in the Mudcrack Y and Poly Y book, but it applies to Hex as well. The first player draws a line connecting the midpoints of the opposite sides of one cell, dividing it half, creating two 5 sided cells. She plays her opening move to one of the two halves. The fewer sides a cell has, the weaker a move there is. You might even require that the line divides the cell into a 4 and a 6 sided cell and the move goes in the smaller cell -- that would be a very weak move, even in the center of the board.

Standard move, filling entire cell:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +---+       +
 \     /xxxxx\     /
  +---+xxxxxxx+---+
 /     \xxxxx/     \ 
+       +---+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

Half move:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +-+-+       +
 \     /  |xx\     /
  +---+   |xxx+---+
 /     \  |xx/     \ 
+       +-+-+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+

One third move:
        +---+    
       /     \
  +---+       +---+
 /     \     /     \ 
+       +---+       +
 \     /    ,+     /
  +---+    /xx+---+
 /     \  |xx/     \ 
+       +-+-+       +
 \     /     \     /
  +---+       +---+
       \     /
        +---+