Forms

Copyright (c) 2007, 2011 Steven W. Meyers

Forms is a two player game played on a nxn square board with this typical configuration. 

 

  • FORM: an orthogonally connected grouping of stones of either or both colors

  • TURN - On each turn, a player can do one of two options:

    1. Capture by replacement an adjacent enemy stone;

    2. Move a friendly stone to an empty cell reachable by one or more orthogonal slides.

  • Any stone or stones not connected to the moved stone's form -- as reckoned after the move -- is removed.

  • Move 2 must produce the removal of at least one stone to be legal (so, every move in Forms produces at least one capture/removal).

  • GOAL - The last player to move loses.
An example

One of the ways for White to win the game is by moving his e4 piece to e2. This results in the removal of the four-stone Black group.  Now Black must either capture White's stone at e2 or he must slide to an empty cell and abandon White's stone (thus causing it to be removed).  Either way Black loses the game since he's made the last legal move.
Next player to move will lose

Can you find out why?

Bill Taylor studied the result of a number of patterns: "I have a bunch of entries here, which are *all* for centre-board positions. I use Conway's N,O,P notation."

N positions (next player wins)

x x o

x x o o

x o x o

- o -
x x x

x x o x x

x x o x o
 

P positions (previous player wins)

x o

x o
o x

x x
x o

x x
o o

- o -
o x o
- o -

- o -
o x o
- x -
 

O positions  (O wins whoever starts)
x o x

x x o x

o o o x

x o o x

- x -
x o x

- o -
x o x

- x -
x x x
- o -

- o -
x x x
- o -

x x x o x

o o o o x

x x o o x

x o x o x

x o o x o

x x o o o

x o o o x

I have done ALL x-o-mixed positions up to 4 stones; and for 5 stones in a line or cross. Bear in mind that there will be another load of X positions which I haven't bothered to put in, as they are just the complements to the O positions. And also note that I haven't bothered to put in positions which are topologically equivalent to others, (they must have the same outcomes).

e.g. x x o x   and

x
x o x   are equivalent;    as are

- o -
x x x    and

- x -
o x x   (by "bending round" one of the forks.)

The author sent me some strategy guidelines:

Working through the above bestiary will serve as an excellent introduction to Forms' tactics.  (Just bear in mind that the outcome is often different when the situation is at or near an edge or corner.)  Before going on to learn about Forms' strategy, it is first necessary to understand why Forms is a misere game:  the all-abandoned-pieces-vanish rule means that it *has* to be.  Otherwise at the first opportunity a player will simply fly a piece into empty space, abandoning everything, and win.
 
Although Forms is a game of elimination, it may be helpful to think of it in terms of a game of checkmate:  any opponent's piece or group of pieces can be considered a "king" and a potential target for checkmate.  Try to isolate your opponent's pieces to make them easier to attack --- an isolated singleton is a particularly good target.  In general you want to keep your own pieces connected, but don't just lump them together.  Instead arrange them efficiently in lines and bent lines; this will make it easier to detach from yourself and therefore give you more opportunities to make a slide move.  (Slide moves are often more powerful than replacement captures.)  Generally speaking, you want to have more pieces on the board than the opponent has (except at the very end, of course); again this will help maximize your slide move opportunities.  Since abandoned portions of the board are removed, you want to be sure that the single surviving portion is a position to your advantage --- it will do you no good to have an advantage in a portion of the board that ends up getting abandoned.  And be careful not to get outmaneuvered in or near an edge or corner, where sliding options quickly diminish.