Oct, 23, 2009

This idea just poped in my head today about a Go like game.

The game is similar to Go, but players place two stones on each
turn. Except on the first turn only one stone is placed.
It is played on a square grid board similar to Go.

Object is to enclose more empty space than the opponent. Players
enclose space by building a connected lines with their stones
to form a loop. The edge of the board can be used in forming
the loop. Stones that are adjacent orthogonally or diagonally
are considered connected. Once a connected loop is formed
any opponent stones inside the enclosed area are removed and
the opponent cannot place stones inside this enclosed area.
A player may place one stone or pass the turn. If both players
pass their turn two consecutive times or if either player cannot
place a stone the game is over. Only the empty spaces inside
the area enclosed by the players stones counts towards the players 
score. The player with the higher score wins.


Oct 24, 2009

Aamir and tried it this morning using a checkers set; 8x8 board.
If the edges can be used to form the loop then it seems very easy
to enclose large area using the edges. And a question that needs
to be answered is which side of the connected line belongs to
the player. The obvious answer is the side which encloses the
smaller area (counting all enclosed squares even the ones with
stones). But it seems possible to create a connected line which
divides the board equally. Allowing edges to be used in forming
the loops seems to add complication to the rules.

So we tried a version where edges cannot be used in forming the
loops. This version seemed more interesting. But then the game
seemed as if it were too hard to enclose any area. We wondered
if a well played game would result in a draw every time. We
tried playing it so that the first person to enclose any area
would win. At first it seemed that the second player to move
would have an advantage, but then we found that is not true and
the first player can defend and eventually also create threats
while defending. It seemed that one player or the other would
eventually form a loop an win. But of course our play was
flawed as is always the case with any non-trivial game. So
perhaphs the game is a draw, but we did not find any clear strategy
to acheive it. Nor did we find any clear indication that the
first player or the second player has a distinct advantage.

But it seems that since the players stones start interacting
right away there might be an advantage to one player or the
other and the play can immeadiately become tactical rather 
than strategic.

On a larger board it would be harder to tell if the game was
flawed.

Need to think more about what makes a game flawed. All two
player games will have the out come of 0, 1, 2 or 'no'; that is
a draw, win for the first player, a win for the second player
or the game has no outcome and plays indefinitely. A game
with no outcome can be considered flawed, but this flaw
can in some games be fixed by introducing rules to prevent 
repitition. However in cases this may not be enough and
the game can go on and on without either player being
able to acheive the goal or draw.
Some games by design will not have 0 as a possible outcome
but can interesting games. So just because the game ends
with the first player winning or second player winnng is
not in an of itself a reason for the game to be flawed.
The ultimate outcome of a game as long as it not 'no'
cannot be a reason for the game to be flawed. 
A game is flawed if there are trivial paths in the
game tree to forced 0, 1, 2 or 'no' outcomes.
A trival path is one in which one player has to make
moves which are all forced otherwise the player loses 
(or gets a very big disadvantage that clearly will
lead to a lose) in
a very short number of moves; like immeadiately or
a few moves later.