Here is yet another grid-based game.

For 2 players, each player with a different colored pencil (or pen or

crayon).

Players take turns filling in any of the empty squares with their

colors, one square per move.

Play continues until every square is filled in.

I give two possible variations on scoring:

1) Player 1 gets a point for every 'contiguous region', of either

color, which is formed from an odd number of squares.

Player 2 gets a point for every 'contiguous region', of either color,

which is formed from an even number of squares.

2) Player 1 gets a point for every square in a 'contiguous region', of

either color, which is formed from an odd number of squares.

Player 2 gets a point for every square in a 'contiguous region', of

either color, which is formed from an even number of squares.

By "contiguous region", I mean:

A connected region of one color completely surrounded by squares of

the other color and/or the grid's border (surrounded in the directions

of up, down, left, or right,but not diagonally).

Example completed game:

* * # # # *

* * # # * *

# * * * # #

# # * * # *

* * # * # *

# # # * # #

So, we have contiguous regions of:

11 *'s, 5 #'s, 3 #'s, 3 *'s, 2*'s, 6 #'s, 2*'s, and 4 #'s.

So, under scoring method 1,

player 1 gets 4 points,

player 2 gets 4 points also.

Under scoring method 2,

player 1 gets 22 points,

player 2 gets 14 points.

Is there a bias under either scoring method for one player or the

other?

What about any strategy?

How does the scoring method affect strategy?

thanks,

Leroy Quet

## Friday, September 19, 2008

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