Amal-Game

Here is a game which is a mix of several other games I
have posted before.
Each of the 2 players has a colored pencil/pen of a color
different than their opponent's.
And I suggest that each player also have some item (such
as a coin) to mark where they had last moved, although
such an item is not a necessity.
Start with an n-by-n grid drawn on paper.
(I suggest an n of about 6 to 10.)
Players place their game-pieces, if they have them,
in opposite corners of the grid.
And each player makes some kind of symbol with their
colored pencil in the square which is at their corner.
Player 1 moves like so:
He can either move up, left, right, or down on any move
(as long as not moving off the grid).
On his first move he moves 1 position, on his second move
he moves 2 positions, then 1, then 2. Generally, he moves
1 position (to an adjacent square) on odd-numbered moves,
and moves 2 positions (possibly skipping over a square
already marked) on even-numbered moves.
Player 2 moves like so:
She can move only one square (to an adjacent square) on any
move (and cannot move off the grid).
On her first move she can move either left, right, up, or down.
On her second move she can move in any of the 4 main diagonal
directions. Generally, she moves up, left, right, or down on
odd-numbered moves, and moves in any of the 4 main diagonal
directions on even-numbered moves.
After a player moves, he/she marks the position he/she was
just at with their colored pencil, if that square was not
already marked with the player's own color.
A player can move onto any square, even those already moved
onto before. But if she/he moves onto a square marked with
his/her own color, even if the other player's color also
marks the square, then the player loses a point.
If, however, a player moves onto a square marked ONLY with
the player's opponent's color (before the player marks the
square with his/her own color, of course), then the player
gets a point.
A round is over as soon as any player gets a predetermined
number of points.
Now, there might be a bias in which player gets more points,
based on who moves first and on the rules for moving.
So there are an even number of rounds, half where each player
is player 1 and the other player is player 2, and half the
rounds the other way.
The scores from each round are added up to get each player's
grand total, which determined who won the entire game.
(Also, if there is only one color of pencil/pen, players can
instead mark each square with their own symbol, such as a
dot or an X or their initials.)
Sample partial-game:
(View with fixed-width font.) Moves numbered:
*..*..x..xo.o..o....*. *. 7. 84 3. 1
*..o..o..*..*..o....*. 6. 5. *. *. 2
o..*..x..*..*..*....7. *. 6. *. *. *
x..x..x..*..*..*....4. 3. 5. *. *. *
*..*..*..*..*..*....*. *. *. *. *. *
x..x..*..*..*..*....1. 2. *. *. *. *
* empty square
x player 1 was here.
o player 2 was here.
x (player 1) has just moved onto a square that o (player 2) had moved
to earlier. (This square is marked with 'xo'.) So player 1 gets a
point.
thanks,
Leroy Quet