Linear Left/Right Game

Take 2 sets of n cards, each set with the integers 1 to n written on
the cards, one integer per card.
(You can also, letting n=10, take the cards 1(ace) through 10 of two
suits of a standard card-deck.)
Take a linear game"board" (analogous to a number-line), a row of
squares onto which to place
the game-pieces (the board containing enough squares, n^2 + n + 2, to
allow for the
pieces to move the maximum possible of moves to the left and right).
A variation might be to have fewer than n^2 + n + 2 squares, forcing
players to move away
from the edges if the situation arises.
Players each have a collection of stackable game-pieces (such as
coins), each player having one of two colors of pieces. Each player
begins by placing one of their pieces on one of the center squares,
player 1 putting a piece on the left-center square, player 2 putting a
piece on the right-center square.
Each player has one of the two sets of n-cards. The cards are first
shuffled. During play, the players take turns drawing cards one at a
time (from a face-down stack). After each card is drawn, the player
places a counter EITHER to the left or to the right, as the player
chooses, of the last piece that that player has put down. The number
of squares to the left/right of the previously-placed piece is the
number on the card drawn.
Each piece is kept in place after it is put down.
Pieces may be put in the same squares as other pieces (of either
color), the pieces being stacked as necessarily.
Scoring: Player-1's score is the PRODUCT of the total numbers of
pieces on each square which contains any pieces and is on the LEFT
half of the board.
Player-2's score is the product of the total numbers of pieces on each
square which contains any pieces and is on the RIGHT half of the
board.
So, players are encouraged by the scoring, but not required by the
rules, to stay on their side of the board.
(Hmmmm...using black and white pieces seems now to be
poltically-incorrect...)
They are also encouraged by the rules to get, in most cases, more
combinations of fewer (but > 1) pieces on as many squares as possible,
as opposed to few squares containing many pieces each.
Example:
n=4 game:
1's-cards: 4,3,1,2
2's-cards: 1,2,4,3
**********12**********
******1***122*********
******1**1122*2*******
******1**1122*2***2***
..........1
******1*11122*22**2***
..........1
So player 1 gets 2 (1*1*1*2) points, player 2 gets 1 (1*1*1*1*1)
point.
Of course, this game would be more interesting with a higher value for
n.
A (more fun??) variation: Players place each of their pieces, on each
move, the proper # of squares to the left/right the last piece put
down by their OPPONENT.
Hmmm....

Thanks,
Leroy Quet