Game of pieces on 2 linear-boards

I might as well post this
(Backgammon-esque, kind-of) game,
which could very fun,...perhaps..
*2 Players (one associated with black, the other with white).
*Each player has k black and k white pieces (similar to Go pieces,
but flat so as to be stackable).
*2 "boards", one per player, which are each a strip of
(2k) positions where the pieces can be placed in stacks.
*Each player places his/her pieces (secretly, so as not to be influenced
by other player), in some arrangement of black and white, onto his/her
board, exactly one piece per position.
The boards are then revealed.
At each player's move, a group of positions
(each selected from 1 to 2k)
is randomly chosen somehow.
(In one game-variation, the number of positions chosen varies
{and is 1 to 2k};
in the other game-variation, there is a fixed number of chosen positions.)
At each move, a player does one of the following at EVERY picked position:
A) If both stacks in same position on the boards are
the player's color, then player moves one piece from
one of the stacks to the other
corresponding stack (in either direction).
If the colors do not match in the two corresponding
stacks at a picked position, these stacks are unaltered.
If both colors match but are of player's opponent's color,
or either or both "stack" at a position has no pieces but
the other is of the opponent's color (if both stacks
are not empty), then leave the stacks at this position alone.
And, if one stack has player's own color, and other stack is empty,
a player (if choosing option A) must move a piece from the
occupied stack to the empty "stack".
or
B) Switch all stacks (of either color) on the player's
own board (only) at the picked positions with the stacks
immediately to the left. (If far left stack is picked,
switch with far right stack.)
The game's goals vary with each game,
and are predetermined by the players.
Examples:
1) After fixed number of moves,
player wins who has most number of his own-color pieces
on left side of his board.
2) First player to get an even number (or prime number, or...)
of pieces of his color on each position of his board occupied
by his color (in the 1st place), wins.
etc etc...
Sample starting-boards setup (for visualization):
* * o * o o * * * o * * o * * o o o o * o o
o * * o * o * o o * o o * o * o * o * * * o
Any mathematical analysis that anyone has to offer?
Any game-improvement analysis either??
thanks,
Leroy Quet