Quadtria's strength is how easy it is to learn. I have experimented with finding more strategic methods of play and devised this two-board variant on the principle of "Looking-glass Chess". It is called Extraterrestrial Quadtria.
Below are the rules. If you play this, please leave a note about how you liked it.
The pyramids were created by the extraterrestrials as a link to a parallel universe. Their subterranean spheres would travel between the universes even as they traveled along the passages.
2 complete Quadtria sets (each set represents a gateway to a universe under the pyramids)
The Object of the Game:
There are two ways to win. You may attempt either of them at any time during the game.
1) You move balls of your color from board to board, trying to block both world gateways by forming a quadtria of your color on each board.
2) You move your balls to create a pattern that forever prevents your opponent from achieving the first goal. To do this you must move 8 of your balls to one board, and in each of the 4 quads there, use a pair of them to fill the opposite corners. Once the opposite corners are filled, your opponent cannot make a quadtria in that quad.
The first goal will be familiar to Quadtria players. It is the same as in the regular game, except to win you need a Quadtria on both boards at the same time. Therefore, during the game quadtrias may be formed (and released) by either player before this condition is reached.
(For those unfamiliar with the original game, a "quadtria" is any triangle of one player's pieces that lies within one of the three square regions (quads) outside of his original quad. - Or also in the original quad after the signal peg has been reversed.)
Prepare two quadtria boards in the normal way, and place them side by side in the same orientation.
Choose the color you will play. You play the same color on both boards.
Decide who will start.
Each turn consists of moving one game ball of your color from board to board, based on the normal quadtria move. That is the ball must move to an open point on the OTHER board. That open point must be adjacent to the point that corresponds to the starting point for the move on the other board.
On your turn you may choose a ball from either board to use for your move.
The ball must move to the other board, it may not simply move on its own board.
Like in the regular game, when one of your initial quads has been cleared of all your balls, so that none remain inside, you turn the signal peg over for that quad. Each initial quad is treated independently, you can clear one of them at a time.
Unlike in the regular game, the first quadtria does not win. There may be more than one quadtria of either player on the same board. Two of your quadtrias on the same board does not win. It is not until a player completes a quadtria on both boards at the same time, that the first goal is fulfilled, and that players wins.
Alternatively, the game may end when a player occupies the every quad on one of the boards with two pieces that are on a pair opposite corners in each of their respective quads. The player who achieves this pattern wins.
Short game: first person to make a quadtria wins. You may not make a quadtria in either of your 2 initial quads until after both of your signal pegs have been turned over.
Other variations: Before starting, change the orientations of the two boards.
Re: Extraterrestrial Quadtria
Please add the subject line "Extraterrestrial Quadtria" which I forgot.