The description for this game starts off very much like that of "Simultaneous Checkers" (see link). I think that name is not a good one, because typically the phrase "simultaneous checkers" means one person is simultaneously playing several different people at different checkerboards. But this is also
a somewhat different game, so a different name is in order.
According to Wikipedia (also linked), checkers is a "solved game", in which it has been shown that when both players play perfectly, the game can always end in a draw. I didn't know that when I thought up this Idea. I was thinking that if, say, the first player could always win, then what might be done to balance that out?
Let's pretend that the first player CAN always win at an ordinary game of checkers, if he or she plays perfectly.
So, enter Duplex Checkers. The first three rows of both sides of the board are covered with pieces, all of which can only move diagonally. It doesn't matter who goes first (it's been so long since I played that I had to look it up!).
I'll assume we are using a red-and-black checkerboard, with red and black playing pieces. Red moves first.
In this overall Game, Red's first move is required to involve the pieces on the red diagonals of the checkerboard. Then it is Black's turn, and Black's first move is required to involve the pieces on the black diagonals of the checkerboard.
Red's second move is required to be a response to Black's first move, on the black diagonals, and Black's second move is required to be a response to Red's first move on the red diagonals.
Red's third move is once again on the red diagonals, and Black's third move is once again on the black diagonals.
And so on.
In this way, as the Game begins, both players are actually going first, in what seems like two separate checkers games. So, if the first player could always force a win by playing perfectly, then obviously this way of beginning a Duplex Checkers game balances things out, so that both could in theory win one of the two games.
Well, that point is now moot, since in actuality a perfectly played checkers game should always end in a draw. However! I promised in the SubTitle that the two games eventually become just one!
The kinged pieces are the key. I thought of this notion before reading all the annotations at the "Simultaneous Checkers" page, and after I did, I thought that [Flying Toaster] (March 4, 2010) had thought of it also, but upon second reading it is clear he was describing something a little different, and was replying to [ilSilvano], which ALSO is about something similar to what I thought of.
Oh well. Basically, my Idea is that after a piece is kinged, and only when it is at the edge of the board (any of the 4 edges), it may optionally move orthogonally just one space along the edge (no capturing allowed!) instead of only moving diagonally. This allows pieces from what was originally one separate game to join the other and no-longer-separate game, and influence the outcome.
Especially the outcome could be influenced because of the precise rules of turn-play for this game. For example, if you are Red and you have a king on a red square at an edge of the board, and it is your turn to move a piece on a red square, you can move it to an adjacent (and empty!) black square along the edge. Black's next play, per the turn-play rules, will involve moving a piece on the black squares, but your king is safe since it is on an edge-square. And YOUR next move can allow you to move that same king along a black diagonal....
Perhaps if Duplex Checkers is played perfectly it will still be a draw. But the first player who gets a king could possibly gain a big advantage....