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Thank you for your comments. As has been mentioned before, this game
suffers from predictable results. This can be easily explained by the very
limited 'play tree', that is, the way different games branch out with
different plays. Since there are only 4 pieces to each side, each with an
average of 2 or less possible moves per play, it becomes easy for a human
or computer mind to analyse all results of a move and play for draw. 

Normal chess is the same, but the number of pieces and average possible
moves make it impossible for a human mind and any contemporary computer.

But I have indeed been giving thought to this variant. It has occurred to
me that Shogi-style dropping of captured pieces could offer enhanced play
branching possibilities, for example. And randomness could reduce the
ability to do the most favorable play. For example, when capturing, the
capturing player rolls a die. With a result of 4 to 6, the capture occurs
normally. 2-3, the capture does not happen and the turn is lost. On a 1,
the capturing player loses his piece. While this classic idea is too
boring for a 'normal chess' variant, it's a surprising twist for 1-D
chess. Or another where you throw a die at the start of your turn with the
die result dictating which piece you can move (e.g. 1=K 2=E 3=W 4=L 5=any
6=none).

I know this variant won't likely become as complex as FIDE chess, for
example, but I have found other uses for it, such as using it to train
blindfolded play. It really helped my memory of piece positions and
threatened areas, allowing me to start playing blindfolded 2D chess
regularly. And I'm sure children could be amused by it, although I suppose
it would be better for them to be taught FIDE chess directly.

It sure beats tic-tac-toe, though :)