I thought that it would be very interesting to add a new factor to the game: time. It wold be just as chess: each player has X amount of time (it should be possible to change it) and a stopwatch and as the player is in its turn its stopwatch shows a countdown. When that player finiehses its stopwatch stops and the other's playe starts. When interrupting the other player's turn to play an instant, the same happens, the player's time who is interrupting starts to decrease, instead of the who is being interrupted.
So there would be another way of winning (or loosing) a game.
against time mode
Re: against time mode
This sounds good but needs to get a bit more thoughts... since the AI can virtually go as fast as the CPU, it would feel "virtual" to beat it. But there could be personal record trackings and stuff like that...