Here's nChess in action, it installs as a regular application in your smartphone's app menu:
In my trial games, I both managed to checkmate nChess, on 'middling', and also lose to the game (embarrassingly), on 'slowest'. This was the hardest level and presents casual players with a challenge, but I still made a few mistakes.
In play, there's a handy 'Undo' button, which serious players will be disciplined at avoiding! Tapping on the 'moves list' lets you check what just happened.
The biggest limitation in nChess is actually one which could be fairly easily rectified by the developer, if he chose to. When the AI is moving quickly, and when the board is 'busy', you have to really, really pay attention to spot which piece it has just moved. Or keep switching back to the 'moves' list. I'd have thought a brief flashing animation (or similar) to show an opponent move, would have been quite possible?