I do the same as I did before I got my computer-connected DGT chess board. I play serious games against engines, by swiveling the monitor toward the board and playing out the game on the board.
Why?
First, to preserve board vision. In the past I've played so much chess on a computer screen, (with white at the bottom, even if I played black) that I lost my 'board vision'; when sitting at a real, 3d board, I overlooked moves I would not overlook on the computer. It took me some time to get my act together again. To prevent that from happening at Go, I now use a real board for a serious game, if it means that I have to play all the moves twice *and* play the computer moves as well.
Second, the real board slows me down. I don't put the move on the screen before I played it on the board. Previously, I sometimes wouldn't think; I hovered the mouse above the intersection of my next move, anticipating the move of the engine. If my anticipation was correct, I'd click without thinking. Sometimes, I would actually click as soon as the 'ding' for the engine's move sounded, only to discover that the fracking thing did NOT play where I anticipated, and that I now was in deep trouble. Using the real board noticeably improved my results as of late, by slowing me down and thus cutting out the impulse moves (and blatant blunders).
(Bill: a lot of 'followitis' has disappeared, and my win ratio against Aya, GNU Go and Cosumi.net is skyrocketing. They're all +/- 5-6k engines, and I expect I'll have to give them some handicaps soon

)
Third: I just like playing at a real board. Call me sentimental or something, but I like to see the patterns forming on a real board, and rearranging the board to count and then finding out I won a serious game by 1.5 point is just different to having the computer tell you 'you won by 1.5 point' as soon as the second pass is done.
I'd love to have a DGT-type Go board. I know DGT is actually thinking about creating one... I hope they do. If they build a computerized board that can use normal stones somehow, I'd easily pay €500 or more it. (The DGT Chess board needs special DGT chipped pieces so the board can recognize each piece; but that it's not necessary for a Go board, obviously). With their chess board, you can just set up the computer/laptop, hit 'Go' (in a Chess program, yeah...), and then play at the board; the engine's move is displayed on the clock. You don't have to look at the computer screen anymore, and you don't have to put the move into the computer. The board does that for you. Now, if they just make that Go board...
The setup looks like this:
I just won a game against Cosumi by 8.5 points, playing black. I actually always count first before I click the final OK. This was not a Moyo game, if anyone is wondering why the territories are so large. I just always pick up all the loose stones within a territory, and use them to fill all the small territories

By the way, this is the
board that I reviewed here, together with the dark ash bowls I got at the same time, and the size 31 glass stones.