Hidden strokes

I mean like mid-rally.  For example,  there's a topspin vs topspin battle going on and one player sticks out an arm and puts a small bit of side spin.  Why don't people do that? 

Ah, difficult to do I think, stay balanced with the arm in the way and then get the arm out of the way in time while playing such fast strokes.

There are several techniques to fool the opponent. I think one of them might involve side spin:

When you have some time before the shot, you make the full topspin stroke swing and then at the very end open up the bat and swing through so as to generate reverse spin. Usually the ball will also end up in a different place, for a right hander that would be the corner down the line instead of the diagonally opposed corner.

The best technique I know for confusing the opponent with spin mid rally is to make a no spin push in the middle of a backspin pushing rally. At the higher levels this will only rarely occur (although I have noticed a revival of the pushing rally among the top players because they want to give away the open-up initiative and attack the slow topspin instead). At our level, there is a bit of pushing before someone decides to open up, usually when there's time to pivot (few people master the backhand open up). If you throw in a no spin push that has the looks of a backspin push, the opponent might return high.

Similarly I know players who execute a topspin stroke swing, only at contact point they manage to not brush the ball but hit it flat. This will prompt the opponent to close the bat for blocking and then hit into the net. I haven't tried this one because I don't see the point of squeezing in a risky trick shot when I have the opportunity to loop.

Alois, correct me if I'm missing the point.