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One player puts the ball in one hand behind their back, and then other then guesses which hand it is in.  Obviously a correct guess allows the player to choose whether to serve or receive in the serve for service rally, normally being to serve.

It gives the sense of being non-symetric in that there is a timing difference, but this is not really the case.  Either person can actually decide first, but not declare it.

What I like about it is that only one of the two has to be random for the whole process to be random.  Provided, that is, it is not repeated.  Repeating the operation might show a bias in either player, and allow the other to take advantage.

The operation is not really repeated, in that in a series of games between the same players the process is only done for the first game, and in subsequent games the previous games looser starts the serving.

It is really equivalent to two sequential blind coin flips.  If either one is random, the total is random.  But it is not necessarily obvious which is random, or if both are random.

I, of course, cheat in that the action of having to hold a ball in one hand, tends to effect the tension and height of one shoulder.  I always choose the side with the higher shoulder.  People over-compensate for the extra weight.  That is there is an information leakage.  You must rest your hands on your hips to correct this.

Of course,  you should also act the part of an all knowing god, and gesture towards the chosen arm to hand over the ball you are going to serve.  This generally unnerves them, as an extra advantage.

The conclusion is something like ' if something that should be random is not, then there is information leakage'

Martin