On the Mathematical Background of Gilbreath's Card Trick

In Martin Gardner's book \New mathematical diversions from Scientiic American" it is described how certain information concerning the initial distribution of a deck of cards survives an arbitrarily thorough riie shuue. This gives rise to a card trick which is attributed to Norman Gilbreath, several other tricks presented in magic journals are based on the same principle. Here we aim to generalize the underlying ideas. We consider sequences a 1 ; a 2 ;. .. with values in f?1; +1g for which the sequence a 1 ; a 1 +a 2 ;. .. of the associated partial sums only has small oscillations. It is indicated how general properties of such (a n) can be used to understand what happens when shuuing cards and how this can be given the form of a card trick. The mathematics involved is rather elementary.