Between mathematics and magic: Josephus legend and the down-under shuffle

There are many links between mathematics and magic: on the one hand, it is usual to see how mathematical principles apply in order to create magic tricks and, on the other hand, several specific techniques in magic give rise to mathematical models providing interesting properties in recreational mathematics. In this work we show this duality relating the famous Josephus problem and its variants with specific card shuffles used in some card tricks. In order to display the educational nature of this problem, we also suggest some teaching activities to develop in a classroom.