Mathematical Card Tricks
For entertainment purposes, we recommend dressing up the routines in a magical cloak. Remember the first rule of magic: Engage your audience!
An important ingredient in many tricks is misdirection: distracting onlookers with words or gestures, so that people either fail to notice or fail to remember some key action on the performer's part. In this way, the subtle use of mathematics makes the magic possible, unbeknownst to the average audience. The magician is likely to be given credit for genuine sleight of hand or other magical powers not actually possessed -- just take the credit and run!
A good card magic demonstration consists of two, or perhaps three, well-chosen and diverse tricks. Be sure to include some audience participation, never do two tricks that are likely to resemble each other from the spectators' point of view, and save your best trick until last. Leave the crowd wanting more, but resist the temptation to show them another three or four you just happen to be keen on that day: for most people a total of five or six tricks is definitely overkill. Maybe do one encore, another stunner you know never fails to impress, then quit while you're ahead -- if the audience leaves the room before you do, you know you've overstayed your welcome!
If you are performing for a ``lay audience,'' you really should think twice before divulging how a trick works. As soon as you explain it, people cease to be entertained and are inclined to think (and say!), ``Oh, is that all it is?'' The (magic) spell is permanently broken, and your stature as an entertainer is diminished in their eyes. If you are performing for intellectually curious spectators, such as colleagues or motivated students, it's different, but you still need to be careful. We strongly believe that people should, in some sense, earn the right to this kind of insider information---merely seeing you do a trick or two, being impressed, and saying ``How did you do that?'' in an endearing fashion just isn't enough!
On the other hand, being mathematically curious is a good start! Give people hints and let them work out some of it themselves, it's far more rewarding than being handed the whole trick on a plate. This applies to you too! -- try to work out the tricks as you go along, you'll be glad you did!
It is also a mistake, in general, to repeat a trick for an audience, even if asked to. There are exceptions, of course, which we note.
Listen to a pro on the subject: "The hardest thing is to convince people that the value of a secret is in keeping it secret ... The secret of a card trick (mathematical or not) is like the punchline of a joke. Both are secrets and both are valuable in front of the current audience until you tell them. Nobody wants to hear the same punchline twice.'' (Steve Beam)