There’s a Conjuring Arts Research Center somewhere in midtown Manhattan. This video features Bill Kalush, their director, talking about and showing some highlights of their collection of books on the early History of Magic.
Of mathematical interest: the booklet features three two-page spreads with pictures of sixty saints each. The same sixty pictures are repeated three times. Each spread is divided into four groups of fifteen. You pick a saint, and in each of the three-page spreads you point out which of the four groups your saint is in. “Of course” this works on the following principle: the first pick narrows the number of possible pictures down to fifteen. The pictures are then rearranged so that in the second round, four (or perhaps three) pictures from each group in the first round appear in each group in the second round; that narrows it down to four (or three). In the third round the picture itself is found.
More pictures here (text in Italian). There’s a simulation of the mind-reading trick by Mariano Tomatis, magician and author. Tomatis also refers to a facsimile of the whole (21-spread) book that he’s prepared, and describes the difficulty he had in constructing it so that it would still work – the book is four centuries old, and therefore difficult to read in some places, but of course there is an internal logic to it. He’s also written the books Numeri assassini. Come scoprire con la matematica tutti i misteri del crimine and La magia dei numeri. Come scoprire con la matematica tutti i segreti del paranormale, as well as other books about magic that sound less mathematical.
(via metafilter.)
God plays dice 
One I worked out in college is to take a regular deck of 52 playing cards and deal them out on the table into three face-up piles. Ask the victim to name the pile in which his card lies. Each time you pick up the piles the same way, from right to left say, and repeat the question. Four times gives you sufficient information to pick out the card. The entertainment consists in doing the mental arithmetic while carrying on proper patter.