Provided that we have a pack containing an even number of cards, there ar e two chief forms of weave shuffle. In the form in which it is used by most magicians the pack is divided in half and the halves are interwoven, card for card, in such a way that the original top and bottom cards remain on the top and bottom. This is called the "out-weave", since the top and bottom cards remain outside the rest of the pack.
It is also possible to weave in such away that one card goes below the original bottom card, and one card goes above the original top card. This is called the "in-weave", since the top and bottom cards have gone inside the pack.
The basic properties of these shuffles are as follows, assuming that we are using a pack of fifty-two cards:
Out-weave—After one shuffle, cards in the top half of the pack move to double their original position less one (e.g., the tenth card becomes nineteenth).
Cards in the lower half of the pack move to double their original position less fifty-two.
After eight shuffles the pack returns to its original order.
In-weave—After one shuffle, cards in the top half of the pack move to double their original position.
Cards in the lower half of the pack move to double their original position less fifty-three.
After fifty-two shuffles the pack returns to its original order.
After twenty-six shuffles the pack has reversed its original order.
Both in- and out-weaves—One shuffle brings together cards that were twenty-six apart (hence the usefulness of the weave in combination with twenty-six-key-card-type locations).
This about summai izes what is generally known about the weave, and more than covers all that most magicians need to know. So, aux armes, mathematicians, and forward into the darkness.
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