## The sigma principle

new principles in magic are fairly rare. This effect depends upon what I believe to be one of those rarities. It is clearly related to the Stay Stack concept (a Rusduck idea; see Cardiste, No. 1, February 1957, page 12) and the ancient principle used in the Clock Effect, which I call the "Ten-Twenty Force." To explore the other related principles here would be a thankless task (and probably fruitless as well). No matter which principles I cite, someone will argue, more or less persuasively, for another principle that I've omitted. Suffice it to say, to the best of my knowledge, this principle, which I have dubbed the Sigma Force, has never appeared in print in quite the form, nor dressed in quite the way, it is here. If anyone feels slighted by my failure to mention his precursor, I can only apologize and hope for some understanding of my dilemma.

Stated simply, the Sigma Force, as I use it here, combines sleight of hand with mathematics to produce a Force that seems exceedingly fair. A spectator cuts off a packet of cards from a deck, then counts down from the point of the cut a number of cards equal to the size of the cut-off packet.

This is not the most logical procedure but it is presentationally framed to seem logical. I will leave for the explanation of the effect all discussion of the presentational elements, and limit this initial description to the underlying mathematics.

If we view the deck as consisting of five elements or banks, as depicted on the next page, and examine the relationship between these elements, it should make the principle clear.

Block L-mmmmmzMsmmmmmMMSm

Force Card-

Block U is a group of indifferent cards. The number of cards that constitutes this upper bank we shall represent as u.

The second block is Block M, which must be made up of an even number of cards. These cards are Mirror stacked as follows:

A, B, C, D, E, F, G, H, I, I, H, G, F, E, D, C, B, A

One could call them "Stay Stacked," but in this application the deck cannot be Faro Shuffled if the stack is to be maintained. Therefore, allowing for the function the block serves, I'll continue to refer to it as Mirror Stacked. For the sake of simple exposition, I will refer to this as Block M.

The third bank is Block L. It is composed of indifferent cards like Block U. We will refer to the number of cards that comprises this lower bank as /. This allows us to state the size relationship between Block U and Block L as:

The Force Card will be arrived at, regardless of its position, within the constraints of the principle, when the spectator cuts the deck.

The Talon is the balance of the deck. The talon need not contain enough cards to bring the total size of the five banks to fifty-two. The size of the talon is essentially irrelevant.

To illustrate the most basic arrangement of the deck when the principle is to be applied, see the diagram below:

Force Card = King of Hearts -—————————

Stay with me now. Following the procedure for the Sigma Force, utilizing a deck stacked as just described, you would ask a spectator to cut off a packet of three or four cards. This instruction would limit the spectator to cutting off Block U and card A of Block M, or Block U and cards A and B of Block M. If you wish to increase the number of possible cards the spectator can cut off, you need only add pairs of cards to Block M. The size of Block M is limited only by the number of cards you can consign to the mirror stack in the application to which you wish to apply the principle. From a practical standpoint Block M might be as large as forty cards. This would allow you to instruct the spectator to cut off a block of up to twenty cards. (You would have to guard against the spectator cutting off only the first two cards but that should be easily accomplished.)

Once the spectator has cut off a packet, you can immediately determine what you must do to assure that the Force Card (the King of Hearts, in this example) will be arrived at when the spectator counts down a number of cards equal to the size of the cut-off packet. You need not know how many cards the spectator has cut off when you make your determination.

Let us assume we are using the deck depicted earlier, but containing nine pairs in the mirror block. The spectator has cut off a packet and the top card of the portion of the deck that remains is Card F in the upper half of the mirror stack (we can call this card F0). You, the performer, would then spread down in Block M until you spotted the "mirror mate" of Card F from the upper half, which is Card F in the lower half (FL). Form a break above FL and execute any of the wealth of sleights or subterfuges that will transfer all the cards above the break, from F,; to the card above FL (we will refer to these cards as the shift group, Block S) to the bottom of the deck. Which technique—Cut, Pass, etc.—is best will be determined by the application at hand.

If the deck described in the previous paragraph is employed, when the spectator counts the cards in his cut-off packet, they will total seven. Counting from FL through the Force Card inclusive is also seven. This relationship, though not the numbers, will be true for all cases.

From a practical view, it is necessary that the performer be able to identify the cards that make up Block M. This information allows determination of the point at which the break must be established in preparation for the transfer of the cards that compose Block S. There are several ways this may be accomplished. The simplest is to establish the stack in a face-up deck. This allows the cards to be identified by their indices. A second method would be to use marked cards. Normal back marks or edge marks come readily to mind. Obviously, the marking system requires only that the relationship between the top card and its mirror mate be determinable, not the value or suit of the card. The effect that follows satisfies the requirement blatantly but cleverly.

You now have the essence of the Sigma Force. In the next few pages, we will explore an application of the Force and the principle it employs. Let the games begin.