Card Tricks > Mathematical Treatment Card Tricks
Counterespionages
Counterespionage' rates as one of the best mathematical card effects. It
is truly representative of the new era in non-sleight card magic. By
further interjecting a bit of telepathy by-play into the presentation as
noted in the comment section, this card trick comes as close to mental
magic as one can hope to achieve.
Presentation
The performer explains that a deck of cards will be used to illustrate
the role of the spy and counterspy in espionage activities. He calls on
two spectators to act as intelligence agents and asks that they each
freely cut off a small packet of cards from the top of a face down deck
of 52 shuffled cards. The number of cards they cut off will from
henceforth be their secretly assigned code number. To avoid duplicate
numbers which would make the demonstration too easy, the first agent (
the spy) is asked to hold his cut off packet to between one and eight
cards and the second agent ( the counterspy) to a packet numbering
between twelve and twenty cards. The number of cards in either packet is
not known to the performer, to the audience, nor to the other espionage
agent.
However, either agent at his discretion can confide his secret
code number to persons within his own spy group ( whom he feels he can
completely trust).
The performer now picks up the remainder of the deck and requests the
two intelligence agents to secretly identify themselves with a special
spy card in the remainder of the deck corresponding to their code
number.
To assist them in identifying their spy card the performer
passes twenty cards, faces outward, from one hand to the other, counting
them in numerical order from one to twenty, and if deemed desirable also
giving their value. The top (face down) card is considered card number
one and the passing from hand to hand must be done in a manner such as
to retain the cards in their original order at the end of the counting
sequence.
Holding the twenty cards as a unit in his hand, the performer asks each
agent if he has been able to conclusively identify his spy card at his
assigned code number (the number that corresponds to the number of cards
in the packet he holds). Each one is also asked if he is satisfied that
no one but himself and his select group of confidants can possibly know
the identity of this card. Following this byplay, the performer explains
that he will now divide the cards he holds into two approximately equal
piles, one face up and one face down. The face down pile he explains
will presumably contain the spy card. Now if the counterespionage
activity has been successful, the other face up pile should not only
contain the counterspy card, but more importantly, this counterspy card
should have cleverly maneuvered itself to be located oppositely to the
spy card for effective surveillance.
Method
The method of bringing about this perplexing card effect depends on a
minor bit of card rearrangement that the performer secretly carries out
after the twenty cards have been numerically counted from one hand to
the other for the spy and counterspy card identification ( note that at
least nineteen cards must be counted across since the second agent might
have cut off the stipulated maximum number of nineteen cards accorded
him ( between twelve and twenty ) for the cards in his packet ).
At this
stage of the card effect then, the performer holds twenty counted cards
in their original order in one hand and the remaining uncounted cards in
his other hand. Before assembling the cards he now proceeds to
unobtrusively count across six more cards and adds them to the bottom of
the twenty card face down packet (making a total of 26 cards ).
He then
places the remaining uncounted card packet as a unit on top of this 26
card packet. From now on the trick becomes self-working except for two
important details.
In cutting the assembled deck into the two halves, make the top
half the face down pile and the bottom half the face up pile ( turned
over as a unit ). Judge the equality of the two halves by inspection but
be quite accurate here for they cannot be different in number by more
than one or two cards. Also do not disturb the order of the individual
cards when splitting into the two halves.
As a second and final vital detail, take the top card off the top of
the face up pack and transfer it to the bottom.
By carrying out these last two details, the placement of the counterspy
card becomes automatically positioned opposite the spy card.
Explanation
Let x be the number of cards that are cut off from the shuffled 52 card
deck by the first spectator ( a number between one and eight) and let y
be the number of cards cut off from the deck by the second spectator ( a
number between twelve and twenty ). The remaining cards that are left in
the remainder of the deck are then 52-x-y in number. The performer picks
up this packet of 52-x-y cards and has the two spectators observe and
identify themselves with the cards X and Y at locations x and y
respectively counting down from the top of the performer's face down
pack.
The performer counts across twenty cards in doing this and then
secretly counts across six more cards. He then brings this packet of 26
cards to the bottom of the other ( uncounted) packet of cards. This is
equivalent to placing 52-x-y-26 ( = 26-x-y ) cards on top of the 26 card
packet. Note that by restricting the total of cards that can possibly be
removed by the two spectators to 26 ( 26=19+7 ), the case will never
arise where the cards left with the performer are less than twenty-six
in number.
By bringing all cards in excess of 26 to the top, it is seen that
this leaves 26-y cards between card Y and the bottom card of this pack
and this in turn means that card Y is positioned as the ( 26-y+1 )th
card from the bottom. Also due to the addition of the 26-x-y cards to
the top of the pack, the X card becomes positioned deeper in the pack.
In fact it changes from the xth card to the ( x+26-x-y ) th card or more
simply, it becomes the (26-y ) th card counting down from the top of the
pack. Note that card X is also located higher in the pack (is nearer the
top than card Y since the number x is less than the number y).
If the pack is now halved and the bottom half is turned over, card x
is still positioned as the (26-y ) th card from the top of the face down
top half but card Y becomes positioned as the ( 26-y+1 )th card from the
top of the faced up bottom half. As a final detail, the top card of the
face up half is taken off and transferred to the bottom. This is
equivalent to moving card Y up by one card making it now the ( 26-y ) th
card from the top. Cards X and Y are now both equally positioned from
the top of their respective piles ( since both are the ( 26- y ) th
card). Hence by dealing out card pairs, X and Y will be opposite each
other when the counterspy card Y is observed at its position in the face
up pile.
Comments
This card effect obviously does not have to be limited to a 52 card deck
but this is a convenient and workable number of cards. In general if n
cards are used, the performer will cut his packet so that cards in
excess of n/2 are brought from the bottom to the top. Also the number of
cards selected by the two spectators should total less than n/2 in
number and the number ranges for their respective number selections
should be separated by several units.
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