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Reverse Counting Card Tricks

Switchcraft
In 'Switchcraft' the card reversal is carried out behind the
performer's back under the pretense that two specific cards are being
switched. There is no reason for the audience to expect any subterfuge
in this action and if anything it would seem to make the trick more
difficult to perform.
Presentation
The performer asks a spectator to specify a number of cards, say
between fifteen and twenty-five. This number of cards is dealt out in a
pile and handed to X. The performer makes the point that he has in no
way influenced the selection of this number except to keep it within a
reasonable figure for the card effect to follow. Spectator X is now
asked to secretly split the packets of cards he holds into two unequal
packets and to hand one of the two packets to spectator Y. This is to be
done out of sight of the performer.
The remaining cards will be shuffled thoroughly on the table. The
performer now instructs spectators X and Y to secretly count the number
of cards in their respective packets. Following this they are asked to
count down to and identify cards in the face down packet on the table
corresponding to the counted number of cards in their packets.
Suiting the action to the word, he presently turns to the table,
picks up the deck, places it behind his back and makes certain
transpositions that are suggested to him as a result of the
concentration of spectators X and Y on their respective cards. Bringing
the deck out in front again and placing it on the table, still face
down, the performer asks spectators X and Y to count down their
respective cards and remove them. When the two cards are turned over,
they are found to be interchanged, a case of pure switchcraft.
Method
The mechanics of carrying out this trick consists simply in reversing
the order of cards at the top of the face down deck corresponding in
number to one less than the number of cards called for by spectator X at
the beginning of the presentation. For example, if X had initially
requested a total of eighteen cards, the performer merely reverses the
order of the first seventeen cards at the top of the face down pack when
the pack is placed behind his back.
Explanation
This card effect is based on the fact that if a given card is the xth
down from the top of a pack that is made up of x+y cards, it is also
automatically the (y+1)th card counting up from the bottom. Similarly, a
card yth from the top of this x+y pack is also the (x+1)th card counting
up from the bottom of this pack. The performer knows at the beginning of
the presentation that the total cards in the two packets held by X and Y
must equal the number of cards that X originally requested, a total that
is equal to x+y. By reversing the top (x+y-1) cards when he holds the
pack behind his back, the performer simply arranges to have the counting
that subsequently follows carried out in a sequence that is from the top
down rather than from the bottom up. One less than the total of x+y
cards is reversed so that the two card locations fall at positions x and
y rather than x+1 and y+1. By carrying out this reversal of (x+y-1)
cards spectator X will find his card at location y and spectator Y his
card at location x.
Comment
A number between 15 and 25 was suggested as representing a handy
number of cards with which to work. However, this is an arbitrary range
and any number of cards can be used as desired.
An intriguing variant on this card effect can be used to good advantage.
A deck is shuffled by spectator X after which he is asked to (1) think
of a number between one and ten and (2) locate and memorise the card at
this same number counting down from the top of the face down shuffled
deck.
A second spectator Y is now requested to give a number between eleven
and twenty. This trick depends on the reversal by the performer of a
group of cards at the top of the face down pack equal in number to the
number given by spectator Y. Other than doing this behind his back, the
card effect is self-working.
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