Half In The Bag (trick)

The 'trick' that makes this work is simple mathematics, and doesn't seem new, but it's wrapped up with new obfuscations. Being purely mathematical, it requires no specialist manipulation skills, and can never fail. Because of this, many of the operations can be performed by the guests themselves, assuming simple card-handling skills. Use of the passive voice implies anyone may perform the action.

What You See


HERE BE SPOILERS


Algorithms/Steps

Setup

Cards are divided into 2 classes, the ruly, and the unruly. P must be able to identify what class a card is in trivially, but it should be hard for anyone else to divine the rule dividing them.

Example rules could be:

The deck is set up by separating the ruly cards from the unruly ones, shuffling each half thoroughly, so there's a genuine appearance of randomness, and then interleaving the two halves precisely. E.g. using the hard rule above, one might get:

S D D D S C D S S C C S H C C H S D H H C D D C C H H C H C S S H H C S H H D S H S D C S D S H C D D D
K 9 6 K A T 2 T 5 J 4 2 8 8 2 5 9 5 J 3 A J 8 K 6 2 K 7 Q Q 3 8 9 6 3 Q 7 4 4 6 T 4 Q 9 7 A J A 5 7 T 3
(Generated using a simple perl script.)

Identifying the 2 Chosen Cards

When the 4 piles are first revealed, they will be:

The two chosen cards are the two that are alone amongst the other type.

Search Steps

Here the guests are arbitrarily renamed A and B where A will be the first guest to be asked to do something. P is called "blind" if which of the 2 cards belongs to which of the players isn't known at this point, and "enlightened" if it is known. If one is enlightened, one may use a blind sequence.

P chooses first

Variation 1 - Choose to Throw

Variation 2a - Blind, and Choose to Keep

Variation 2b - Enlightened, and Choose to Keep

4-Sided Die Chooses First

Get the guests to number the piles and roll. Accept that as your choice made for you, and follow whatever "P choses first" algorithm matches the chosen pile.

A choses first

Path 1 - Choose to Throw

Path 2 - Choose to Keep

When Both Cards are in a Single Pile

Similar to the above, except it's easier for everyone to pick a thrower, there being only one pile that needs to be kept, but alas you can't go from blind to enlightened.

Endgames

Explanation

There's no force, the trick works no matter what cards are chosen, all cards are equivalent. Similarly all cuts are irrelevant, the merely rotate the cards, and if you consider the top and the bottom to be adjacent in a loop, nothing ever changes. And there's definitely no need for the perfomer to take a peek at the top half of the deck whilst the two guests examine their cards.

The taking of the two cards, and their replacement, swaps their parity. If the two classes were interleaved precisely, dealing 4 piles would group cards of the same parity together, 2 of each parity, so the cards who've had their parity swapped in the selection stage will end up in the wrong pile.

To see the simplicity of the mathematical principle of parity being used, use one of the terrible rules suggested above, one where it's abundantly clear which card is in which class.

Novelty

The core seems to be the same as "Neither Blind Nor Stupid" by Juan Tamariz, from a quick check of am old grainy youtube video of him performing it (absolutely brilliantly, I might add), and it works for the same mathematical reason - a parity swap of 2 cards.

The difference is that the trick is couched in the deceit that the guests will be using telepathy to guide each other to finding their cards, that the dealing is into 4 piles rather than 2, and that dealing into piles is performed repeatedly. The fact that the cards can be detected upon first reveal means that additional full shuffles of remaining cards can take place without affecting the trick, the performer can always contrive that unwanted piles are discarded, no matter the outcome of the shuffle and deal. This is all obfuscation, the only actual trick is identifying to two cards with out-of-place parity, and hoping that the audience don't detect the stage in the performance where this happens.

Future Work

I'm working on a version which uses "modulo 3", and 3 piles, rather than "modulo 2" (parity) and 4 piles …