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Topic: Will The Cards Match formula
Message: Posted by: sieler (Dec 16, 2007 02:09AM)
Awhile ago, some posters asked for the formula for Larry Becker's "Will The Cards Match". The formula, and some notes...

At any stage, you have "n" cards left. You have to spell a word with: (n * k) - 1
letters, where "k" is any constant greater than 0. "k" can be chosen differently
each time. It's that simple, but perhaps an example will help.

At the start, n is 5 ... because there are 5 cards left. The word "Will"
is four letters long (n = 5, k = 1, so (n * k) - 1 = 4). Let's assume you spell
the word "Will", and take off one card from each pile.

You now have 4 cards left, so "n" is 4. The word "the" is three letters long (n = 4, k = 1, so (n * k) - 1 = 3). Let's assume you spell the word "the" and take
one card from each pile.

You now have 3 cards left, so "n" is 3. The word "cards" is five letters long
(n = 3, k = 2, so (n * k) - 1 = 5). You could have used any word that is
2, 5, 8, 11, 14, 17, etc., letters long ... they are all of the form "(3 * k) - 1".

Said differently...here are some word lengths you can use for various numbers
of cards:

5 cards: words of 4, 9, 14, 19, etc., letters

4 cards: words of 3, 7, 11, 15, etc., letters

3 cards: words of 2, 5, 8, 11, etc., letters

2 cards: words of 1, 3, 5, 7, 11, etc., letters

Let's try six cards ... yep, words of 5, 11, 17, 23, etc., letters!

A note on performance ... I've found it useful to subtly mark the backs of
the cards so that I can easily tell if the pair I'm about to remove match.
(This falls into the category of "error detection".)

Why do this? Failing to reverse the order of one of the two piles is a common
mistake. If the mistake is caught early, you can recover from it ("error

For many presentations of "Will The Cards Match", and variations thereof,
you don't care what order the pairs are produced in ... and you have no control
over the order, either. For some variations, however, it is necessary to know
which pair is being removed (e.g., if you're pairing up words that will be
used to form a sentence later). Those "subtle markings" I mentioned earlier can
provide that information for you.

Message: Posted by: TedLashley (Dec 16, 2007 03:15PM)

Thanks for this information! I've really enjoyed using this type of effect made up in custom-designed large cards, and adapting the message to whatever group or type of show I'm doing. Your formulas make it easier to customize this effect even further.

Message: Posted by: Snidini (Dec 16, 2007 10:42PM)
Stan, is this formula based on the Gilbreath principle? It really is a great little effect that presents itself for any type of show as Ted posted.
Message: Posted by: sieler (Dec 17, 2007 01:24AM)
Re: "is this formula based on the Gilbreath principle?"

As normally presented, no. The Café has some good threads on Gilbreath,
and Jim Morton has a good explanation at
http://pages.cs.wisc.edu/~roy/magictalk-wisdom/discussions/gilbreath.html, which he summarizes:

> The short explanation is that when two groups of cards in reversed
> sequential order are riffle shuffled together, the lower cards in one packet
> will force their complement out of the group at the top of the other packet.

In "Will The Cards Match", we aren't shuffling the two piles together ...
we're using modular arithmetic to rotate them. For example, assume "Will"
was being spelled and every "shuffle choice" was the right-hand pile. That
pile started with some card on the bottom, and that card is the match for the
card on the *top* of the left-hand pile. After moving four cards (of the five)
from top to the bottom of that left hand pile, you see you're left with
a matching card on top of the left hand pile ... because you moved n-1 cards.

Some people want to apply the Gilbreath principle in the preparation of the
piles, thinking the could take the two piles (one in order a.b.c.d.e, the other
reversed (e.d.c.b.a), shuffle them together, and Gilbreath says that the the
top five cards will have five unique cards, and the bottom five will have five
unique cards. While that's true, there's no guarantee that the cards in each
set of five will be in the order needed for Will The Cards Match. That's simple
to demonstrate, BTW: Assume we have (from top) 1,2,3,4,5 of diamonds, and
(from top) 5,4,3,2,1 of clubs. We start a riffle shuffle, and the cards
fall in this order: (bottom) 1C, 5D, 4D, 2C, 3C, 3D, 2D, 1D, 4C, 5C (top).

We see that the top five cards (starting from the top) are 5C, 4C, 1D, 2D, 3C ...
five unique cards ... and the bottom five are also a set of five unique
cards. But, the top five are NOT in the reverse order of the bottome five,
nor are they in the same order (i.e., you can't easily reverse them). Thus,
a demonstration that although Gilbreath works for *its* purpose, the result
doesn't work for "Will The Cards Match" purpose.

You could take 1,2,3,4,5 of C, 1,2,3,4,5 of D as a stack of 10 cards, cut (and
complete the cut) to your heart's content, and then take the top five and
reverse their order ... that isn't Gilbreath, but it will result in two piles in
the order needed for "Will The Cards Match", after apparently "randomizing"
them :)

Hope that helps!

Message: Posted by: sieler (Dec 17, 2007 01:31AM)
Elsewhere in the Café people have posted alternate phrases.

My favorite is "Fire, Air, Water, Earth" (I learned it from Gene Neilsen),
which I use in an African shamanistic themed presentation (the shaman is using
these words to tell the "story of creation" during a test of a candidate to be
a new shaman ...

The candidate makes the left/right choices ... and instead of cards, they're
stiffer board-like things that I called "bones" and broke in half (and
then reversed one half ... that's where I first learned to mark the backs
for error detection!). If the candidate would make a good shaman, he/she must
match at least three sets of bones ... only the great shamans match all five.

When I do it to "Will You Teach Harry" (to test a potential teacher
at Hogwarts) or to "Will You Learn Magic" (to test a potential student to see
if they are a wizard or a muggle), I sometimes say that only two wizards matched
all five (Harry and Dumbledore), and He Who Must Not Be Named matched only four.
(If someone points out you can't match four, I reply: he cheated :)
Message: Posted by: TedLashley (Dec 17, 2007 08:36AM)
One of the ways I used this principle was for an effect in the library shows I did back in 1996, when the Olympic Games were held in Atlanta, GA. I made two sets of the five Olympic rings (red, yellow, blue, green, black) and the key phrase (written vertically on a large card):


And guess what? The 2008 Games will be in Beijing, so you can do the Olympic Ring effect with the phrase:


I made up sets of large cards using the stiff cardboard pieces used for stiffeners in comic book protectors... you can buy packs of 100 very inexpensively at comic book stores. They measure about 7.5" x 10" or so. I do the artwork on the computer, printing it on plain white paper; cut out the artwork and glue it in position on the cards, then cover the faces of the cards with clear matte finish adhesive-backed laminating material (found in the shelf paper section at my local Wal-Mart. You may cover the backs, too, if you wish, but I find it uneccessary.

Hope someone can use this. :)

Message: Posted by: sieler (Dec 17, 2007 12:56PM)
Ted...I'd not thought of using numbers, thanks!

That obviously opens the door, in some cases, for birthday/anniversary dates
(e.g., (fudge 2) 15, October, David Jones ... for an October 15 (or any 2-digit
date in October) birthday.

Message: Posted by: sieler (Dec 17, 2007 01:09PM)
Fudge...I forgot to define "fudge" :)

In some cases, it's desirable to start a "Will The Cards Match" effect with
a first word that is one or two letters too short, or too long.

For example, if you're doing a party for Jim, who wants to propose to Marcia,
you might want to use the phrase: Marry Jim Please Marcia (with five cards).
The first word normally has to be 4 letters long, and "Marry" is 5.
But, recall that the formula is (n*k)-1. If we choose k=2, then that's 5*2-1,
or 9. So, our first word could be a 4 or 9 letter word. "Marry" is five,
so how do we get the extra four counts done?

"Fudging" would mean doing four "shuffles" before officially starting.
For example, I'd describe how to shuffle by actually moving a card from the
top of the left pile to the bottom, and again for the right pile (I've done two
now), and then explain that they get to choose "left" (and I'd move a card from
top to bottom on the left pile) or "right" (ditto, for the right pile) ...
and I've now just done an extra four, so the five for "Marry" adds up to nine,
and I'm fine.

Similarly, if your first word is one letter too short, just demonstrate the
shuffle once. If it's two letters too short, demonstrate the shuffle twice.

Message: Posted by: TedLashley (Dec 17, 2007 10:57PM)
I'd like to mention that depending on what venue I'm performing for, I've made up custom sets of cards with different colored rose bouquets (for garden clubs, Mother's Day, etc.), different colored saxophones with music notes (for a H.S. band booster club fund-raiser), different colored Christmas trees (for holiday shows), various jungle animals (for another library show), and even various income tax forms -- schedule A, schedule E, form 1040, etc. (used when I performed for a CPA staff dinner).

I always get one person (on my right) to hold the large sign with the words on it, and I call on audience members (while still seated) to direct my dealing from which pile and when and if) I should switch piles while spelling.

It always gets a BIG response, especially since the spectators seemingly have control over everything!... I love the effect because it's so easy to customize for a theme or particular audience.

There's a published version perfect for the holidays that uses 2 sets of six cards, and the phrase used is "Peace, Love, Joy to All." At the moment I can't recall the book or author, but I can find it if someone needs to know.

Message: Posted by: Patrick Differ (Dec 29, 2007 03:30PM)
Works ok for translating into a foreign language, too.
Message: Posted by: Andy Moss (Jan 16, 2008 06:07PM)
I use ten cards and like Sieler/Stan have created a story based about the universe and the elements Fire, water, air and earth. Summarised very quickly the story goes something like this:-

The universe starts in perfect symmetry. Peaceful but rather boring as there is nothing actually happening. God then decides that in order for there to be life there must be beings with a sense of identity. Unfortunately his first creation -the Devil- takes it upon himself to create chaos in the universe.God then creates humans with freewill to sort things out and to correct the balance.

The backs of all the cards are subtly marked.I start with the card halves displayed on the table with all the halves matching and with the universe cards on top.(perfect symmetry)I then gather both piles up from top to bottom into one pile.

I then apply a thorough 'Charlier shuffle' to appear to completely mix up the cards into a 'chaotic pile'. (the devil wrecking havoc in the universe) Since the shuffle cuts the cards I make sure that my last move, which appears to the spectator to be a part of the mix up, is to cut the pile to regain necessary order. Since the backs of the cards are marked I only have to look at the top face down card to know how many cards to transfer from top to bottom to achieve this.

I then reverse deal first five cards onto table to create first pile (this is essential!)and then place remaining five cards face down on table as they are to create the second pile.

Finally I ask the spectator to play the part of mankind. (using inuition)
End result=order in the universe again.

Anyway that is how I apply the effect. Hope it helps.This is a wonderfully simple effect that appears to the lay person to be completely baffling.I don't generally like spelling tricks but this one is the exception.

With best wishes Andy.
Message: Posted by: sieler (Jan 16, 2008 06:29PM)
Andy writes:

> I don't generally like spelling tricks but this one is the exception.

I feel the same way ... I have two spelling effects that I do (Will The Cards
Match (or some variation), and Jim Steinmeyer's "The Nine Card Problem" from Impuzzibilities (which I present differently, using two participants).
Message: Posted by: challengedmichael (Jun 5, 2014 05:50PM)
These are wonderful ideas, Thanks Ted for the thorough explanation, I have been looking for the formula so I can modify my performance, and Thanks Dr. K.
Message: Posted by: tpratt38 (Jul 23, 2014 02:35PM)
Great info thanks for the tips, I will work on this and if I get anything good I will share it here.
Message: Posted by: camperted (Dec 24, 2016 01:13PM)
Any suggestions on how to "subtly" mark the matching cards?
Message: Posted by: marc_carrion (Dec 24, 2016 08:08PM)
Why do you need to mark them? Follow the instructions and they will match.

Message: Posted by: sieler (Jan 6, 2017 05:30PM)
Marc (and Camperted) ...

Yes, if you do it right the cards match. That is, the individual pairs match.

But, you have no control of the order of the pairs.

In some versions of the effect, one wants to ensure that the pairs are put down (or handed out) in a particular order ...
for example, if you're spelling "Will You Teach Harry", and the cards have the words "John Can Teach Harry Potter"
(one per card (unknown to the audience), and you've got five people standing up ...
IF the cards are marked, you know which pair to hand to which person ... they can then do a big reveal of the
final phrase. (Of course, absent marking, one could peek/glimpse, but ... why make things harder and
more suspicious? :)