Binary Think-a-Card
(Mergel Funsky)
(written by Simon)
[To download
pdf file of seven individual Binary Charts –Click Here]Mergel Funsky excitedly told me that the idea for
these charts suddenly came to him in his sleep. The basic
mathematical idea underlying them is of ancient vintage, and has
been
used in many similar tricks, with playing cards, numbers and other
variables. But Mergel was inspired to apply the concept to the
memorized deck and to the Aronson stack specifically.
I liked Mergel’s creativity, but I told him that these charts were
only “half” an effect – and they are in need of another half to
make the effect complete. These charts allow the performer to
learn the identity of a playing card that is freely thought of by
the spectator, but the effect clearly isn’t complete without a
strong revelation of that card, that somehow ties into and
justifies the use of these charts. Mergel replied that he had
done the hard part, so it was up to me to come up with a viable
presentation.
Since Mergel has done the drudge work in preparing the charts for
the Aronson stack, I’m offering them here. Anyone who uses a
different memorized stack will need to prepare his own set of
charts, but once the basic binary system is understood (and it’s
not difficult) you can create a set in a few hours with a word
processor.
Let me first present Mergel’s charts and explain their use.
Afterwards, I’ll offer some presentations I’ve played with to
date.
The Charts
There are seven charts comprising the set. One of them simply
sets forth all 52 cards, in order by suits. Mergel calls this the
Full Chart, simply because it displays the full deck. It actually
doesn’t play any role in the binary calculations, but it
establishes and visually explains the organization of the cards
that applies in all of the charts. It’s thus an extremely helpful
aid to orient your spectator on how and where to quickly look for
any particular card.
The remaining six charts each look like a random hodge-podge of
face up and face down cards, with the important caveat that the
face up cards each occupy their same respective positions as is
shown in the Full Chart. This makes it very easy for someone to
quickly determine if a specific card is face up on a chart –
without having to look through each and every face up card shown
on that chart. For instance, if you want to quickly determine
whether, say, the Five of Spades is face up on a particular chart,
all you need to do is look at the third row down from the top (the
Spades) and look at the fifth card from the left. It will either
be face down, or will show a bold 5♠. You don’t need to check
anywhere else on that chart.
On the pdf download, Mergel has intentionally omitted putting any
titles or chart “numbers” on his actual charts, because he didn’t
want to give any hints to spectators of any underlying systems (or
foreclose or limit any particular presentations you may devise).
But in fact the remaining six charts are specifically
distinguishable, and you’ll need to be able to quickly identify
each one when you present the effect. For learning purposes
Mergel has given each chart a name, as follows:
Chart 32 – the only chart that displays face up the Ten of
Diamonds (Aronson stack number 32)
Chart 16 – the only chart that displays face up the Eight of Clubs
(Aronson stack number 16)
Chart 8 – the only chart that displays face up the Six of Clubs
(Aronson stack number 8)
Chart 4 – the only chart that displays face up the Two of Hearts
(Aronson stack number 4)
Chart 2 – the only chart that displays face up the King of Clubs
(Aronson stack number 2)
Chart 1 – the only chart that displays face up the Jack of Spades
(Aronson stack number 1)
There’s a practical reason that Mergel has used these “numerical”
titles, which will become apparent shortly. For convenience and
ease of use, I (Simon) suggest you write a small “32” on the back
side of Chart 32, in the upper left corner, using light pencil.
This will help you quickly identify the charts, because you’ll see
the penciled number as you hold up a chart facing the spectator.
Your thumb or finger can easily cover the penciled number as you
flip through the charts, so they will appear blank on the back.
In a similar fashion put the appropriate identifying penciled
number on the back of each of the remaining five charts. With
this tiny cue, you will instantly know which chart is which. The
chart number (32, 16, 8, etc.) is the only thing you need to know
to implement the working of these charts.
Finally, stack all seven charts in a pile, with the Full Chart on
top, and the rest of the charts following in order (Chart 32, then
Chart 16, and so on).
Using the Charts
Let’s jump in and immediately run through an example. We’ll omit
any patter or presentation, because we simply want to understand
how the charts operate.
Display the pile of charts, showing the Full Chart first so that
our spectator, Ginny, understands how the entire deck is laid
out. Then ask Ginny to merely think of any card on this chart.
Since all 52 cards are displayed, she in effect has a free choice
of thinking of any card in the deck. For our example, let’s
suppose she thinks of, say, the Six of Hearts; we, of course,
would not know this. Make sure she understands the overall layout
and remembers the location of her thought of card, merely to help
her in looking at the next charts.
Once she has thought of a specific card, show her the next chart
in the pile (Chart 32) and ask her whether or not it displays her
card. You can remind her that all the face up cards are in their
proper places, to make it easy for her to check. Wait for a Yes
or No answer, and after Ginny responds, flip to the next chart in
the pile, and repeat the process. For each of the six charts,
Ginny must look to see if her thought-of card is displayed, and
she must answer truthfully Yes or No. That’s it.
After you’ve shown her the six charts and have received Ginny’s
six Yes or No responses, you will know the identity of the card
she’s thinking of.
How? Well, it’s clearly no secret to anyone who’s read thus far.
All you need to do is add up the chart numbers of each of the
charts to which Ginny responded “Yes.” That total is the Aronson
stack number of the thought of playing card.
In our example, when Ginny views the first chart (Chart 32) it does
display a Six of Hearts, so she will say “Yes” (so the performer
secretly remembers “32”). The second chart displayed (Chart
16) does not show a Six of Hearts, so she will say No. The
performer need not do anything, because she gave a negative
answer, so he continues to remember his running “total” of 32.
The third chart shown (Chart 8) also does not show a Six of Hearts
and thus Ginny gives another No, and the performer still remembers
32. The fourth chart shown (Chart 4) does in fact show a Six
of Hearts and Ginny will answer Yes. Because this is Chart
4, the performer adds 4 to his running total of 32, and then
remembers the new total, 36. The fifth chart shown (Chart 2)
again shows a Six of Hearts so Ginny will again answer Yes.
Because this is Chart 2, the performer adds 2 to his running total
of 36, and then remembers the new total, 38. The final
(sixth) chart shown (Chart 1) does display a Six of Hearts and
Ginny gives another affirmative Yes. Because this last is
Chart 1, the performer adds 1 to his running total of 38, and then
remembers the new total, 39. There are no more charts to
display, so that’s the end of the procedure. The performer
winds up with a secret total of 39 – which is the Six of Hearts in
the Aronson stack.
That, in a nutshell, is everything you need to know to use these
Binary charts.
Practical Tips
The reason Mergel organizes the pile of charts in High to Low
order (Chart 32 is the first chart shown) is simply because he
finds this simplifies doing the math in his head. In this
fashion, as the running total increases, each time you receive an
Affirmative response you only need to add progressively smaller
and smaller numbers, which he finds easier to work with. I agree
with Mergel, but remember, this suggested order is totally
optional. The charts could be shown in any order. As long as you
know which chart is which, all you need is to show all six charts
and to know (and keep a running total of) the chart numbers that
generate affirmative responses. If you wished, Ginny could
herself choose the order in which to give her responses, because
it makes no difference.
Do give the spectator a comfortable opportunity to look at each
chart. You don’t want her inspection to be rushed, or her answers
to be hasty. If she gives a wrong answer (for whatever reason)
the trick won’t work.
You’ll soon discover that the “patterns” or sequences of Yes/No
answers are all over the board. There aren’t any short cuts, so
you’ll have to go through all six charts. (An exception: if Ginny
thinks of the Nine of Diamonds, you’ll know this after you’ve
shown the first four charts, because you would have received
affirmatives on charts 32 + 16 + 4, which already is 52, and the
total can’t go any higher; thus, in this sole case theoretically
you wouldn’t need to display the final two charts). But, as a
practical matter, you need to be prepared to add up to six
numbers. Once you’ve done it a few times, it’s not difficult.
If you want to dress this up a bit, you could make a more
“permanent” prop by binding the charts with a comb or spiral
binding. This creates a little flip book that you can display a
page at a time. A corollary benefit is that the charts are always
in the correct order.
Simon’s Applications
As mentioned, the real challenge is to devise a presentation that
creates a logical context for using these charts. Mergel
demurred, saying he has more important things to do, so I’ll
outline three ideas I’ve experimented with. Each is viable in its
own right, but these ideas may stimulate you to see come up with
even more engaging themes.
Random Shuffles
In this first presentation, I talk about how it takes seven
shuffles to fully randomize a deck of cards. I display the charts
as one sample of a sequence of seven shuffles, and say that the
first chart shows the deck in complete order, at the start (Chart
1). I then explain that in these studies, for each shuffle half
the deck was turned over and shuffled into the remaining half, and
then a list was made of which cards wound up face up or face
down. I ask the spectator to think of any one card in the deck as
a “target” card, and to follow whether it turned face up or face
down after each shuffle. This sets the stage, and I now go
through the display of the charts, and receive the spectator’s
Yes/No responses, per the basic procedure. After showing all six
of the numbered charts I explain, “Those charts are the results of
the first six random shuffles. But the seventh, and final
shuffle, was the most amazing of all – because it violated all the
laws of probability. In fact, it was so unique that I saved the
actual deck for posterity!” Here, I point to a cased deck that
has been in full view on the table from the outset. I open it up
and remove the deck saying, “Despite all odds, after the final
shuffle, every single card was face up – except for one.” Here I
spread the deck and indeed all the cards are seen to be face up,
except for one face-down card. Without asking her anything, I
turn over the lone face-down card and it is seen to be her thought
of card!
The method is amazingly simple: just use an Invisible deck. The
charts provide you with the card’s identity, so you know which way
to remove the deck from the case and where to split the roughed
pair.
[Mergel Funsky’s additional note: If you’re familiar with the
ingenious presentation of shaking up an Invisible deck in a large
glass cocktail shaker fashion to show them first all mixed up face
up and face down, and then immediately all facing the same way
except for the single selection (Simon says this idea has elements
in it from Steve Bedwell, Jim Krzak and Robert D. Michaels) you’ll
see how it could be readily applied here. You would apparently
perform the “seventh” shuffle in real time, and then show the
amazing result].
Triumph
This second presentation is really a corollary of the first idea,
but it uses a regular deck instead of an Invisible deck.
I have my deck in Aronson stack order. I follow the above
presentation and after the last chart is displayed (and I secretly
have learned the thought of card) I offer to display the “seventh”
and final shuffle “in real time.” Using the Open Index concept, I
secretly bring the thought-of card to the top of the deck without
looking through the faces (using estimation, a bottom glimpse and
an adjustment if necessary). I then perform a fairly standard
version of Triumph (using Zarrow shuffles, to maintain stack
order), and show the cards apparently mixed face up and face down
using Daryl’s display sequence. For the climax, I spread the deck
and all of the cards are face down, except for the thought of
card, which is face up and staring the spectator in the face.
(The deck remains still secretly in order, for your next miracle).
Fortune Telling
This third presentation uses fortune telling as a hook. You’ll
first need to decide on six general topics to use (for example,
Health, Travel, Friends, Work, Money and Love). You’ll also need
the ability to give either a genuine cold reading or a
tongue-in-cheek “entertaining” reading, with something to say
about each of the six areas.
Begin by explaining that many fortune tellers use playing cards,
and ask your spectator to merely think of any card, as her secret
lucky playing card. Show her the first chart, telling her that it
has to do with Health, and ask her if she sees her lucky playing
card. Regardless of whether she gives a Yes or No, act as if
that’s significant, and offer her a one-line “reading” (comment,
joke, generalized prediction) about her Health, well-being,
beauty, etc. as though her Yes or No answer actually helped
determine your comment. (Example: “No? Well that’s positive.
An absence indicates no major health problem on the horizon, but
of course you need to constantly stay vigilant.”)
Then proceed through each of the remaining five topics in a
similar fashion. I save Money and Love for the final two simply
because those two topics seem to generate the most interest.
Your spectator may think you’re pulling her leg, or are
fraudulent, or whatever, but by the end of these readings you
will, of course, know her lucky card. You can now reveal it
however you like. One simple but surprising way is to verbally
incorporate it, as part of your final reading, “But I must caution
you that your quest for love will be successful if, but only if,
your lucky card happens to be … the Jack of Clubs.” The Invisible
Deck provides another simple revelation: point to the deck on the
table, saying, “As a fortune teller, I reversed one card in this
deck. Don’t tell me what your lucky card is, but let’s take a
look.” If you want to get more elaborate, a pocket or wallet
index could be used to produce her lucky card. In all of these
revelations, there’s added strength because you “commit” yourself
before she utters the name of the card she’s merely thinking of.
* * *
Good luck in experimenting with your own presentations. Mergel
says good luck too.
been
used in many similar tricks, with playing cards, numbers and other
variables. But Mergel was inspired to apply the concept to the
memorized deck and to the Aronson stack specifically.