Binary Think-a-Card

(Mergel Funsky)

(written by Simon)


To download pdf file of seven individual Binary Charts – Click Here


Mergel the MagicianMergel 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 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].



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.


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Good luck in experimenting with your own presentations.  Mergel says good luck too.



Copyright Simon Aronson 2014