Bart Harding Secret
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Mr. X presents . . . The Bart Harding Secret
Memorized Decks and Algorithmic Stacks
A memorized deck is a powerful tool in both card magic and mentalism. But unless you work with one frequently, you can get rusty. This can make you less likely to perform memorized deck effects, potentially creating a vicious circle. Of course, stacked decks based on algorithms are easier to learn (and to re-learn if you get rusty). And my favorite effect (using either a memorized deck or an algorithmic stack) is “Test Conditions” by Richard Osterlind, which can be found in Dynamic Mysteries or Mind Mysteries Volume 2 (where it is labeled “Challenge Mind Reading”). It therefore should go without saying that I revere Osterlind’s Breakthrough Card System (BCS), especially because its algorithmic rules are much easier to remember (or to re-learn) than a memorized deck. But unless you memorize the BCS, all you know is “the next card.” While that is enough for many great effects, it is not enough for every memorized deck effect, such as ones where you need to know the card at a given position or the position of a given card. In addition, while it is not hard to set up a deck in the BCS sequence, it does take a few minutes and, more importantly, it requires one’s conscious attention to do so. In other words, there is no way—at least as far as I know—for one to rapidly (i.e., in less than a minute) or automatically (i.e., by a procedure requiring little conscious thought) go from a deck in New Deck Order (NDO) to the BCS sequence. Of course, one can always use the Si Stebbins stack, as that stack easily lets you know “the next card,” as well as what card is at any position (and vice versa). See, e.g., Si Stebbins Unplugged (Trickshop.com). In addition, you can quickly go from NDO to Si Stebbins order using “The Si Stebbins Secret” from At the Card Table by Darwin Ortiz. But, as many have noted, the Si Stebbins stack does not look natural or random because, among other things, the cards are arranged in a strictly alternating red-black sequence. To be sure, there are many effects where this may not matter because the spectator sees few of the cards. And even in tricks where a spectator looks at the cards, he or she may be unlikely to notice this arrangement, at least consciously, because of other factors. For example, when a spectator is asked to look through the deck to find a particular card, he or she may be too focused on that task to see that the arrangement is not random. But even the possibility that someone might say, “Hey, why is every other card red?” is © 2014 misdirects all rights reserved
enough to keep most of us from using the Si Stebbins stack in such situations. All of the above issues can be resolved with the Bart Harding Stack because (1) the original version easily let you determine what card is at any position (and vice versa) and because there are ways both to (2) easily determine “the next card” and (3) both quickly and automatically go from NDO to stack order! I developed methods for (2) and (3) around 2004. In addition, in writing this manuscript, I discovered another source that presents basically the same method for (2). See 1 http://tinyurl.com/ne9n3so. (I also recognize that there may be other previously published sources explaining (2) or (3); however, I am not personally aware of any at this time.)
The Bart Harding Stack (BHS)
The BHS first was published in 1962. It looks random and is based on a simple algorithm that, even if you forget it, you can re-learn it in minutes. The algorithm lets you determine the location of any card in the stack. In particular, for any number from 1 to 52, you can determine the card at that position in the BHS stack; likewise, for any named card, you can determine its position in the BHS. I debated whether to reveal the BHS or its algorithm in this manuscript. Ultimately, I decided to do so because the system is over 50 years old and the original sources for it are 2 not widely available. As such, this manuscript would be of little use to many, especially those newer to this area of magic, if it did not explain the system. In addition, it would be virtually impossible to explain what I have developed without revealing the stack.
The BHS and its Algorithm
Here is the BHS:
I learned it from The Bart Harding Card System Incorporating Alan Shaxon’s “Name-A-Card” (Peter Scarlett Magic 2002).
This stack is created by an algorithm that associates each number from 1 to 52 with a different number from 1 to 52. Here is the algorithm: 1.
Take any number from 1 to 52.
Reverse its digits. (If it is a single digit number, put a zero in front before reversing.)
If the result is greater than 52, subtract 5 from the first digit and add 5 to the second digit.
For example: 1 becomes 10 (since 01 reversed is 10); 23 becomes 32; and 41 becomes 14. The only difficult cases are when the reversed number is greater than 52: 26 becomes 62 which then becomes 17 (because 6-5=1 and 2+5=7) 18 becomes 81 which then becomes 36 (because 8-5=3 and 1+5=6) Now that you know the algorithm, you just have to know how to use it. For that, you need to imagine a deck in Sorted Order:
Note that the suits in the Sorted Order deck are in Clubs, Hearts, Spades, Diamonds (CHaSeD) sequence. The Sorted Order deck plus the BHS algorithm let you know where every card is: Where is the Four of Hearts in the BHS? Well, it’s 17th in the Sorted Order deck, so it is the 17 → 71 → 26th card in the BHS. 3
Where is the King of Hearts in the BHS? Well, it’s 26th in the Sorted Order deck, so it is the 26 → 62 → 17th card in the BHS. The Sorted Order deck plus the BHS algorithm also tells you what card is at any given position in the BHS: What card is 45th in the BHS? It must be the 45 → 54 → 09th card in the Sorted Order deck, which is the 9 of Clubs. What card is 24th in the BHS? It must be the 24 → 42nd card in the Sorted Order deck, which is the 3 of Diamonds. Now, one may fairly ask, “How do you know the position of a card in the Sorted Order deck?” In other words, how do we know that the Four of Hearts was 17th, the King of Hearts was 26th, the Nine of Clubs was 9th, and the Three of Diamonds was 42nd? To be sure, apart from the Clubs (the first group of cards), determining this does take some mental calculations (i.e., adding or subtracting 13, 26, or 39, depending on which of the other suits you are dealing with). But this becomes fairly easy with practice (especially with practice visualizing the Sorted Order deck). Finally, there are two cards that are simply exceptions to the BHS rules: the Six and Seven of Clubs. They are assigned to be the 6th and 7th cards, respectively, in both the stack and in the Sorted Order deck (which at least makes them easy to remember).
The Modified Bart Harding Stack
In working with the BHS, I developed two very minor modifications that make the stack both easier to remember and which reduce the number of exceptions for the techniques described herein (i.e., going between NDO and BHS and determining “the next card”). First, the Sorted Order deck I use is in Spades, Hearts, Clubs, Diamonds (SHoCkeD) sequence because that provides a built-in reminder of the sequence of the suits: Spades are the first group (just as a Spade has one point); Hearts are the second group (just as a Heart has two rounded edges); Clubs are the third group (just as a Club has three leaves); and Diamonds are the fourth group (just as a Diamond has four points). This is not an original idea of mine, as it has been used by others in the literature, including Richard Osterlind. Second, the first and last steps of the algorithm are slightly different. Instead of “Take any number from 1 to 52” and “If the result is over 52,” I use “Take any number from 1 to 50” and “If the result is over 50 . . .” In other words, I do not include the Queen and King of Diamonds in the system. I just let them stay at positions 51 and 52 in both the stack and the Sorted Order. Thus, the Six and Seven of the first suit (i.e., Spades, in my modified system) are no longer exceptions: the Six of Spades is card 15 and the Seven of Spades is card 25. That said, there still are two exceptions—the Queen of Diamonds and the King of Diamonds—although there are fewer exceptions for other purposes, as shown below.
t Modified d BHS, whicch looks jusst as random m: Here is the
ng those alreeady familia ar with the BHS, the foollowing disccussion exp plains To preveent confusin each tech hnique firstt with the orriginal BHS S and then with w the Moodified BHS.
D Determining “The Next C Card”
For a giv ven card, to o determine the card th hat comes next n in the BHS, B just im magine the card ten to th he right in the Sorted Deck:
s by th he green arrrows, the ca ard after the AC in thee BHS is thee JC; In other words, as shown 5 is the 2H H; the card after a the KC C is the 10H H; the card d after the JH J is the card after the 5C 5
the 8S; the card after the JS is the 8D; and the card after the 3D is the KD. One way to remember this is “add 10 to the value and keep the same suit; if the result is above 13, subtract 3 from the starting value and go to the next suit.” Now, the “add 10” rule does not work when you get to the Four of Diamonds because, among other things, there is no card “ten to the right.” But there is a solution. For the Four through Jack of Diamonds, just imagine that the Sorted Deck restarts with AC, 2C, etc., and add 17 or 8, as follows:
For the 4D and the 5D, add 17: Thus, the card after the 4D is 8C, and the card after the 5D is the 9C. Another way to remember this is “add 4 to the value and go to the next suit.” For the 6D through the JD, add 8: So the card after the 6D is the AC; the card after the 7D is the 2C; and the card after the JD is the 6C. Another way to remember this is “subtract 5 from the value and go to the next suit.” Finally, there are four exceptions to the above: 6C, 7C, QD, and KD, so you must remember: The card after the QD is the 3H. The card after the KD is the 4H. The card after the 6C is the 7C. The card after the 7C is the 9S. In summary, the following rules let you know the next card for every card in the BHS: 1.
For all Clubs (except 6C, 7C); all Hearts; all Spades; and the Ace through Three of Diamonds: Add 10 & keep same suit; if result > 13, subtract 3 instead & go to next suit. 6
F 4D - JD, For S Subtract 5 & go to nex xt suit; if result re < 1 ad dd 4 instea ad.
R Remember fo our exceptioons: The card affter the QD T D is the 3H.. T card affter the KD The D is the 4H. T card affter the 6C is the 7C. The T card affter the 7C is the 9S. The
M BH HS, “the nex xt card” rulees are somewhat simpler: For the Modified 1.
F all Spade For es; all Hearrts; all Clubss; and the Ace A and King of Diamon nds: A Add 10 & ke eep same suit; if resu ult > 13, sub btract 3 insstead & go o to next su uit.
F 2D - JD: For S Subtract 5 & go to nex xt suit; if value < 1 ad dd 4 instea ad.
R Remember tw wo exceptions: The card affter the 5S is the QD T T card affter the QD The D is the KD.
G Going from m NDO to B BHS (and vice versa)
After rem moving the Jokers and advertising g cards, an American A Bicycle deck looks like th his:
I developed two methods for going from NDO to BHS (and vice versa): a dealing method and a faros plus cuts method. For both, you must first go from NDO to Sorted Order:
Going from NDO to Sorted Order
Hold the NDO deck face up in your right hand for an overhand shuffle, then: (a)
run 26 cards singly and face up into the left hand;
flip those 26 cards face down with your left thumb and fingers;
drop the right hand half onto the left hand half, maintaining a left pinky break between the two halves;
riffle up the back of the top half of the deck and get a right thumb break under the KH;
pick up the top half of the deck (maintaining the right thumb break under the KH);
pivot cut the top half of the right hand cards (using the left first finger) onto the left hand cards; and
drop the remaining right hand cards onto the left hand cards.
If you are using the Modified BHS, hold the NDO deck face up in your right hand for an overhand shuffle, then: (a)
run 13 cards singly and face up into the left hand;
drop the face up right hand cards onto the face up left hand cards;
pick up the deck with the right hand, keeping it face up, and again run 13 cards singly (and face up) into the left hand;
turn the left hand packet face down with the left thumb and fingers and drop the right hand cards face down onto the left hand cards.
Now, from Sorted Order you can get to BHS by dealing or by faros and cuts as follows:
From Sorted Order to BHS by Dealing
Hold the deck face up in your dealing hand. You are going to deal all 52 cards onto the table in a certain fashion. Note: you will be dealing from the top of a face up deck, but as you deal each card onto the table, turn the card face down before dealing it on the table.
D Deal the first two cards in one pile (the KD and d QD):
Deal the nex D xt five cardss into five piiles from lefft to right, starting s beh hind and to o the le eft of the fiirst (two carrd) pile. Th he second piile should be b behind th he two card d (KD and QD) pile e:
Deal the nex D xt five cardss into five piiles from lefft to right, starting s beh hind the row w you ju ust dealt:
You now hav Y ve 1 two-carrd pile by ittself, and 10 piles behiind it. Dea al the rest of o the ca ards onto th hose 10 pilees (starting g with upperr left, going g across thee first row, then across the se econd row, then back too the first roow, etc.). In n other word ds, after thee first wo-card pile e, you are just dealin ng the rest of the deck k into 10 piles p in a 5 x 2 tw arrangementt.
There are no T ow 11 piles. Using the numbers beelow, pick up u pile 1 and d place it on n pile 2. Then pla ace that com mbined pile onto pile 3. 3 Then pla ace that com mbined pile onto pile 4, and so o on, as you gather up all a remainin ng piles from m 5 through h 11:
1 10 8
The cards arre now in BHS T B order except e for seven s cards (5C, 6C, 7C C, 2H, QH, QD, K KD). These e cards can n be reposiitioned by spreading the deck and a making g the foollowing adjjustments: a.
outjog g the 7C; inssert the KD D in front of the 7C, leav ving the 7C outjogged;
outjog g the 6C; inssert the QD D in front of the 6C, leav ving the 6C outjogged; and
strip out the 6C and 7C and d insert them m in front of o the QH ass you remove the C, and QH and a place th hem on the face of the deck. d 5C, 2C
Iff you startted with a Sorted Or rder deck in SHoCK KeD order, the deck is i in M Modified BH HS order after a step (e) (e except for fo just one e card: the 5S. That card c iss easily rep positioned by outjogg ging it and d inserting it behind the t QD. *
In n theory, on ne could do the above shuffles, cu uts, dealing g, and picku up in front of o an audience (e.g g., under th he guise of breaking in n a brand new n deck an nd counting g the ards to mak ke sure there are fifty--two). Likeewise, the rearrangeme r ent of card((s) at ca th he end coulld be done as you rem move other cards, c such as the Acees, for a speecific efffect. That said, I thin nk the real value v in thee above proccedure is th hat it is a way to quickly and automatica ally go from NDO too BHS ordeer. Indeed d, once you u are w the proocess, it can n easily be done d in less than a minute. coomfortable with
Frrom BHS to Sorted Orde er by Dealin ng To transform T m the deck frrom BHS too Sorted Ord der, just tak ke the face up u deck and d deal itt into eleven n piles (exacctly as above) and pick them up (exactly as ab bove). The deck iss now back in Sorted Order O excep pt for seven cards (6C, 7C, 2H, QH H, JD, QD, KD), w which may be b reposition ned as follow ws:
outjog the 7C; insert the QH in front of it, leaving the 7C outjogged;
outjog the 6C; insert the 2H in front of it, leaving the 6C outjogged; and
strip out the 6C and 7C; insert them in front of the KD, as you outjog and remove the JQK of Diamonds and place them on the face.
If you started with the Modified BHS, the deck is in Sorted (SHoCkeD) order after you pick up the 11 piles except for one card (JD), which is easily repositioned.
From Sorted Order to BHS by Faros and Cuts
Starting with the deck in Sorted Order, perform four perfect in faro shuffles. The bottom card will change from KD to KH to KC to 7S to 4D. The deck will now look like this:
(These shuffles can be performed both quickly and accurately with a new Tally Ho deck, as Tally Ho cards faro shuffle perfectly and easily straight from the box.) Now spread the face up deck until you get to the 7D. Cut at that point, leaving the 7D on the face. Place the cut cards in a pile on the table, with the 4D at the face. Continue spreading until you get to the next Diamond, cut there, and place the spread cards in a separate pile on the table. Keep doing this, but whenever you see a Diamond immediately followed by another Diamond (i.e., when you see the KD, QD, or JD, each of which is followed immediately by another Diamond), leave those two Diamonds together in making the next pile. For example, the 2C, 9H, 6S, 3D, and KD will be one pile, not two. When you are done, gather the piles in the following order: (1) pick up the pile with the JD on the face and place it face up in your dealing hand; (2) pick up the pile with the 6D on the face and place it on top of the JD pile in your hand; and then 11
3) continue with the remaining pilles in the following ordeer: Q, 7, K, 8, 4, 9, 5, 10 0. (3 m out, and insert them in front off the QH, ass you Finally, outjog the 6C and 7C,, strip them t 5C, 2H, and QH an nd place thosse three carrds onto the face of the deck. remove the The sequ uence (J, 6, Q, 7, K, 8, 4, 4 9, 5, 10) is i easy to remember beccause the 2n nd, 4th, 6th,, 8th, and 10th h piles show w the 6, 7, 8,, 9, and 10 of Diamond ds, while thee 1st, 3rd, 5th, 5 7th, and d 9th piles shoow the J, Q, K, 4, and 5 of Diamonds. (The “ju ump” from the t King to the Four ca an be remembeered becausse the AD is i behind the JD, the 2D is behiind the QD D, and the 3D 3 is behind th he KD, so itt makes sen nse that the 4D and 5D piles would d fall therea after.) To go froom Sorted Order O to the Modified BH HS with farros and cutss: HoCkeD Soorted Order,, give it fou ur perfect in n-faros. In the processs, the With thee deck in SH bottom card c changes from KD to t KH to KS S to 7C to 4D D. The deck k will now loook like thiss:
a make piles p with Diamonds on n their facess exactly as above, but when you get g to Spread and the Jack k, Queen, an nd King of Diamonds, D set them asside in theirr own one-ca ard piles. Then T pick up the t piles ba ased on their face cardss in the folloowing orderr: A, 6, 2, 7, 3, 8, 4, 9, 5, 5 10, J, Q, K, which is ea asy to remem mber becausse it compriises two seq quences tha at are interla aced: “A, 2, 3, 4, 5” and “6 6, 7, 8, 9, 10”” (with J, Q, K at the en nd). Finally y, swap the 5S and JD. ng method, the faros and cuts method m cou uld be used d in front of o an As with the dealin mple, one cou uld open a new n deck an nd explain that t it takees seven shu uffles audiencee. For exam to truly randomize the deck. As you ex xplain this,, get the deeck into Soorted Orderr and presents five shuffles (an ( overhan nd shuffle and four fa aros). perform four faros,, which rep ure, you shoow how card ds in a given suit “like the Diamonds,” Then, wiith the cuttting procedu are alrea ady widely distributed, d , even after just five sh huffles. Theen go ahead and do a coouple false shu uffles “just for good meeasure.” (A All that said d, I believe the primarry value forr this techniqu ue is simply to quickly go g from NDO to BHS and practice faro shufflees!)
From BHS to Sorted Order by Faros and Cuts
One can also transform the deck from BHS to Sorted Order with faros and cuts. For this, take the stacked deck and give it four perfect in-faros. In this process, the bottom card will change from QH to 4H to 5S to 7S and to 8S. The deck will now look like this:
Now spread the deck face up. As you do so, cut off piles of cards with each change in suits. First spread the Four through Eight of Spades into your right hand, and set those five cards down in a face up pile. Do the same with the Hearts behind the 6H (creating a four-card Hearts pile); then set down the 6C (creating a one-card Clubs pile); and then set down the Diamonds behind the 10D (creating a five-card Diamonds pile). You now have four piles, one for each suit. As you spread through the rest of the cards, break the spread at each change of suit and add the card(s) to the applicable pile on the table by either adding the new cards on top of the pile or under the pile, depending on where those cards belong sequentially. For example, the next pile from the deck will be all the Hearts behind the QH (a six-card pile), which go onto the 6H pile. The next pile has the 9C on its face and it goes onto the 6C. The next pile, with the KD on its face, goes onto the 10D. The next pile, showing a KS, goes onto the 8S. The next shows a 2H and goes under the QH pile. The next shows a KC and goes onto the 9C. The next shows a 5D and goes under the 10D pile. The next shows a 3S and goes under the KS pile. The next is the KH (by itself) and goes onto the QH. The next shows a 7C and goes under the KC pile. The suits now are separated—and in Sorted Order (except that the 6C is after, rather than before, the 7C and must be moved). To go from the Modified BHS to Sorted Order with faros and cuts: Take the stacked deck and give it four perfect in-faros. In this process, the bottom card will change from KD to 4H to 5C to 7C to 8C. The deck will now look like this:
Now sprread the decck face up. As you do so, s cut off piiles with each change in i the suits.. For example, spread the e Four throu ugh Eight of o Clubs and d set down those t five ca ards in a facce up pile. Doo the same with the Hearts H behin nd the 6H (creating ( a five-card Hearts H pile),, and then do the t same wiith the Diam monds behin nd the 10D (creating a six-card Dia amonds pilee). s through the resst of the carrds, break the t spread at each cha ange of suitt and As you spread add the cards to th he applicablle pile on th he table by adding thee cards on top t or underr the relevant pile. he next pile are the Heearts behind d the JH (a five-card pile), p which go onto thee 6H. Thus, th The nextt pile has th he 9S on itss face and makes m a new w pile. Thee next pile is i the JD, which w goes onto the 10D. The next pile p has the KC on its face f and goees onto the 8C. The neext is D. The nex xt is the AH H, which goees under thee 10H pile. The the QD, which goes onto the JD S on its face and goes onto the 9S S. The nextt has the 5D D on its facee and next pilee has the KS goes und der the JD pile. The next showss the 3C an nd goes und der the KC pile. The next shows th he KH and goes g onto th he JH. The next n shows a 5S and goes under th he KS pile. ds are now in Sorted Orrder, exceptt the KD is out o of place and must be b moved. The card d above, I be elieve that these t methoods for going g from NDO O to BHS (orr Modified BHS) B As noted are bestt used simp ply to get a new deck k into stack k position quickly q and d automaticcally. Howeverr, the “faro plus cuts” method of going from m the stack to Sorted Order O can more easily bee used as an n effect on itts own: t stacked deck, showiing it is mix xed. Perform m the four faro f shuffless, as you exp plain Spread the how som me people arre able to memorize m th he order of a shuffled deck d and th hen very qu uickly “sort” th he deck by separating s a the suitss and placin all ng the cards in each su uit in numeerical order. “Indeed,” “ yo ou can say, “the world record for sorting s a sh huffled deck k is just oveer 36 seconds.” Then ha ave someonee get ready to time yoou with the timer on their t cell ph hone. d and “soort” it with h the cuttin ng proceduree. For the best Finally, spread through the deck presenta ation, learn to place each group off cards face e down ontoo its correctt pile. Alth hough this requ uires some practice, att the end, you y can dra amatically stack s up thee four piless, flip over the deck, and spread s it on the table too show every ything in orrder! 14