An Introduction to Full-Deck Stacks This essay discusses two common (but very different) types of full-deck playing card stacks. The first is the sequential stack, which permits one to determine the card following (and, in most cases, that preceding) any given card. Such stacks are designed to be “circular” (indeed, they are sometimes termed “rosary stacks”); that is, the pack may be given any number of single complete cuts without destroying the sequence. Examples include the venerable Si Stebbins (a numeric progression: see analysis below) and Eight Kings (a mnemonic progression: Eight kings threatened to save, nine fine ladies for one sick knave. = 8-K-3-10-2-7-9-5-Q-4-A-6-J) stacks. There are mnemonic sequences other than Eight Kings (cf. Five Trees, Furry Kitten, Hungry Jackass, Jackass Ate, Nine Jacks, etc.), and numeric progressions other than Si Stebbins (see discussion below), but the concepts are the same. The basic versions of these classic stacks exhibit a rotating suit (and thus alternating colour) sequence that is not very desirable, though there are simple schemes for eliminating this. Arguably the best sequential stack, however, is Richard Osterlind’s Breakthrough Card System, which is easily learned and displays no obvious ordering of any kind. The second type is the memorized deck, in which you simply(!) know the position of every card, and—conversely—the name of the card at any location. Clearly, this is also suitable for anything requiring a knowledge of preceding and following cards, but it enables a much wider realm of possibilities. There is no “secret”, per se ... the stack is simply memorized. There are, however, four alternative approaches to the learning process. The first is simply to do so by rote memory. Decide on the pack arrangement you want to use (ensure that it appears to be random), and just sit down and memorize it. It’s not as difficult as it sounds, but it’s not trivial either. And some people do find it beyond their capacity. The second approach is the use of classical mnemonic tools as a “stepping stone”. The well-known mnemonic alphabet (T/D=1, N=2, M=3, etc.) can be used to devise images for each of the 52 positions in the stack. Similarly, images can be created for each of the 52 cards in the deck. Then scenarios can be imagined, pairing the card images with their corresponding stack position images. So when given a card name (or stack position), one can recall the associated images to reconstruct the relationship, and the corresponding position (or name). This won’t be truly useful/effective, of course, until you have learned the relationships so well that you no longer have to think about the images, but can simply (and instantly) recall the association directly. The most widely-used such stacks are currently those by Simon Aronson and Juan Tamariz, extensively described in their respective books, though this solution can be applied equally to any of the many other published stacks ... those by Steve Aldrich, Laurie Ireland, Bob Klase, Ed Marlo, William McCaffrey, Herbert Newell, Claude Rix, Rusduck, Mike Skinner, Rufus Steele, and Audley Walsh, to name only some of the better-regarded ones. It’s also worth noting that Bob Farmer has devised an easily-learned mnemonic system (not requiring knowledge of the mnemonic alphabet) for memorizing arbitrary playing card sequences. Another useful playing-card-specific mnemonic code can be found in lesson seven of David Roth’s venerable Memory Course. The above two approaches yield a pair of useful benefits: they allow for the most random appearance, and they permit stacks that have been “wired” to perform certain effects (poker deals, spelling tricks, etc.). They are challenging to learn, however, and also have a significant drawback: unless you are regularly doing a lot of memorized deck work, it is easy to forget a particular association in the heat of performance. A third approach is used in Martin Joyal’s Six-Hour Memorized Deck, and Chris Matt’s Six Kicks stack. In place of a classical mnemonic system, these each employ a set of “rules” (Joyal uses fourteen, Matt thirteen) as stepping stones to enable learning and remembering the necessary relationships. By way of an example, the rule for the four deuces (2s) in the Joyal stack is “even positions containing the digits 2 and 4: 22-40-42-44”. The equivalent rule for the Matt stack is “positions ending with the digit 2: 12-22-32-42”. One can see that these are not precise, specific rules (they are more like clues), and some additional memorization is clearly required. Nonetheless, such an approach makes it significantly easier to get to the stage where you can match card names and stack positions. But there is no magic road to the point where you can instantly recall those associations ... that will take a similar amount of time in any case. The fourth approach is an algorithmic one, in which a formula of some kind is used to relate card values and positions. This approach is particularly popular among those who want to do memorized deck work, but not make it a life’s work (particularly mentalists and others who don’t do a lot of card work, but recognize the miracles that can be performed with a memorized deck). Its advantage lies in the fact that a single algorithm relates any card name to its corresponding position (and vice versa). This yields two specific benefits: first, it enables one to perform a significant number of “memorized deck effects” without truly memorizing the stack; second, if the memorized relationship is temporarily forgotten, there’s still a reliable (albeit slower) fallback position. Although it’s possible to compute card positions with the Si Stebbins arrangement, it’s not very easy, so few consider using it in such a fashion. Probably the best three algorithmic solutions are the Bart Harding stack, the Charles Gauci stack, and my own QuickStack (I know, sounds a bit self-serving, but many prominent performers agree with this assessment). Each is easily learned (less than half an hour’s effort for most people). Without going into detail (and revealing information that is not mine to reveal), here is a brief comparative summary of the three: The Bart Harding stack (published in 1962) is the most random-appearing, and will withstand the most intensive scrutiny. The algorithm is not completely consistent, having a couple of exceptions. It also requires the most calculation, and therefore takes the longest to convert between card names and stack positions (though it’s still considerably faster than much of what’s out there). Here are the first dozen cards: 10C 7H 4S AD JD 6C 7C 9S 6D AC JC 8H QuickStack (from my book, Mindsights) occupies the middle ground; it’s not quite as random as Harding’s, but will still withstand pretty careful examination. Doing the conversions is notably faster than the Harding system. Here are the first dozen cards: 10H 5S 3C KH 2S 9S 7C QH 6S AD JC 8D The Charles Gauci stack (from his lecture notes, and also sold separately) is the least random appearing of the three, with regular suit rotation (thus alternating colors as well) and clearly detectable sequences, but the conversions are a bit faster than QuickStack’s. Here are the first dozen cards: 3H 6S 9D AC 4H 7S 10D 2C 5H 8S JD 3C Note that the basic concept of Gauci’s stack (published in 2002) is identical to that of two others ... Boris Wild’s (published in 1996), and Jack Yates’ (1978). In fact, all of these are modified versions of the Si Stebbins stack (1612), itself a variation of the Horacio Galasso stack (1593)! Some versions are quite weak ... the Wild stack, for example, is comprised of 13 four-card groups (each in strict sequence, both numerically and with respect to suit), with all the courts cards clustered at the end, and thus unlikely to survive any but the most cursory examination. This is not necessarily a show-stopper (any card arrangement can be hidden by a sufficiently skilled performer), but there are no commensurate benefits: the computations necessary for Wild’s name/position conversions are no simpler than with (for example) QuickStack, which offers a considerably more random presentation. Anyone interested in further details of this “Si Stebbins family” of stacks can explore a spreadsheet that I constructed to illustrate the algorithm. Occasionally one reads disparaging remarks about algorithmic and rule-based solutions, claiming that they are not “real” memorized decks. This is uninformed nonsense (and a common consequence of confusing the organization of a stack with the issue of whether or not it is memorized). A memorized deck is simply that, and that alone ... one in which the practitioner knows the positions of all 52 cards; the method initially used to learn the card name/position relationships is irrelevant. With any approach, translations made while you are still in “stepping stone” mode will be too slow for some effects (though perfectly sufficient for many others). It’s certainly true that in the case of an algorithmic solution, one can simply learn the algorithm and never actually memorize the stack (this, in fact, is one of the benefits of this approach), but then it’s not really a “memorized deck”. If you want to know the card at position #46 in the Aronson stack, you either just “know” that it’s the eight of hearts, or you apply the various mnemonic rules to work it out: four is an “R”; six is a soft “J”, “SH”, “CH”, or “G”; that suggests a “roach”; that reminds you of a hive filled with roaches; the “H” in “hive” indicates a “heart”; the “V” is an “eight”. In QuickStack, you either “know” that #46 is the seven of hearts, or you use an algorithm to work it out: four is the fourth bank; six is the (+1) seventh card, a “seven”; the natural suit of the fourth bank is the (four-pointed) diamond; the seven is the same colour, or a “heart”. Neither approach is “better” in any absolute sense; they are just different. The tradeoff is that the algorithmic solution can be learned a lot more quickly (a single algorithm vs. a mnemonic alphabet, 104 word images, and 52 word-pair relationships), but constrains the order of the cards, thus limiting (though certainly not eliminating) the possibility of “built-in” tricks. If you use either approach regularly, you’ll find that you soon “know” all the card positions anyway (though it’s nice to be able to calculate them if you forget!). By way of a summary, here is a brief comparison of the tradeoffs associated with the four different memorized deck techniques: rote memory mnemonics rule-based algorithmic ease of learning the associations most difficult difficult moderate easy capability for “built-in” effects extensive extensive quite limited very limited backup strategy if memory fails none fairly poor poor good It’s important to understand that “ease of learning the associations” in this comparison refers to exactly that, and not the total time necessary for translations between card positions and values to be performed instantly, without conscious thought. The latter is primarily a function of practice, the acquisition time being roughly comparable in all cases. Many excellent stack effects, of course, do not require this facility. Realize also that there are occasional (very specific) exceptions to these general characteristics. For example, the use of classical mnemonics to memorize a sequential stack yields a good backup strategy when translating from position to value (since, if an association is forgotten, one can recall the previous card and then apply the sequential rule); unfortunately, this also nullifies the “built-in” effect capability. For the sake of completeness, I should also mention that both Barrie Richardson and Lewis Jones have published clever algorithmic systems that are extremely easy to learn, but cover only half the pack: either all the even cards (Jones), or all those of one colour (Richardson). These can be quite effective for certain effects.