Doug Dyment - Calculated Thoughts

IlIRJIIIIDIlIS IIlIllll filii III lUI This particular layout also lends itself well to usage with Flash Squared presentations, as described previously In this section. Interpreting Natal Squares, John Wells Style ~ late John W!!II$-a thoughtful ~dj~min8 frill!f1d. and e)(treme!y accomplished re .. der~was an early recipient of the Natal Square calculation method. absent any methodology for interpretation of the nsulting square I yantra. Coru;equently, ,oIul developed seve",l ideas othis own for interpreting those results, whio;:h! include here (luge!y in his own words) for those looking to explore further uses of this highly functional impromptu orade: 1U>.!1t>l' $'I1I~rt$ll'rt amstrucltd in th! pl'OU$$ of making the Y"ntr~. and I inlvprtl tIlch of Ihtm as DIU rif IN: 115,roIogictll h"ulln. TIu! "PI"" Iql rom!' is I~ firsl ""~, and lhi: Pl'08rtSSion "dv.:ln~ dockwi~ around Ilrt Sljlllfrt. This am tllSiJy ~ usnJ in rHldilion io-m ill pl.a of-lhe method giwn !ry Oou8. 17rt- IJUlioJl ""d horium/Il/ II1TOW!I 115 ustd in -lic-Iac-IOt.'- II.IIt1trology" could I1t 1I~~/UUJrIl. If I« lilkt IN: pht"~1 point of JMw.-/lulllm p=nIl 15 "alrlflucna of Iht immtdUllt ptlsi Qnd immtdillit jw"lT-c-tiltn. Irtilling ~ four unkr uUs lIS Qn inl~n «ltd "nil pumil Iht fol/~ s Khmul..M Iht "pper lint rtprtStn/$ Iht i .. flu lift, 21. y"" <0" ~"d ,h"",,,si' """"1" of ,I., ,<>pi< in Rid>I«i W, .... ,,,·, 1'1."""""" M.,;,- (1'.1')8 . .'it 1\001. MN),,,"""I ... ~..,. of hlo """'" boo>l.. . U;. No« Ih< ,h"llv"1 '" .... ,u""",,,,,,,,h--Jc.,,.:1opW ""'1'V"'tc . 0«I t". So..,,, ".I", («pt.in<<i ............ 1)-1; "p"'.-.:«I .. >fl,,, ",- _h.>,.-h bn< j., ,ht "oa •• ",1.11 ~

52 lilt thougllt lift '" II~ sitftr; ~fou r sidt Sljuarrs IItr pa/lnns of bthGmor; Imd 1M boUom rowhtt emo/ional slalt. 1'h.! Itft coillmll row/II ~I pilSl i"fI"nI~ 1M lop lind balloon mtlv, 1M p~l; IIlId 1m rightmost column, tlrt ful ll.Tr. (lIS irr II~ 1..0 Sh" $/j,,,,,d. 1M dinctionlllity is /I IIUIU" of pn/trmu. Some /l1I/hors muI lilt :;qUiin' from Itft 10 righl a.! pilSl goi"S IOWIITds lilt fu ' urr., cIlht 15 uia W1Sa. I dtm'llI5r this wpprwc/r, bill il nwy find fr!XJT with some. In using lilt $qUIIUS 10 depid Iht I15lro1ogiOlI IrcrnMS, tht 1111"1/1tr$ iN Ilrt SqlUl,", following &pharial, lin i lllt rpnltd /IS tlrt 1111'01 Mapr5. Numbers 11001'(' 22 ('lin 6 ther lie Imzled 115 individl/al dig;/s or redllctd in llu S/litulnrri foshion /0 /I singlt num~r. I hlillt' hIld milch SllcedS with this ItcJmiqllt. In TtIldlrr8 Iht sqUllrt, 1>I1l [JIll tmphllSiu alllntclioll$ bl':f'wWI MUSt posililm lI"d "'II1IW. whcr 1M amJ rtp~lIti"g" artain sign ItpptIITS in il5 prupo Iro~; e.g., IIv HriropMnl in UI' !I«Ot1d hou~. / look for rql('lili"n of IIl1ml:tt1$ ... milly, any pdtlJ!'rltS 'lull $lIggtSf tlrnn~lvtS 115 IfWningful. My tr:pI,,,,,,'iorr for 1M yo:Inlfll rruty alsllilt of inkrt$I to same. F(Jf' I1IOSI slUm; I simply gire .lxIsic upliInation of tlluch/Ill jac.ts, tHot.gh for olh~~ ftmrilillr with ,tandard numeroiogy- I (On"lZSt nllmtl'lllogiCli/ "",dyr;i:; ,hlllllgh cIlWiCII/ rtdudion with_ in this "",mttri, tl:po>l'ISion. Standard numerology d'QWS tilt vibr'lliory jnf/utnct'!i of any numbtr into a point. The !fIlnlra eJ:"P<'''ds il into mllltipit dimensions. I ffllUU Ihal'$ nol prtcilidy rorrtct, bUI it's a WIIJIlo make sense of the pr«tSS for tltcse who "Imow Ihei, numerology" alld hiliit'll" 5tt1I this befort. Thtse, thani;folly, .. rt fow. A final naie is lilt list of tht y.zntnl ~ a qutstion ... nswtrillg droict. &a!1I5e lilt twdllt' Itcusa gcwm tJOITious thillgs, Mllrly .. ny qutStioll CIIn lit IllIdrtSSttl by Ilf'plyillg lilt /MI,,,'''g of Ik C/lro in" pdrlicular ilJu"rt. Ont might, ill doing group ~illgs, prtptIrt " Y"n/,a for 1M ammt ~It, ""d IIJISWlT any ques/icru: asUd from the SljlUlrt. All a/lema/roe iii /0 follow tilt ItfId of CIl:S<lIIOVIIZ, wItc !Iud his -lIumtrlll calC1l!us" to ",,:;we, qutsticm, for modulolls Vendian ncbla. Qmf/Q"/ tilt CCI'7ItrShmts of a ptTSOn's ""1IIt" (lilt firstltllt, and first ron50IIQn/ of the first nnd 111$1 namts of Ihe qutr(nt) int" numbers, and make II sqUart to IIn~r tOOr qutstions as uplaintd ab<rot. Anything thllt can plQusib/yllt rotIvtr/ed to numeric dlltll (/1/1 be 5ubjtclttl I" Ihe -calculus-. Gturgt J!.m1trson's kryloord

IttJllli'fue" CIlII lit profitably used in Ihi$ fashion. Th. fir$1 four leiters uf lilt W(lrds (ar Ihe corller$/Ollts of two W(lrds) b«Q"'t lhe WIler >quarts at the Y"n'ra, lind qutslwns <m IVtswtrtd lIS detailed prrvwII$ly. The Y'ln' ra is greal {1m lIS II ""'IIIi(" Itdtnology, lind Dollg:t method i5 tile rrl5;est rllt allII. IIcross 111111 "''fuilTl lIa aibs or memoriZillion uf numbers; I IMllk hi", for $hll,;ng il With lire romm"ni/y lit IQ~. 2'. ';""'!t< lI. A..s.r..., ...... 1"'11d<.o "', .... '1""""" .. ,I,,,,"· ,,,.:In. «<h,,,.!,,," """ bo: r...."" "' I .... 1tioI< , 1" 11.,, &oM;""""","", Kh""r- 19HI I'!' ,.... 53

Fair & Square (An Honest-and Classic-Magic Square) All of the foregoing LeOKls us to the pinnacle of magic square work: a method for the honest production of perf~~ and seml·perfed magi<: squanos,.ln thI! traditional ~shion (where the squall!: is being constructed for a spedfic magic constant). one in which we simply bite the bullet, abandon trickery, and construct them for real, "from scratch" . Over the years, I have described severaL techniques for acmmpllshlng this. What is presented in this 5«tion builds on the previously described ard.ilecture of the Foundation Square, and is lo my mind the most satisfying solution: the culmination of a kind of uni6cd theory" of magic square creation. Doing it For Real: Just How Difficult Is It? Traditionally, this has been a challenging task: _ eral substantial books h.lve been written on thetopica, and evenso<alled $impli1ied~ methods that I have ~ ""(jUice significant memOTiulion and calculation. Fair &: Square. however. offe rs a radically different solution. ~ated Specifically lobe easy (well, easiu anyway)both to learn and US(', Building on the Foundanon 5qua1l! eliminale6 most of Ihe non' trivial math,. and results in an incredibly utisfying solutiOn,. m~king the feat fully impromptu, and freeing you forever from \he problems .nd Prop!! assoctatro with trick solutions '" all in an, ,, Indy valuable skill, To be .ble to perform this Munder 1m" is not trivial, .nd is IIdmiHcdly not for twryolV, but it's not llull difficult; if you're even moderately comfortable with arithmetic, I eIlCOUnIge you to give it a try, l • . Th ... ,...,h m."c.I ",kn;.".,,,,,,, d""ribinJi ,h, , ... """'''"' of. ~ •• "I""" "f",m ..,..,.h", .,,, Som 0.101', 11." .. "" "Prfoo;o.: 1b. /n." $mm "rio. M"f'< s,...,.. (c»< .. ,,,, 199)), ~I'P ' C,alt< MtGo .. ~ Snader. Mlw s,..- I~lc o {'J<y. 19UI. \"" ...d 0 ... 011< ~, '''' A ..... "I' AI.,., ."r-o',if M."" ~ o.-.~ ... _ (Cl.<p:nlW, Wyom;,,,, 54 19611, IS",",

Building on vVhat We Know If you have maSiered the Foundation Square methodology, you al1'1!8dy know more than half of whal is !U!CeSSary to perform Fair h Squa re. All squares modelled OIl this ardlitecture will be perfect" whomever mathema tically possible (semi-perrect otherwise), will ronta in no duplkate ""lues (exo>pt for magicconstant5 below 30, for which this cannot be avoided), and will sum to the magic constant using all of the combinations shown at the beginning of this section, Exploiting the Architecture Much of the hmagic" in this square stems from the fact that there are actually four gepara te, Interlocking 4-ctl/ grell/f", as illustrated here (the asymmetric nature of the individual groups is whit makes their memorization difficult in traditional methods). If you lake the time to examine this architecture carefully, you will appredate thlt each of the 36 combinations guarQntMt to add up to the magic constant contains exactly one square of each colour (the l'('nt;lllUng 16 combinations are only va lid for perfect squares. and rely on other ma\h.ent;ltical properties to function correctly). We have already seen (in the FoundationSquare) tha t the perimeter cells can easily be calculated once the values in the four cen~ ..",Us are Specified. An that remains, tru,n, is to learn how to determine the exact four sta rting values that wHI yield the optimal quares that Fair & Square can produno. And three o f them are easy as well. If you M w:n', yet mastered the Foundation Sq"are, take the time to get it down really solid. Th"n, once you are tMrlJloIghly fomiliar with it, adding the ad d itiona l steps for Fair & Square is quite straightforward: 55

you'll be amaz.ed at how easy it actually is. Tadc.ling both :asks a t the same time will prove more challenging than they need be. Mastering the Mathematics Shown ~ is the dassic perfect magk sqUIre, using the numbers 1- 16 to produ« the magic corutant 34. The four interior number!! were produ~ in the clockwise order indicated (A -+ B -+ C .oJ DJ; the first vllue (that for the A~U)is termed the Initi al Fill Vdue . 16 2 7 9 5 11e 14 0 4 10 8 , 1 15 A 3 13 12 6 Once this Initial Flll Value has been determined (and we'll get to that shortly), the remaining three numbers Ire formed with just simple I dditions; the numbers to be added are Ilway5th~ ,.,me, and must be committed to memory. They are, In order: 7-3 -3 Forperfect Jquares, knowing these three Hstand.rd increments'" is suffieient. So. in this case, the Initial Fill Value (I) plus 7 yields 8, the va lue for the Ik:ell. The C-<RU receives g + 3, or tL And the o-cell is fillNi with 11 + 3, or 14. Other perfee:! sq~ are constructM using different Initial Fill Values. which we shall shortly learn how to determine. But perfect squares are only possible for magic COIt$I.nls ,'''', t xcrollhirty by ~" ttlUl m~llipit cf fo~r (so, 30, 34, 38, 42, 46, ... t 21 not quite II quarter of all possible integers. For the remaining thMe quartetS, the third 29. M .. ,"'ft,.,kio", wOH ,..-II ,.... ,ho , • ..",... <000,,", of }II .... " ..,.. y..w . r<.f«, ~ ... " . .. i , .... ..J., in , •• t...uI .. m t .... .,h .." . pooi<l .. .. ,,,,,,I in ,Ik "'-«II. r", .. " t __ ~ i>ow<-< •• _ 56 ~ io <r' ''''.J,. .......... ......... hi ... "fW< "."" ... I": ... ..,,.,....r in .. U J(,,,._ ,,.;.,.n,..

(D-<:elll increment will not be three. Consequently, we must determine not only the correct Initial Fill Value, but also the Remainder (R).. the amount by which to further il\CI1!105e the value in the fourth interior cell (0). Determining the Initial Fill Value and Remainder The actual calcula tion involved is q uitestraightforwud: Take the desired magic ronstan t: Subtract 30: Divide this by 4: »by n-30 _ 42 42+ 4 ", 10 (R = 2) The quotient (10, in this example) becomes the Initial FiU Value, the number to be placed inlo the A <t'l1 of the square; the remainder (2, in lhis example) is used as the addition'll ildjustmenllWeded 10 determine the D-<:ell value. The subtraction of 30 is pretty easy, as you are only subtn.dillg a sillgle digit (the fina l digit of the magic constant remains unchanged). Rlr ronstanlS greater than 100, you miy find it simpler to cou.nt backwards by tens (e.g., 123 ... 113 -t 103 -t 93). The division by 4, while simple with ~1I magic rorutants, becomes a bit more cha llenging as that number incruses ill size. Over the years, I ha ve experimented with a variety of Nclf!V('r" tcclmiques (some of my own devising. some from others) to ease too burden, coming finally to the ronclusion that it is be5t accomplished by simply doing it, using the long division method thaI you learned in school. TI-.ere are il least a couple of reasons why this is the case. Most traditional applica tiON of the magk square stick to tw<KIigit magiC amstants, in order 10 keep the arithmetic easy for . u diences 10 follow. And given that you probably learned the 4>< lable from 4 to 48. you can already handle the majority of !he po66ibilitie$ with no actu.l loog division needed. The rest (magi( constan ts 82-99, whim entail dividing numbers from 52 to 69) shouldn't prove p"ticularly difficult either. So take hearl, and practiCE'.lII As a bonus, yOl.l will shortly find that you have learned the 4>< table all the way up 104><17-68 (which is just five more Ihan the 12 you likely already know)! Jon. An <'<{II.", ",oK"'" ,001 ; •• .. "I"., "."' .... ,.."..",... ~", ... l '" p...J"", ...p: " •• " .,," in ,he " "I>';n ..t. .. h 1"" ;n,<n<i ,o OJ""'< . ........ 'f'<'"Ii.td ( .. >01 r ... ) R>OI>;k 'f'J'O .. " . ... ,I.>\k..., do ,~;,.. .. ....... >Oro< cakol"'H ~ 57

58 Even larger magic constants should not be unduly daunting. Remember that. in most:;;om.arios, you em initially write the magi( constant in some visible location. S(I you will have that to eo'15Uil (remembering that the actual dividend is that constant less 30) white you ~re performing the division. And you can write the quotient i~ly into the A-eell as you are working it out, 00 there is a limited need to retain inJorma tion in yoor heitd, apart from the remainder at the end (.and a suggestion for doing that folLows shortly). Filling In lhe ~uart F~llng in the square is straightforward: enter the Initial Fill Value in the "'-<;ell, then fill in values for Ihe 8-eell by adding the first slandani increment (7).. the C-eel1 by adding the 5ealnd increment (3l, and the D<e11 by adding the third (3) plus any Remainder (R)_ Finally, fill in m_ the 1l'1it-1N . twelve perimeter rells---using the Foundation Square Remembering lhe Remainder Recalling IN I1!:mainder afler having just performed the simple arithmetic for the 8- and C-cells <:an be aided using a simple "finser mrmory" trick. Imagine the fingel'$ of your non-writing hand to be numbe~ as llluslTa~ al right, below. As you begin your divisionby-fou ... placeyour thumbon the '1)"" (inde~) finge ... as in the familiar ~? ~ sign. indicating a R'mainder of tero. If, upon completing the d ,vunon" YOll have a non-crero remainder, simply shift your thumb to the approprlate finger tl,l record same."

Coping with Smaller Magic Constants The mllgic constant must ~ 30 or greater to avoid duplicate numbers in a 4><4 magic squa~. If you don't mind duplicate5,. it's possible to produce functional squares for magic constants u low as ZO (enllbling the ~lItion of squares fo[ the full range of adult ages, a useful presentational benefit). Two simple adjustments to the calculations are needed for magiC oonstants in the range 20-29: t. When calculating the Initial Fill Value, subtrbCI 20 instead of JO. 2. When filling the D-ce\L. compute it!; value U$ing the A-<:ell (below it) as a starting poin t, ra ther than the C-cell (to its left), as Illustrated he~: A filling middle etlIs (co nslants 30+) filling middle ~115 (cons/alits 20 - 20) Optionally, you can fill the D-cell as always.. but deduct 10 from its value (so, C-cell-value + 3 + R -10). Thls introduCe!l an extra step (subtracting 10), but some may find it easier 10 n!memboer. Magic lIquares for constants under 30 contain duplicate numbers,. so can never be pe[Wet (though they produce the correct results for all 36 basic combinations). A Concluding Presentatiorwl Suggestion Knowing how to create a mllgic squan! truly -from 8Cntch~ frees one from tl-oe constraints of trickery-b.ased methods, One way 10 exploit this freedom ;, by writing the numbers, as you calculate them. on ix t~n individual Post-lt® notes, placing tach in its proper position as you proceEd. This not only seems more impromptu.. it offers II useful alternptive to the need for a special board or pad on which to draw the square. 59

• I I

Fu Deck Stacks A Selection oj SurrcplitioU5 Sequences

, j I r Ii'jj

Fu Deck Stacks In magical pulan<.:e, ill ~slack" is ill specific. intentiOlUl1 ordering of ards. A ~5tacked deck~ can ~ partial (50_ ofllle eards ue Imnged in a stick) or ful l (~ II ofebe canis are SO .!Tanged). This inrroduction discusses two common (but very different) type$ of full-dtdl. air<! stacks. Although the focus he"", is on playing cud stacks, the principles apply equally to other types of cards (Zener, (;1m!, etc.). Sequential Stacks A sequential stack permits one to detetmine tho:: card foIlow;ng (and, in mosl cases, tlllt pffl'tding) any given card. Such st&do:.s are relative in nature (i.e., no particular card is designated u being at the top of the deck)' and designed to be Mcyclic"" {indeed. they are SOfO('times termed -dm.Jlar" or -rosary- stacks~ Consequently, the pad: may be given any number of single complete cuts without disturbing the functionality of the stack. Classic e~amples include the venerable Si StebbiJlsl' (11 numeric progn.'5.~ion in which the val ue of each card isoffset from theprevious one by 5(lmc COf'ISlant) and Eight Kings (a rhyming mnemonic progression: Eight kings threatened to save. nine fine ladies for one sick \:.nave. 8-K-3-1(}...2-7-9-5-Q-4-A-{)-J) Slacks, There lire mnemonic sequences olher than Eighl Kings"'. and numeric ones other than Si StebbiM". but the ooncEplS remain the 5ame. The basic versions of thl!Se classic Slacks elfhibil a rotating suil (and thus aJrem.ting colour) ~uence 1 .... 1 is not very desirable; there are techniques for eliminating this, but they add to the complexity of the neld-suil calculation. Better (more deceptive. and iust ;JS e;JSily used) stacks eri5I. howe~-er. 31. 11>< ...... IIn;I ""so ._ . .... k ..... ",;~ I"'bishrd" J~1J . boo! poopuluio<d br 15'_ (.,.H".1 ....... $I Soo:bI>I ......... (:-J T.a. _ n.. ~ n.,.N.- 1t.fo<_!II9!). 'n.. ........... 'D • f"l\;!,. 01 .. .><b, .>II 01 ......... . '" ...." ..... 01 "" H<>r><", G.ob.... .. od<. ""'" ~ ("~ tI, (A"" 8rlI_ .... ,Ii ~ .... "' .. _ {I ~l). CU, ..... Iy. ,ho...., I> ...w....:. ,,,,-, SoeNIl~, hl--U: co."'')' '" ....... "" """t<, f"'....,~ I, u>«I .. ""'n'"'''''' "' ..... , (.>0 did (,;., ....... 1, .u So,"", ."1""''''' In''! .. 1.. F, ... T,..,. 1'''''1 /(''''''. 110.", JM*">,. "' ..... ~"', Nin< Po'h, V-fo"., .. " 1oA,.,.J ""cloob'«Ilr mo"y ""'er>. }I, l,oJo:N •• whuIo. fJ.,lly '" "''''' ....... """ b«n .....,r"I~'" ""'" 'M )'o~,," ""n, dltli:t<nt 1""', ....... oJ "<1""" I",,,,,,,,,,,,, . .... 1< ~. 0< "..." Ii)' 6,,'1l, bu< """' ....... """ ........clio,.., ..... n., ,,(tI~· " RI, 63

64 For5l!qUentialslacl<.s. the prindpal goa l is ,n effective compromise between (l) the ease of detennining the neKI_ ll1d p~vious-car s in the st~ ~nd (2 ) the degree to which the slack appeaB to be a random IIS$Oltment of cards.. "New deck order" is an example of an arrangement in which it is trivial to determilW ,djoining cards, but one that does not look at all random. At the other "xlK'tlle is a stick like /tkhIrd Ost",lind's Bl't1lldhrowgh Oml Syslml, in which it is difficultM to determine th,t the cards are ord~ but that requires a considelable numbel of "plocessing" steps in ordet to make the next· and previouil-Card determinatiollS. More COlllemporary sequential slacks (including my own DAO and 4D S/fI(Ks, descdbed later in this book) strive instead for an optimal compromise somewhere between these extremes, combining an eaSO" of operation comparable to that of Stebbins/Kings with an orderil1g thai appears random to all but quile rigorous examination. In truth. IIIl accomplisMd artist is not plagued by audiences deJl13nding to examine the cards. It's w~ to recall that superstar mefttalisl Chan CllNSta built his stell arca~ on the Cighl Kings $lack, and .... Oflck:11$I IIlIIgici.DS Stewart J~ and Gene ADdenon chose !be Si SIdl/lins .bo~.lI olbers! That laid. unless neceuary to exploit the paniculu orclcTin, ofStebbiDSlKings-likc systems. there il simply no good reilson for modem...:lay entertainers not 10 employ more deo:eptive approaches. Memorized Stacks A memorized stack (aka "mcnlOrized deck". "rnemdeo:k" ) is one in which you slmply(!) .brow the position in the k of every card, and-conversely-the name of the card at any position" . Gearly, this is suitable fOf anything requ iring knowledge of the pr«eding and followins cards, but it enables a mud! wider tulm of possibilities. There is no "trick" to this; as 1m- name suggests. the st,ck is actually memorized. ~~, however. four alternative .pproachH to the learning process. j~ . iJilli<ol, for ....... _I<. ,ho, , .... ,h",,,,i<i>nt. "'" "'" .... ~Iy d<..~i,,-.j . • '1<0. 1)0 .... , .,.."r ... ,hi> ~·',h ,he ""."1" of " pid!» • • ....., .. i ... ·, d.<~ . .. ]>"fo,">Cd br .......".,..,. '"'put" .... !do ...r.,. '" bminr. tho: "rder aI ,.". ta/tlo in. "u\,.h"lt\od <h •. s..do ... "-,,,,,,10 •• oJ<, .... 1'"'''''oiI)- COH«ro ,htmo<l.n with ,t.. ""' .... 01 1 .... '1011.1 of ,,,", inodl.wool aN~

Rote Memory The first, and most straightforward, is with the use of rote memory. Decide on the pack arrangement you want to use (en5ure tha t it ap~a rs to be mlldamj, and just sit d own and memonu it. 11'5 not as d ifficult as It soun ~ but iI's not trivial either. And some ~Ie do fi nd this approach to be beyond their capacity. Classical Mnemonics The second approach is the use of dagi",l mnemonic tools as a "stepping stone". Thcwell-known mnemonicalphabe\ (T lo .. !, ~2, Moo3, etc.) can be used to devise images for ucn of the 52 positions in the stack. Similarly. images Can be created for each of the 52 ca rds in the d~ . Then S(enarios C<ln be imagined.. pairing the card images with their correspond ing stack position images. So when given a ca rd name (or stack position), one can recall the associ l~ images to reconstroC\ the rela tionship, and the corresponding po6ition (or name), ThL~ won't be truly useful/effective, of course, un til you have learned the relati(>n5h.ips so well that you no longer haw to think about the images, but CiIJ\ simply (and instantly) re.::all the assodatioos directly. The mosl widely-usro such stacks lire CI.lrrently those by Simon ATOI\SOn .nd Juan mari~ extensively describN in their respective books, though this solution can be applied equally to any of the many other published stacks ... those by Steve Aldrich, Uourie Ireland, Bob Klase, Ed Marlo, William McCaffrey, Herbert Newell Claude lUx, Rusduck, Mike Skinner, RufusSteele, and Audlcy Walsh, to name only some of the better-regarded ones. It', also worth noting that Bob Farmer hall devised an easilylea rned mnemonic system (not requiring knowledgeof the mnemonic alphabet) for memoriting arbitrary playing card seque~. Another useful playing-alrd-specific mnemonic code can be found in lesson seven of David Roth's ~rable Memory Cou~. This lind the previous approach yield a Pilir 01 useful benefits; they allow for the most random appeill"iU>Ce, and they permit stacks thai have been orgmized to perform very specific effects, commonly s~m g tricks (which I have never found to be particularly strong material), poker duls, and the like. They are challenging to luln. however, and h~ve a signifiC<lnt d.."wback., unless you rr:glliarly do a lot of memoril.~ deck work, it iseasy to forget a partkular ~ssodation in the heat of performance. 65

66 Rule-Based A third approach is used in stacks such as those proposed by Martin Joyal" and Chris Matfl". [n place of a classical mJ1emoruc system, th e~ employ a ~t 01 "rules" (J oya[ u~s fourteen.. Ma tt thirtet'n) as stepping stones to enable learning and remembering the nffessary relationships. 6y way of an example, the rule for the fou r deuces (2s) in the Joyal stack is '·even positions containing the digits 2 and 4: 22-40-42-44". The equivalent rule for the Mati stack is ·'positions ending with the digil2: 12·22-324 2" . One can see that these are not alwayt; preci~, $plrific rules (they are often more like dues), and some additional memorization is c\early required. Nonetheless, such an approach makes itsignificantly easier 10 get to thestage where you can match card names and stack positions. And no system offers a magic road to the point where you can iuslclnlly rmllI those associations. Algorithmic The fourth approach is an algorithmic one, in which a formula of some kind is used to relare card values and positions. This approach is particularly popular among those who want to do memorized deck work" but not make it a Lil,,'s work (particularly menta lists and others who don't do a great deal of card work" but recognize the miracles that can be pt'rfonned with a memorized dffk). Its advan tage lies in the fact thai a single algorithm rela tes any card name to its oorresponding position (and vice versa). This yields two specific benefits: first, it enables one to perform a significant number of "m"morized deck effects" without Iruly memorizing the stack; second, if a memoriud rc1atiomhip is temporarily fO'lol1en, there's still a COnsistent, reliable (albeit slower) faHback position. As with sequential stacks (which are also simple algorithmic methods), a variety of approaches have been proposed. Here are a few representative examples: Jack Ya tes (1978), Boris Wild (1996), and Charles Gaud (2002) have each created modified" versions of the Si Stebbins stack. They're not particularly random in appearance, with regular suit rotation (thus alternating colours as well) and dearly detectable sequences, butlhe calculations can be made quite quickly. J]. ),I,nin·, .ud. '""'5 " hh , J"'" d<>1 01 "",ful i.ro,",,,'" ~n fooU-<kd ,uclo, in K'·" ..... t. i. ".&h' in hi, 1'" 5iJ<.H •• , M.m,1iwilJ.d, (Sa,d •. WA. 1997). }8. Ch,;, M."."'ili KKk.." '''ok 11""""') «,,~ lOOn 3') .... t,huup. it·, p'",ib!e '" <»ml"'" ,,,d I"'>i';om with ,I.: 0"ti .. 1 SI ""bioi", """F,"<f\,. i,', no, ""). cO»". '" f<.w """,Ok''';''$ it ~ ""'"" • ia.b .....

The other end of the spectrum is ~pied by the Bart Ha rdi.ng SI&ek (1962),. which is very random in appearance (though. having at least four repeating patterns, will not withstand i.ntensive scrotiny). 11Ie plgorithm is not completely consistent either, having four exceptions. which must b@ rote memorized. Finally, it requires roMiderable calculation. thus takes the longest of all these examples to convert between card names and slack positions. MOn! recmtly, -rhe Solution" stack, proposed by Atlas Brookings & Raven Ga irloch, offers a Similarly random appearance to the Harding sta(k. The algorithm is q uite complex, howevel; involving four d ifferently-sized "banks'" of cards, half a dozen different rules,. and arithmetic with two-digit numbers. Further, more than a sixth of the cards DT(' not add ressed by the algorithm. so must be rote memorized. QuickStack 3.0 (described later in this section) is my own contributlo" to this gen~. It is specifically designed" I tetradistic stade_ which by definition is not completely random in . ppearance, but will still withsta"d casual f'xamirlati()n. Doing the COflversioru;. howeYet; is considerably (aster than with the Harding system. The Q Stack (Also mine, and described la ter in this section) offers yet another approacnlO an algorithmic solution. incorporating the fastest algorithm I MOW that )'if'1ds an examinable stack thai is truly random in appeuance (unlike many p:leudo-random sequences.. it f'xhibits v.luf' and suit pairs, longish runs of idCl'ltically..coloured card5, etc.). Finally, nOie thai both lewis Jones'" and &rTie Richardson" have published clever algorithmic systems thai are at~mtly cuy to learn. but cover only halflhe cards in the pack: all the eve" values or all the red suits, respI1CIively. l1>ese can ~ quite effedive, howevel; (or cerlain ap lic~tions. "Real" Memorized Stacks? Occasionally one n.'ads dispa raging remarks d aimlng lItal a!gorithmk and rule-based solutions are not 8rcal 6 memorized decks. This is uninformed nonsense {and a common C(/nsequ~ of confusing the organization of a Slack with the issue of whether or not '0. Ltw .. J<>n<o· -M."""y.o.n- ..... Ii,,, I"'Llahtd 10 ~ Go"''''''''' (,""odoo. 1993) 1'1'. ~_' 9 ... ,.I "'''f< ««0<1, .. h .. ",nniw. s, ... wh H ... "", (1d(.l"'hli.he.i. 2004) 1'1' .1- 9Il. 41. Il>,,;' Il>duol>< .... -l..uy ~ .... ,M......,riml o...k·. 6,., f'VI>liohN ;.., , ho; Clvi,,,,,.. 1'1')7 '-' of Oub 71 "'ou<i",, ;, n_ , .. il}' "",oJ In ~ hook. A<t rn (S.,"l< .lOO~) pp. ~l-~). 67

68 it is memorited). A memorized deck is simply that, and that alone: one in which the practitioner has memorited-and thus blQWS-lhe positions 01 an 52 cards; the method initially used to lea rn the card name /position relatiooships is irrelevant. With.my (non-,,*,) approach, lnInsbtionl made ,..hi leone is sti II learning the $lIIck will be 100 slow for some effects (though perfectly sufficient for ~y CHhen). I,'. ceNinly true that, in the cue ofan Il&Onthmie $(Itutiof\ ~ can simply learn the algorithm and roever actually memorize the stack (this,. in fad, is one of the 1Nn¢ls of thi$ approach), but then it's not really a memorized ded". U you want to know the card at position ' 46 in the Aronson stack, you either Just remt'JTlber that ifs the Eight ofHtMIS, or you apply the various JTmemonic RIll'S to work it out: four is an "R"; ,ix i, " soft "J", "$H", MCH", or ·'C"; that suggests a "roach"; that reminds you of a hiYi: fil\ed. with roaches; the "W in Mhive" indicates a "HeaN"; the "V" is an "Eight". In Q uickStack 3.0, you either remember that ;46 is the Act o/Diamcnds, or you use an algorithm to work il out fortysU denotes bank four, the seventh (6+1) nrd. an "Ace"; the natural suit of an Ace is Spades; In the fourth bank.- it is three (4-1) greater. a ~Dia mond". Neither appro;>ch is '"better" in any absolute sense; they are just different. The trade-off it that tbe algorithmic !IlJrutiOl1 Ciln be learned much more quickly (a Single, straightforward algorithm V5. a mnemomc II.lphabet, plus 104 words and thrir associated images, plu,S2 imagepair relationships). but constrains the order of the cards, thus limiting the possibiUty of building in arbitrnry effe\:ts (but !lill enabling the incorporation of plot mdltocWlpgits, an Iiternative pn:fe~ by many). An~ using either approach regularly will $OO!I remember ,II tbe can:! posirion$ anyway, though it's nice 10 be able to calculate them if you forget!

A Summary of the Trade-Offs roo mnemoniC$ ~ ............ _oflNrning ,." difficult moderate . .., the a$fOC:ialiQns" difficult backup stra~gy - lairly poet poo< ,ood if n>ernory f~ils<> liupport of random - , ood very limitN! limit"'" "buill,inn effecu" It's important to understand that "ease of kamil'lg the associations" in this comparison refers to exactly thaI, and not the additional time necessary to reach ~ stage where translatioN; between card positions and values COIn be performed insllmlly, without consciocts Ihougill. This is primarily I function of practil::e. being comparable in all COIses. And many excellent -memotixe<;! deck effects" do not require this facility. oil . l>1f\<",,,, p«>rl. 1.0" If<,,"~ k.", "~ ,,)·k,. '" ;, j, , .... r-It.!< '" """""Iy .,t... .. ,,,ri« ,h" k.",;"~ "1>«' 10, .11. I M>"<."",np«<l '0 d<:><,;be ,I>< ...... ",,,",,,""11 '"P' ,..t ""J'<''''''''''. 4). ·11><"", of ",« .K."'.,. '" , b.,;,;,t ,,....,,,,.,,,, '" "" ........ ,...,....,;,J "",J Ji<Id<' fir,oct""''' i»ck"l' '""<p" ("""'. if ....... ,d.,.." ~ "',.""n. 0"" .... on"). "'" """".;.>1 .. I. ;n """'l""''''''' ""h . .. ...J io«,~ ,",,,I), ""fOn .. 1W<I1. mk ~ ~"M,fi<> ,I>< ,""l,~. o;lI'= lid .... .,. +I. '" l ... h """ 0k"<0>«)' >not ,t...;aI .. """' .... Col" I ........... ,h ... , ............ of """" __ t... ,,_od.t.l>lt r ............. -.."'" ..... "" __ .. in "'WOO' of..,...-Jic aJ<l ,rid>. B •• th;< bdl, ,"", _ .., ...... "" -.. ,.;do ",he. """' ...... .M ........ hO<J,.. c.. ..... ......... ,a,- .,..,.....,ri< oooI.'iow Iao<I< • .. #1.....0... ",.,.Jio"" ..... k.. <><.) ..... 1>1.: • .,.." ....on:r of"""......,. .. ""'C diC< ... ...... " h, ... COOl be ..... J;I><>.l '" ptodu« _~ .....,;.p r ... (*" . • h~ ;. ~.iy ..,.. Q."d .. ",""" .lOU ....... < ... mI~ Moo, "'!w If;",t..l<d __ ld "" .... ,tw, oIus b "'1""-'" mn~ .ha, onI)o ""'1''''' ' ~rul"· "n<qIO<. p<Nn<r.,.;n..I o;lI'",,, «opc<ioIr .-lw:a ,,,,,,,,,If,, .. ""'" ",«k""m;".,j br....--....,~ 1"" < .." • .1 .... AI.... -'><kr,,,, •. '" _. hc!;.w, du, ..... "",><l~,;,; " ... ~ I. the ,,""'!;'">, ,,1'.,11 " .. b.' V<" ,k. j .. ,iy <<101~",J J""'" T."",; .. • ~., t.....;", .... .I hoi 1 .... 1,.i.·..tl"""·"rl<l ' M" ,,,,,,"i<>" .""k'" """T ,..",. <y<." .. liy ,,,no "OIJ,od '" ,II< "w of. ",u"uc.lly 'y"n"",,,, m"k .. k" p,i ... .,. ''''" (in f..". I", 'bh;k;,;"'n Sf..,..' n"y to< ,I.< I .. · .. , .. "",], .. bk of , ,.d, """s... .. ·"h j .. "'"" ... ,' ""',;.,,, ... d 104:h1,. ...... t.k ..,J.,;"t. I",," "" ,1.:"", """'" 0"'"' ... . ~ " . "'+1' " . .... l. J' A. 1 • . ' . '. So ,t.. ... __ Oft ,,.. .. " .. ,.I .. ""'" """Id h.o,~ ,,,,, M ....... 69

70 'vVh ich Is the "Best" Stack? 1 hope that the above exposition will help lay to n.ost the absurd notion tha t theft is a "best" stack. There is not. despite an abundan« of grandiose proclamation!; (with very littloe falional justification ) that the prodaimer's personal choio> of stack is such. Were that the casE', it would be the stack that everyone uses.. My own view, for the ~rd: I. No stick is "best" for everyone, though any particular stacl.: 11\8y be ~besl· for your needs. Anyone claiming otho!rwis@ is either naiW, or marketing. 2. AlmNI any stack. (including simple ones like Si Stebbins and Eight Kings) offers one or more advantages over other stacks; otherwie;e it would have long since disappeared !Tom the scene. You might not consider such elements advanl ageou!\, but that's to be expected (see point 11). 3. If the stack that you are using appean su ffid entiy random (no obvious recurring sequences of values, suits, o r colours, say), and you can call oot the stack in seqUetlCf! (for a ~tial SI<Id;}or randomly (with po6itions. for a memorized deck), at a cadence of not worse than about one second per (ani" then that stack is probably sufficient for your needs (though it may lack some feature for a Specific Irick), and you likely havc no strong reason (beyond intellectual curiosity) to e)Cplore others. If not, you might. 4. There is no compelling reason (otill:'r than marketing) to campaign for others to use the same stack tl1a t you do. Quite the opposite, In fact: the fewe.- people who use your favourite stack, the less widely it's known,. and the more ~ptiv e it will remain.

On the Ordering oJ Paying Card Suits (or, why being CHaSeD is bad for you) Each individual playing card is identified by a unique combination of 8 value and a suit. The (numeric) vnlu~ I~ se<;juenlial in nature (if we assign ll, 12, and 13 to the Jack, Queen, and King, re$l"'Ctively); as such, we Can order them easily, exploit their odd-even nature, use them in mathematical opefll!ioos, CIC. TIle melh,xl$ underlying many effects are based on thi' numeric property oflbe valUCII. It', ~ually useful to assign such characteristics to t1w ,will;. Moot people order the suits by memorizing a sequenre, usually one that alternates the colour$. M such orders are largely arbitrary. they an> difficult to remember. so we use mnemonic lieU, such as CHaSeO, SHoCkeD, DuCHeSs, CoDfiS H, and HiS DeCk. TIle drilwback o f this approach is tha t it simply yields an order, and fails to assign useful numeric meanings to the individual suits. Should we nee:! the third value in a numm~1 sequence (such as 1, 2, 3, 4, 5, ... j, we instantly know that it is a three, but when we try to do this with suits, we require e~ traneoU5 thinking ("let's ~, I'm using the CHaSeD order, so [he third one i5 I Club ... HellIt ... SpiZdtl#). Similarly, if ~ wish to mah use of a suit's v.lue for some romputational purpose, we are left with questions like NWhat is the value of a Hea rt ?" An obvious ana logy here is the Larin alphabet. While most people know theu.,utna(ABCDEFG ... ), and thus can lfUld;lydctemtine which clll"~<; er (0110"'$ ~. few know the ",,"'Vial toll,," of !he letters (!beir poxitions), and ~.n instantly name [he 17th letter. or know It which position ~R~ faill. All of this is far (rom ideal. For contemporary playing cards, though. the problem is easily !"@S()lvM, by ~ploitin& the nah.ual numerlc.1 values suggested by the artwork of the standa rd French suits, indicated by the points or lobes in their shapes (as depicted here), which in turn yield an obvious order: 71

72 + I 2 3 • This particular ordering (which corresponds to the SHoCkeD Il\Mmoni" though such ;In aid is no longer required. o r even desinod) has additional useful-and memorable-significance. Spades are widely coru;iden!d tIw! It suit (hence the decora tive Ace of Spades). The major suits (d. Contract Bridge) are together, and pre<:ede the minor suits. The even suits are red, and the odd suits are black: black being the ~odd" colour makes sensoe, as black isn', re~lIy I colour (bu t rather the absence of same). Further, the black 5ymbols themselves are somewhat odd in design. enpying limited recot,nition by nonCMd-players; the Hnrt and Diamond, on the other hand, are ironic shape$. univel'Sillly~ . Conseq...ently, \hi:;; is my personal cho~nd strong ~mmtntbtion-for the most effective playing ClIrd suit order. A coroc:q>I dating back at least to 1952." it wasona the mO$I prevalent ordHing used by European magicians. though has of lale been supp\anted then! by the much inferior CHa$coD SI!'1uena (a victory of imitation over imagination. with a consequent 10115 of functionality). But on~ you adopt and intemaliu i~ you will often be reminded of itsadvantage&, and immediately and forever know that the third suit isaQub. H. J. IW»<W o..d! (ab "R.oododl") pubI;,I"d "s,..t.. 11t , Cl.Jbo l"li , .. """ .. ;" ~ '''"P' ;''' (t ..... US. M»' 19521. ps- !O:!G.

Hiding a Sequence in Pain Sight (]t'!; All DOlle With M irrors) In many card effeocts, it is n~ry to arrange the cud s using an ordering that is known to the entertainer, but appears random to the Il,Idienre. One method for doing this i5 an arithmetic progression,. a! typified by the classic Si Slebbini 5CquenU': 3-6-9-Q -2 A-4-7 -~ -K There are two drawbadts to this approach, First the ordering is not thai difficult to spot. depending on the cirrumslances. This can bot alleviated tn a degft!e by int:n'llsing the increment. thout;h at the cost of making the Sl!que~ hardu to c;dcuI..te. The seoond drawback, and the one thai most concerns us here, is the d ifficulty of determining the position of any particular value. For e~ampk:, wh.i<:h is the ninth card? It takes some counting (or calculating) to work out that it's the Ace. Another method for obfuscMing order is the use of doggerel sequel1Oe$, $Urn as thedassicEighl Kings myme(d@SCribedpreviously under "Sequential Stacks-}. 8-K-3-Q-2 -7-9-5-Q-4-A-6-J This ordering is not possible to recognize as such,. thus an improvement (in this N'sp<'Ct) over the Si Stebbiru; method. ]t does nothing. however, to solve the problem of determining po5ition: again, which is the ninth eanH Nothing short of counting (or memorizing the associated position of each value) will N'veal that It'5 the Queen.. A thin:! technique--cme that will see usage inseveral d\apters of this book nne 40 Stack. QuidcStack 3.0, The Q Stack, and Menologue)-- 73

74 makes useol value / position pairing~ in which the value of each c~rd ina pair repn!Sel\ts the position ofits oompanioo card; I subsequently refer to these as ~m ror pairs· ... In addition to their random appeilrance, sequenC1!5 built using such pairs ne~t1y solve the position problem. Here i5 11n e.ample: 7-W -5-K-3-9-A-Q-6 -2-J-8-4 Like the doggerel sequence, it isn't possible to deduce the order by inspection. But unlike that solution. determining the value II any given position.-..oc the position of any specific value -is instantane()U$,. with no neoess<lry calculation: the ninth cud is a Six (and, !imil~ y; the sixth caul is a Nine). These p;!irings are not arbitrary. I have e~perimen ed wilh several over ~ year.;. Initia lly, they were sele.:tt'd primarily for their mnemonic values, bul as I grew to understand the broader uses of the technique, I realited that their malhematical relationships could be slg:nificant as well. Thus emerged the particular arrangement as shown above, and used insever.l methods described in this book. Learning these mirTO' J>l'ir5 is mnarkably simple, as suggested "'~ The Ace H) is pa ired with the 7, as handwritten 15 and 75 ne quite similar (as illustrated); in fact, ffii!.JIy of U5 draw crossbars 01'1 our ~ in order to distinguish them from ones. Consequently, the Are (1) is in the 7th position, and (conveniently) the Seven is in the 1st position. 17 The 2 is paired with ~ 10, becaU$l,' 10 is the binary equ v~lent of 2. You could also reoogni:te that the 10 is the only card in the pack with a twCKtlaractervllue. Or that Two and Ten are both three-letter names beginning with a hard -r SOUnd. Or think of the rountdown sequence: ... 2 ... 1 ... O. So ~Two is the lOihcaul in the group, ~nd the Ten i3 the 2nd cml. 41i. I <.10)'" • ~ ODd • I.>If ofbd;¢.",& "' .. k ~ _ ""&!n.1 ""h .0< (:>1>:,,«1 by .... "" "') ...... ........! cod """ """ .......... .., "r.-J. A, ..... I>..pt<n<. Iw;nmo<t. t ...... " .. 11, .... """ ,1>", ,hi.. _ _ dot ~ .... b-.: ....... ..... "" publioh<.t lor H.")' Rioc<, I. io """"""'" 1')88 coloo_ .. l.\·u ·1.\ ....... _ (\Iol 71, No. ' , PI' :la-)OI, '''-P ho .... <leo", ,,,,w_ J ,ho ~ ~ _ ,,,r .... Oh. Hb,.... .... • >IuJ ...... _ I",,;,,p 'pp<:If ... Iu." -.. pwd) lot .... _ """,""" ..tom.. .... ,.. ..... d.oo>b<d 10: ....... ..... 1oc-.o,1aI f"'P"n;" ,I>.., ",-.It, ,t".", . odVt .. .,...... _,e""I. Ulnn,.., R""' ,luooll,"8 M .wi .. "'" m...,h .. ho d...;, •• l.

The 3 is paired with the 5, iJo!.eau5e the 3:5 5 two ch.iIrllClers are visually similar: roIa ting ~ diagonal stroke of a 3 upright yields a 5 (n iIIuslrated).Thus the Three is in the 5I:h posiHon. and the Five is in the 3rd position. The 4 is paired with the Ki ng nn as H4H and HKH ,re both three-stroke rnar~ 4 +¥- and simiillr in appeu anre: tilting the upright stroke of a 4 to the Jeft produ~ a K (as illustrated); you could also ~an that 4.1 + 3. The Four, then, is in the 13"' position, and the Ki ng (13) Is in the 4'" position. 69 The 6 h paired with the 9, which it resembles w~n roIated 180 degrees (as illustrated); the coupling has other popuillr connotations as well. C"'""""!. ....... tly, the Six is in the ~ por;ition. and the Nine is the ~ card. The 8 is paired with the Queen (12). memorable because the 8 exhibits a distinctly R~ue fema~ $hape. This puts the Eight in the I~ pCI<!Iltion" and the Qu~ (12) in the 8"' position. Finally, the Jack (11 ) stands alone (a consequence of there being an odd number of difft>rent card vaiUl's), having 1\0 paired card; thinkof the knave u a loner, or as II being the only pair (of ones) in its own right. This leaves the Jack in the 11" position. Most people find it quite easy to learn these relationships. and are thus able to respond almost immediately to. card val"" with its corresponding position (as welt as the ~rse, obviously, responding to a position with i~ associated card value). Adding Default Suits For ~ applim:ions. it is additioNlly neo!$SIIty 10 assign an easily· remembered default suit to ead> of the card. values. Aoonvenimt way to do this is as folJ.ows: The lower-valued ~rd of any pai, (A/7, 2/10, 3/5, 4/ K) specifics thfl Suit of both Cilrds in that pair. Thus for the A/7 pa ~ the A<% (1) is the lower vl lue, ~nd specifies a Spade (suit value. 1) as the suit for both the A« and the~ Similarly, the Thn!e and Fiv~ are both Clubs (3). For the two c~ in which the lower ~rd valucex~s four (6/9 .nd S/Ql, simply use half of this value. Thus for the 6/9 pair, the suits are h.lf of 6, which is Oubs (3); for the S/Q pait the suits are half of 75

76 8, or Diamonds (4). Another way to remember these is that spot cards that are mullipl~ of three are Clubs, spot cards that lire multiples of four are Diamonds, and the King and Queen always ~ar Diamond s. The remaining un:!, that standalone Jacil, i$ a Heart {21. as this loner is a true romantic.. Or, if you p refer, because hoe functions like a pair (2) aU by hilT\5@1f. With these suit rules, we have now spe<ifitd II complete set of 13 cards:

The DAD Stack (An Optimized, Sequential, Cyclic, Playing Card Stack) Rationale Numbered among the te<:hnoJogies of m)'5lery entertainment is a vast assortment of sequential playing card stacks. Given their great variety, and widespread usage in an exparu;e of d«eptive effects, il is natural to ask which one is best". As is usually the case with questioTls of this nature, the correct ~ponse is that there is no universa l "bes , only the best for a given set of criteria . The two hasic (and alS(l, unfortuna tely, conflicting) requirements for a sequential Slack are that it: 1. appe"r5 completely random,. with no obvious ordering. and 2. employs ~ simple method to determine both the next and (ideally) p revious card{s) in thf. Sl!<j uen~. RKtoard Ostedind's appropriately-titlO!d 8rtakthrough C"rd System" arguably best satisfies criterion 1, liS it d isplays no obvious ordering of lin)' kind. It dQe$ not. however, fare q uite so W('lt on c,iterion 2. The <:lassie Si Strobili, stack, di5Cll55ed earlier in this section,. o ffers perhaps the Simplest calculation method, though suffers from an all too obvious ordering (of both values and suits) that yields to even a f<lidy casual inspection. It can reasonably be argued that all of this is academic, that allY card arrangement can be amrealed by I sufficiently skilled entertainer (much like the proverbial red thumb tip). Pemaps, but most entertainers continue to seek ever more deapti vt' (yet practical) techniques. to make it as difficult as po5I!ible for their audiences to d«luce methodology. In 2<lOB, Mid : Ay ~ proposed II SIlK¥" thaI falls nicely between these two ideals, being both S<ltisfyingly simpk" to compu~ nd deceptively random in appearance. To be sure, it is not quite as random as Osterlind's, nor quito! as simple as Stebbins', but to my mind it offered the d05est thing to an ideal compromise when it was released. 41. 0.",11 .. ,/". 'P!'_n Ii", "' ~' I"' Ii< .. lon In 1. ',~!.r""fIt c:,,_ " U<tf ~...br ~!.p<, 198)) ~A , " J'" "')'I'CI SIl" III.~ ~r>' ..... ' tA-<>S'l ,, <b.:ri"'''' "' Mrl "'y«>. ,""Ie 1.1._ p' i~ .. <lr J"'IbIw,oJ, lOOII). l"1" I I 11.;. ...,,>bk . -boolt Pf<"<"'" fuUr'"'"' ..... · """'5- """,,,..-Ul "",",.II"" .... "Ii<>S ' po<k ..... pt.,;"' ........ 77

So do ~ nero yet another stack? Yes, in my view, ~1.lSl' it is possible 10 signifu:anl\y improve upon the Ayres teduuque for detJennining suit progression". Ergo, the DAD Stack. AU of the above can be visualized as it sort of twlKiimensional Hlandscape· of solutions. with one a)trs for comple)tity of method (which transl~ es to ease of use), and the 9l'COI1d for delectability of any stack ordtnng. as shown here. .il' 1 o Sequential Slack LAndscape SI a.btIintltuQ trB)(ngt let 01) Complexity A perfect solu tion would lie direct:ly at the origin (bottom left comer) of the graph. although it is hacd to imagine how such a nirvana mighl be adUew<!. Hut tnt closer you come \0 thai point.Il\f~ better the sl ack,. in my view. HOetectability" is difficult 10 quantify. but a deck of cards in DAO order was submitted to the lale magical lunU!'I8ry Eugene Burger. who was informed that it was a stack, and chal1(,nged to detect any order. His inability 10 do so after kn mi"~t<'5 of = tfuf $I udy suggests thai such a slack is sufficienlly random for all intents and purposes."" .r. ""'",o.....d~Md.w.tcd,~ ............. __ ... "'~ulIypublido<.l ._. anol ._aood _ ... ~ !)NI ... __ ........ loIJ. ,.., .. ""_ i.:;;. ... --....:t ... ,....,.u,y and ........... __ .. noiI) ' Sud. • p«><>n. JI- ~...,It ~ ,,_. -.101 _ ~ ""I' J , .... _ ... .. ,....,. .......... ....J.:ri"ll'. 78 ..... ,"" .. ..,.. " ... w."'j~ n." ob;\i'r "'" 101"''''"'' , ..... ,h" ....... .., " ......

Understanding the DAO Th combin~ i. ",,"""" key i , n ,>, sight "k s "" from k (p~"" mT@O! CJ~atol'$. d~Mick ') ill Ayres supplied 1M notion of a Stebbins-like progression that uses the (varying) suit values, mther than a find number. as iIlCTemenlS. It was Ridlard Osterlind'S ubJ1'aklhroush- discovery !ht using the value of the fill/awing card to help determine its own suit grea tly simplifies theconstruction. And I contributoo thespecific suit determination method, mnemonic aids. ~nd calcul ~tion shortcuts. Hence Dyment·Ayres·Osterlind". Here is the DAO Stack, in its entirety: And here a re the two simple calculation rules for the following (UtugetH ) card, using the suit values explained in the chapter -On the Ordering of Playing Card SuiiS": Value, the current card's nllmeric-w/llt plus its $ui,-o,at. Suit; for ~1I.1)Il1 utd t a rg I' t cards. the SOl11K' colo II r as the cu rrent card; for (IIUI-lJfIlutd target ca rds. the following suit (in $lIi/-(mlu) To remember the tvI'."" vs. odd d istinction,. recall that "evenH can mean "the same- (e.g u Hl1le scores _11' even.H), which implies Iht SIImtcoWlif. whel1'a5 -odd" indudes the connotation of -more than the indicated quantity", which implies advancing the 5uit-order by one. An example (Five of Spades): add the value of the card (5) to the \ I. AIR"I:., .... ,,""!t -.. ".- '" ~'",.l>,jft ' "". 10.> ...... ," ,n>! I'ri "'~ of "" "ru..,,,,, (f ....... l: ,t.;, .ip. . .... n"'" .of"".,,,, ><0,";')' ..-.I";",." " ... ~ l("",(",io ..... ). 79

80 suit-order (I), yielding six; this is an even number, so the following card is the s~me C()\our ... the Six of O ubs. Another ex~mple (Ace of Hea.rts~ add the value of the card (1) 10 the suil-order (2), yielding three; this is an odd number, so the following card is the suil after Hearts ... the Th«*! of Clubs. "Wrap-Around" Calculation Shortcuts When calculating values following the face cMds", adding the ca rd value to the suit value will sometimes yield a result that exceeds 13. In suchcases, 13must besubtracted from that result in order to arrive at the new card value. This operation is made easier for most people by exploiting the fact that subtracting 13 is the same as subtracting to, and then 3. So simply drop the leading "lw digit from the interim result, thensubtract 3 from the remaining digit (which will always be 4,5,6, or 7). Alternatively, some will prefer "counting" from the current card to be easier than doing this sort of -wrap-around" arithmetic. An example of this(Queen ofOubs): rather than think ·'Queen is twelve, plus three(Oubs) is 15, but that's bigger than 13, so I have t05ubtract .. :., it's much easier to think ~ King ... Ace ... Two"; this is an even number,so thefollowingcard is the sarne oolour ... the TwoofSpades. With either approach. whenever the current card is a King.. "wrapround~ calculations can be eliminated entirely, as the numeric-value of the target card is simply the suit-order of the King. An example of this (King of Oubs); the following card is a Three; this is an odd number, so it's the suit after Oub ... the Th"", of Diamonds. The arithmetically adept might choose to extend this kind of thinking to the remaining face cards as well. If a calrulation for a Queen will ~wrap around~ (which it will for Hearts, Clubs, and Diamonds), subtract one from the Queen's suit-orde r to obtain the target card's value. A "wrap-a round" calculation for Jacks (only needed for Clubs and Diamonds) can be replaced by subtracting two from the suit-order. If you find any of these ~shortru s~ confusing. or forgotten in the heat of performance, simply ignore them: the two bask calculation rules suffice in all situations! ~l. ·tt.: ,,"1;' ,,,,"·f,,,,,, ""d ,t.", -".,4" .round" k ,he 1," 01 n;.. ... onJ.; 1"" ",Ish' <"'><00< '" «"""'"'" ,h" <p«k>I ...... ,"" "oJ pr««Iio, ~>< &;, '"' Sp.d<o.

A Probably-Not-That-imporfant Observatio7! El mln~ti g the odd-even distinction in the second rule (simply advancing the su it-order in ~II cases) produces II functional stack as well similar to the Si SIdJbill5 model, with llbooJt the $lime level of difficulty in cakul" tion (i.e .. triY"']). This stack" is somewhat more random in app<aramr than that dassie (thus a modest improvement), but- with its strictly roliltional values and alternating-colour suitsnot nearly as deceptive as the DAO. Working Backward The prior card in the DAD sequen~ i~ easily determined as well. using II fairly obvious inversion 01 the stack rules for going forward: Suit: for rotn-wlutd current canis, the $Ilmt colour lIS that card; for odd-wl ~d current cards, the preceding suit (in $uil-order) Va lue: the CUlll!Tlt card's lIuml!, ic_11«! minus the ,,,get card's suil-onltr An example (Eight of Diamonds): this is an even um~ 50 the prior (~ t. rget") card is the same rolour, thus Hearl$; subtract that suit-order (2) from the OllTeTIt card's va lue: the Si)c of Hearts. Habituation Sequential stacks are easily praaiced, particularly in odd momentswaiting in queues, suffering through oommerci~l_when you·re looking to sc~pe tedium. Simply choose a card a' random, and then compute the foll owing card(s). When this becomes trivial, practice working backward in the stack as wdl. Remember thai in the forw ard direction. the y~ e is computed firs!, followed by the suit; when working in reverse, however, det.!nnine Ihe su;1 first, I~n the VAlu",. H S.k·~' "Id ",,,,.10 ro« . ...,..;o..dy proj>OO<>l b)' J. lb ...... I"II>d< (.ob ·R.wduo:ti. wwlc< , .... "II< . ......... IIw .. 0,..,. 1);,,""""'- in I'I«,~< "'"",0< (I...., 'l~ ~. lo1'r 1,)l). !'S. 1010. 81

AppliCil tion The DAOStK\( isa powerful. deceptive, easily-acqui~ tool that can reemployed .. lmost everywhere a sequentia l ful1oded< playing-card stack ts required. The -Poker ~- routine, found elsewhert! in this book. provides an illustrative example of how the use of such a simple tool can be parlayed into a strollg. audience-pleasing presentation. A Con tribulion:: Frega's Flimflam Thiseffed, oontribuled by George Frega. was originally conceived as .. demonstration of the iff~ ce between telepathy and clairvoyance; other pre1entahons are possible, of OOUI'!le, as appropriate to the character of the entertainer. Effed: A deck is shuffled and spread ~cc down, left to right. A participant isinvited totouchacard, somewhereinthe{appro~im tely) middle third of the 5pread. The cards to the right of {Le ... bovd the chosen card He pushed ..side, squared up, and the block turned f .. ce up, with no 5uspidowi handling (this an be done by the participant, if ~red). The participant is instructed to ill5eTt the seleded card.. still flO« down and untoud>W by the entertainer, somewhere into the middle of the face-up packet. Now the participant i5 a&ked to select a dividing point somewhere ne .. , the middle of the remaining spread. This time the ("a rds to the left of the chosen division are removed, squared up. Dnd (now being considered ·out of piay- ) set well apart from the other!l, leaving the remaining (ideally, no more than tenor so) cards untouched. The participant gathers up these rema ining cuds, mixes them thorwghJy, and then spreads them in a fan fKing towards her (thereby seeing their faces for the lint Iirl"le). The enterlllinf!T proceeds to re .. d h.t-r mind by determining every tard in tlw: f,n; e;t<;h u rel successfully named is dropped on the table. Finany, it is pointed out that nobody knows the identity of the face down card in the tabled packet, 50 ;1 annot be determined by telepa thy. As /I dimu,. the entertainer names this card \l$ing clairvoyance, and the tard is rev"" ied to ve rify the claim. M~: The deck isstacUd. Any sequential stack may be used. but as the Cilrds will be rlllmed in stack order, irs b.-st to \lSI' a 5)1!;tem thatexhibils no obvious sequence (such as alternating COIOW1 or simple nwneric progressiOl\'5); obviously, the DAO Stad: is ideaJ for this. The shuffle is false. "J'lw card atop the facc up pile (the originaJIy removed portion of the 82 ~)lICtSas a Hkey card~, identifying thecardstobc ~led.

The buried card will be that following the key card in the stack ~uence. The cards viewed by the participant are merely those that continue the sequen~. When George performs this, he turN; away from the parlicipant as she picks up the batch of cards, and rema illS turned away while naming them (with an Annemann-style glan~ or two to eflsure tNt he's naming the correct number of cards). A Handling Va ri ati.;IJ1: Rilther than leave the remainiI\g arm in a spread (following the initial card selection), they can also be squared up, and the participant invited to rutoff a small pKket to be used for the first revela tions (though this mea!15 additional handling of the chosen cards, thus is not quite as "clean W ). 83

84 The ~o Stack (All Alternative, Sequential, Cyclic, Playing Card Stack) A DAD Elaboration In this chapter. I describe the sequentia~ full-deck, playing card stack thai I personally use. It is, essentially, the DAO Stack with one additional C(lmputation step. So let me begin by stating that, for the ~at majority of entertainers, the DAO Stack will prove a better choice, and is the one that I generally recommend. That said, here is a full description of the 4D" Stack, ror those interested. or merely curious. Rationale So what's "wrong" with the DAO Stack? Nothing. really: it's highly effective, and, on the sequential stack landscape (see previous chapterl, ocrupies the position closest to the origin. which suggests that it is the optimal such slack lor the majority of applications. Which is why I most ""ooI1UT\E'nd it. lt does exhibit, however, a minor discrepancy, albeil one that is faitly easHy oo~_ If we examine the card values only, we see that they actually fall into short uclumps" of increasing value: (A,2,5,9,lO,KX4,6,l O,Q)(3,4,7,J,QI etc. Now in all my (considerable) experience with the DAOStack,l have yet to have anyone inspect the card:; in any detail, let alone notice this partiUllar characteristic, but of course I am not so foolish as to challenge audiences to "examine how random these cards are~! (Further, as mentioned <'arlier, some pretty heavy-hitting card folks have had an opportunity to examine this stack in detail: aU have failed 10 detect this.) I'm aware of it, though, and as a solution is at hand, it is one that I employ, though it ""quires an exira step in the calculation process. That step comes as serond nature to me, thus adds almost no extra time; others.. howevel; may not find this to be troe.

The Additional Step I simply mJk~ u.o;e of th~ mirror pairs described in the ch~pter on NHiding D Sequen~ in Plain Sigh ~ (to review, th~ ~re A /7, 2/-, 3/ 5, 4/ K, 6/ 9, 8/ q, j), As l use these in several applications, I find that J know them well fnough to swap the values almost without thinking. If yOl.l (at some point) fi nd tha t to be true for you as WE'll. then you may find value in the following. The 4D Algorithm Here are the rules. slightly adjusted from the DAO Stack for the 40 Stack. First, for f~nnining th~foIlawi"8 card: V;olue: the mirror or the current aord's IIWlmric·ooIut-plus-suil- - Suil: for rom-VII/ua target cards. the $/Imtcoiowr as the cummt <: rd; for odd-1XIIutd ta rget cards, the following suit (in suit-wdtr) An example (Ace of Hearts); add the value of the <:ard (1) to the suit-order (2), yield ing three, whose mirror is five; this is an odd number, so the folklwing tard is the suit after Hearts ... the Fiv~ of Oub!!. Similarly, for determiniug the prior card: Suit: for n>f!1I-VIIlutd current cards, the samt £'Olour as that card; for odd·valwtd curreut cards, the preceding suit (in Silil-ordtr) Value: the mirror of the current card's IIumtric-wlut minus the target ca rd's 5uil-ordtr An example (Eight of Diamonds): this is au ~ven number, SO the prior (Ntarget'" ) <:ind ;5 the Nmt coiow, thus HearlS; subtract that suit"<lrder(2) from the mirror of the current card's value (8-Q) ... the T~ of Hearts. Finally, then, he,,~ is the 40 Stack, in its entirety: A. ,11+ , 4. -3. -3+ -9. -4. · 9<fo -8. -6+ -6. -n ' 54 0. · 4+ · n -3. -n -Ilt -7. -Q+ ·II. -J. -H -0. ,7+ 2. ,:). -A+ ' It, K. ·7. -6. -2. ' K+ ':). -6. -Q . -5. 9. -J+ -7t -J. -8+ -Jt -II. -8. ·8. -2. -9. -2+ ·3. 85

86 As peded, the various calculation iShortcut$ deso::ribed under -rht DAD Stack" apply to this alternative version u well.

QuickStack 3.0 (A Tetradislic, Algorithmic, Playing Card MemDeck) Most "n!('rlaine" a", aware of the potential of . full-dKk 51l1ck that awxiate$ each ca rd with its position in the ded< (i.e., a memoriud deek" J. A8~at deal of literature exists on this stratagem, which makes possible a variety of ·impossible conditions" effccl~ obtainable by no other means. The considerable reputations of entertainers such as Simon Aronson, Mike Oose, and Juan Tamariz dllpend in no small measure on their command of this technique (and their writingsoffur a goodly number of astounding effu<:ts that depend upon its ~). Sven Bert Allerton. arguably ~ (ounde!" of close-up magic (and unquestionably one of its most successful practitioners), adhered to the admonition that "You can take II stacked deck and follow any grut artist with cards, and your s~al()r'$ will think you are the belfer mag cia .H~ The Weapoll of Choice Earlier in this section. I compared the four methods used to develop and leam memoriz.ed fuU-rle<:k playing .:ard stack!;, The QuickStack 3.0 solu tion faUg into the algorithmic category, employing a single, common formula that relates the name of any card to its position in W 5t,.:\(, and vice versa. Rather than incorporate specific Ntricks" into w stack (which appeal to a circumscribed audience in any event), QuickSlaO: 3.0 employs a tetT~istic:" design,. one that suppom entire dasses of effects. Here ;s what top card man Alan Ackerman says about this approach: I pvsonQlly tm ,,/utll t~ Idradidir $/lItk i, Ille Slrongnl of al/ $llIm. Most mmwriud dtCk tffocts (lin be do~ with ""Y Slack-fO)Wr clloia of slild is goillg 10 be ""~d all 1M ftw H . '11 ... q."m Woo ".ip..tty "",rib<d ,,, lh "..<>to. ... "l"",..J to,- Rub<" 1'",;'" I. /Ir,,~) )j" (;;.,..u,. M"1k.t .. A~p"" 19Sft), PI:- }Ii V>. A .«tod~.1o: ,<><I< ~ ""' In which . "'l""'" nl cvd •• Iu<.!t ""P'"'" .d fu., ',n"" !h,,,,,,,,,,,,,. "" ...... It moJo rq>""' ..... 1m Ch.n Catwto. ~ 1Hnt •. (" ...... A"","""" , AI,. A<k«""'n - 87

\ 88 t/frds Ihal art bllUI in. The IVlSQn I Ihnl! Ih~ It/radlslle stack is so ftm laslie is I/'t ell/ling ,,"'Ii ~ I/,nl you (lin do if)fOll know how 10 foro $I,uff1t. AMlhtT wtmderfol proptrly is lire /lbm,y /0 gtl Inlo afllll slay-sloKkordO'. J do II quid 1«OO,d dml dnroo-- dtllling 26 COI15«1I11"" $«OOuls willr 1M lop ami ~-"!J Idrlldi$tic sid is nOW III II slay-sl«l ".dtT. Steve Keyl adds to this line of thinking. noting that: ~ rolalio"a/ on1tT of III#: slack IIl1ow:s fo, t/f«IS tlrlll matt u~ of 1M Cilbrtlulr principk in a way thai non-rotationlll slm:u do 1101. For tramp/f, I often pnform a mtmory dtmonsl'lIlion t/f«1 wlotrt /I,t cards IITt shuffled by II p"rlirip,ml, who /I,t " dtlll, aliI 13 cards. I look. III Ihe group of cardJ for frwc' l/uJn two 5«I>nds lind h""" 11m" rt"IrHlVt /I cllrd fllct-dOl~n . 1"hm 1 loot OW, III#: 12-aard pW:tt lind It/I l/Iro, wIoid! !:fI, d ;s mi~i"g (Nllit only, 140n ', "lInl#: 1M suil5). TMy dttllOllllllWloo IJ, dtlll '''tmld""" /I bltrlju hQnd 12 C1/rdsJ, a"d I It/I thtm whIIl l/od, blactjQd hand amhrins. Fi".l/y, Ihty $h1lJJ1t I~ rrmllining 26 C1/rds /horollghly IIlId lilkt 0111 a full poUr I.lmd, wIIiclr /ilm IIbIt /0 nIImt. QIIidSllla III/OM mt /0 go inlo Ihis t/f«1 III auy lilnt.1t is simply "01 possiblt 10 do Ih i, wilh /I "onroll/liona/slack. Addilionl/liy, Ihtrt IITt mllny o/ha GilbrmllrbIIstd rffrclsllrlll /ITt very tIIsily ac!lit!ltd Will, QuickSlllck. / Cmlltd II gaff-fru Invisiblt Det:k-wSld on MichMI Ciou's idtlls ill Workers 5, which lOtI? ilZ lurn ooSld on Allan Acktrman's Impromptu Uilrll-Mtr11111 Deck from Las Vega! Kilrdma-l"", uses QuickSlack 11$ its primllry modus ClpCQndum. My lloU'JII'! prtsf",a'ion tr1d$ up hRlling two ",.ds SfI« 1tIl in an 1I"'fIU'S,iollnbljl 'Qndo", nwrhod. Thtr1 I I. oul lilt QuickSlad.sed tmd sp-.:/ II /«f dow.. on lhe Iablt 10 show Ihill bolh Itllmal C1/rds II1't foa lip ill 1M 4 ... d ct.1I1", oftlr"t <ltdl QllidSlad: makts producing llot pair of <»nfs _y n>m if YO" dOIl 'I mtmoriu llot Ia ck.. Htrt IIrt a aluplt '" alh", Imn.glr/s ... Aft'" II single foro shuffle, 1111 1M Czlrds /lrt SIQC~4 by mQled pairs. Af/n I do 1111 cff«1 or tu.:J wilh 1/1#: rtgular stack, I faro shllfflt Qrr4 hIIvt som ... .:me pick 1/ CIIrd. ,o,f/er II quick hollom glimpse, I know wlre lhtT Ihe malt" is on lop or bellom. [pllim iI off 10 a pockrl or wallet and $how lluII I prtdicltd IJ~ mlllt of llot d!0St" (iI,d.

FoIluw;nK a Sloond faro, all/n~ alrd$ M t' laid ou/ AS fourof..,-kind 5<'Is. I no"" oomronc lIamt allY !>II/ut alld tJrtn drallUl/.rnlly produ« tad. of Ihtm from an IlPpilfP"'/y shuffled dtck. BffilUSl I I;-lI(nu lilt ""'al;,,,,111 onltr, I Cd" rot" MIN pt'Oplt ""m~ lilt suils j" lilt ordtr lhal In~ wi/I ~ produml. 1'I,i$ nnw foils 10 imp"'5$. Haven't yet mastered .. credible raro shuffle? With considerably less prDcliet', you COI n likely get very good at bringing Ihe match of a ch~n card to the top or bottom of the deck (using a cut or pass, for example), "xploiting the fact tha t the matching card will always be found in the centre of the deck Even those for whom farashuffles area distan! dream can reap the added benefits of a tetradistic sta ck One of QuickSlack'! strongest advantages is Ihat i! is compatible with Eddie Joseph's powerful ~Staggered~ prinCiple."" The !atl.' Aldo Colombini's streamlined version of this, "'Twists of Fate M , is a masterful routine'" with five d istinct phases" of seeming ooincidences. completely sleight.free, and (;In be performed directly from the QuickSlack .rrangemenl (furthermore, it's a froe d ose!;. unlike some arbitr .. ry spelling plot). QuickStack 3.0 exhibits no apparent ordering of the suits, $Q the sequence DppeiIB quite random. To convince yourself, you might Ill,ange a deck of uros as follows, and see if any other IMIl a fairly careful inspection suggests a prea rranged 5eC]uen<:e: 7. m. ~ K. ~ 9. , . Q+ O. 2. J. 8. 4. 7. m+ 5. K. 3. 9. , . Q. 0+ 2+ J+ 8. 4. 7. 0+ 5. K. 3. 9. A. Q. 6. 2+ J+ 8. 4. 7. m. 5. K+ 3. 9. ,+ Q. O. 2. J. S. 4+ Ii you're conl~nl with the random appearan<:e of thissl;><;1<. )'QU'U be pleased to discover lhattneconversion from any card's name to its corresponding position (or vice versa) is straightforward, consistent, IUld both learned and remembered quite easily. S7. d",', hriltl ,", ; .... ~ ,J""ji<,j ;n hj, I:>0oI. of ,t... <I"\< "," ~ _"",W""'lt;.,lon. UM. 114~1 . .... Ald.', """i"" ~ d.,. """'q, .... ,oJ ",~jn...J ;" , '<..:hi,,!, vok\< "'l< koo, !)ftI? ,- '19 'n.. """ito< I. """"'I .. j. ""'''''''', .... , ,).." ... "'''''' .... ~ r..", .. __ " ",b.., of,,,,, r*- ~ pM."I,j". 89

9Q An A~IIClt ve Aside . My first published work" included a description of CZIl1ckStack, , ~runner of the stad:. 10 be d-=ribed he~. Subsequently, I impro~ (m..de faster) the method of suit ca lculation. and .djusted the mirror ~irs to be more broadly USoi!ful. This was published as QuickerStack. in retro5pec1 an unwise choic@ 01 names, as when I made a further improvement (another adjustm""'l in the mirror pairs. again for more ge~ ali:red IpplkabiUry), ! found myself ill the difficult position of not knowing what to call 1M revision. "Quickl'StStack" was out, being not only presumph.lollS, bul also incorrect (as my Q Stack. which employs a considerably d ifferent approach. is quicker still, and more random-looking. 'hough it abandons the useful len-adistic property in those pursuits). So [ have (in my OWn mind II lnst) retilled "QuiderStack" t() be "QuickStark 2.0"; ronstquently. the (likely final) version described here beromes "QukkStack 3.0"'_ If you hive thoroughly memori72<l any of the predecessors to QukkStad 3.0. there is likely no compelling reason to . QWckStad< 2.0 is a bit faster than t~ original, and the minor pairs in QukkStack 3.0 are exploited in other material presented in this book. For memori:red stack functionality, however, all thr~ lUe equivalent. Learning t/Ze Algorithm As with most algorithmic stacks, the namel position rela tionship takes some explanation. Do not dismay, hoW<!ver: it has been designed to be r.o pid and d irect in use, and mosl people will find that they can ma nage It reasonably well .fter no Il'IOre than half an hour's prarnc@ with cards in hand. And thaI', for the complett, 52..:ard pac:k! As preYiou.sly alluded to, QuickStack 3.0 Is org.nized as fCUI B.mks of thineen ends each; these Banks are numbered one (I) through four (4), Bank 1 being Iociak'd at the top of the (fact-down) pilei<. The stack is most easily learned in tlute steps: (1) relating the values and pDliitions in Bank 1; (2) determining the suits in Bank 1; and (J)extending the method to the remainder of thede<:k (j.e., Banks 2, 3, and 4). GO. IOu ' ... ,1uftIc fLY (,bn", . .. """""""'1 ........ 1Iovt ",,~.,. "" , ....... ,.,.;'" "'" .. ruMoh m,-iob. NeIL '" ~ ~"h,,,,, I. ... -.- 0I"'T """ioo. _"'f ...... _, ,),., ' .... 01 di,.

Beginning: The Values & Su.its Each Bank contains thirtPOm cards, Ace through King (1-13). n.e first stage consists o f learning the numerical position of each card in the fi~t Bank, and ilS suit. Thls is remarkably simple, aslhey are exactly as described in the earlier chapter. Hiding a Sequence in Plain Sight. The suit .. ssoriated with e..m value in the i>-card sequence is considered a "base suit"'; the suits in other Banks ,re defined in relationship to these base suits, so they_like the numerkal positionsmust be thoroughly memorized. But again a reminder that, while all this may sound complex in explanation, it is easily learned, and designed such that transposing from a card name to its position (or vice ye!SII) can be done with surprising ease. To ",ite!ate, then. this is a list 01 all!3 cards in Bank I: I 7. II. + K+ 3+ 9+ At g t 6", 2. J. S' H When giym any of these card IUIm~ you should hi! able to respond rapidly with ilS stack position; conversely, when given a nu mber from 1-13,)'QIJ should quicl<ly rec...u !hec:ard at that position. Work with these until you know them thoroughly, and then move on to the next stage. Contin u.ing: The Other 39 Card Values To leam the positions of the cards from the remaining three Banks, we just apply some simple addition to the Bank we've already learned. You'll need to remember the numbers 13, 26, and 39 (the position HoffsetsH for Banks 2.. 3, and 4, respectiyel y). A simple nmemonic tedmique for this is to recall the m ultiplication t~ le for thlft: 3 " 1 _ 3;3_2 _ 6;3><3_9. ReoIIi that the positioning of cards within Sanks 2, 3. and 4 is identical to that of Bani<. 1.lherefore, in order \{) find the stack position of a King (for example) in Bani<. 3, simply add its st<mdard position (4) to the Bank3 0ffset (26). yielding. in this case, JO; thus \he3\)'t'cani in the deck is a King. lhe Qu<:>en in Banlr. 2 would be in stack position 8 (its standard position) ... 13 (the Bank 2 offset); thus the 21" card is a Queen. The Ace in Bank 4 would be the 46. card ;n the deck (7 • 39). The offset calculation can be made less error-prQne with the use of a trick that works for any two-digit number: perform the operation in two llteps. adding (or subtracttingl the tens portion first, then the remaining Onts. To add 13, in other words. first add 10. then add 3. To subtract 26, first subtract 20, then 6. Adding 39 is simpler still: first 91

92 add 40, then subtract 1 (or, tosubtract 39, first subtract 40, then add 1). A 'td"'iq,,~ 111111 t~'irt 'y diN,iNala II~ nud for doi~S arithmetic with 1M nllmbtrs 26 .nd 39, will ~ deicrilltd &hrJrlly. Concluding: The Other 39 Card Suits The suits (which of COUf'5e d iffer in each of the Banks) are first computed as in Bank t {the '"base" 5uitsland then "adjusWi" to a different suil for I':ach Bank. This is acwmpJishcd by i.ncTementing the base suit by the previous hank number; in practice, however, the step is a much easier one, the adjusl€d suit being simply: • in Bank 2 ..... <me greater than the base suit • in Bank3-theother suit of the saml': eolour as the base suit • in Blink 4--onI' less than the b~ suit So a Two, for eumple, which hilS II base suit of Hearts (2), becomes Oubs (2 I Il in Bank 2, Oill~S in Bank 3, .. nd Spilde (2 - 1) in BanI< 4. Remember that the S\JilS "wrap around", with Spades illUlWdiatl':ly following Diamonds: thus. King.. which has a base suit of Diamonds (4), ~5pades (4 + I) in Blnk 2, Hl':arts in Bank 3, and Oubs (4 - 1) in Bank 4. The BoHom Line We have now specified the complete 52-card sequl':nce for QuickStack 3.0: 7 _ II. ~ U 34 940 A_ 0.+ 6+ 2. J " e. 4t (Bank 1) 7. II .. , . X_ 3. 9. 1. a_ 6. 2_ J_ e_ 4_ (Bank 2) 74 11+ _ n 3_ 9_ .. _ a. e_ 2. J. 8't' 4. (Bonk3) 7. II _ , . X4 3. 9 . ... a,.. 6. 2. J_ 84 4+ (Bank 4)

Makillg Life Easier: Some Conversion Shortcuts The most difficult atep of the pl'OCt'SS is unquestionably that of converting bttWffn the (relative) positions in B.~nks 2,. 3 and 4 and their corresponding absolute positions in the stack. (Irs trivia l in Bank 1, as the two num~rs are identical.) Fortunately, an ingenious t....:hnique"' completely eliminates the need for addingand subtracting 26 al>d 39 for Banks 3 al>d 4. As a consequence, 75% of the anU in the stack can tie Iocattd with at most one singJe..digit addition. 1be rest (those in Bank 2) an' managed by simply adding or subtracting 13, not thai difficult a task. Converlillg from Stack Position to Bank + Position All stack positions in the forties (i.e., #40-49) are in llank 4, and the position within that Bank can tledetermined simply by adding one to the rightmost digit. Thus card #4ft is Bank 4, position 1 (41 0 ~ l);card .47 is &nk 4. position 8 (.( 17 + 1); ~. Thinking of ' 50--52 ;IS forty-Ifll, fort~lrotll, and fo ty-/wt! ~, exle'lds this trick through the remaining Bank 4 stack positions, so 1 is Bank 4. position 12 (51 11 .. H Or you can simply remember that these fi nal three are positions II, 12,. and 13, respectively. Similarly, all stack positions in the 305 (.»-39) are in Bank 3; in thi$ case you add four (instead of one) to determine tlw position. Thus card H6 is Bank 3, position 10 (316 + 4). The rema ining Bank 3 Slack positions ('27-29) Ca n be similarly converted, by adding four and dropping the fl!suhing tens digit, 50 card . 28 is in position 2 (8 + 4 _12 _ 2). But it's probably just as easy to remtmbo!r that Ihfst initial th~ are simply positions 1, 2, and 3, ll':SJX'<:tivtly. Bank 1 Q no conversion Bank 2 '" ±(lO + 3) 123 Bank 3 '" 31 x ± 4 ~, .J1>"", "'>0 «"" "" .~ ~, "<' b" ,""" .. .., 1<-,,". ~, if J""''' ~"'n i. ,J,,'..Jy .... I,"t """.h."" ,,, il> lun,,_ " "'osh' be " .... ~, ... i~.ili< .... '0 ,,,", ..... mm .. r ,;,. """ ... .1 , ....... W<~ ho."f< ... ". ) .... h.".< 5-,<1<\1 ""' .. r .. n~I"Hy w;,h """ h ... .. "Jr b.xt> «Wm'II1'od M·h .. ~ • ,"'''K!)' ",1Ii6rn, '0 "",""",,,,,, • ..,j _ m. """"I. 93

94 Converting from Bank + Position to Stack Position The pl'K'tding technique; <:an be used in Ihe reverse direction as wel~ by subtracting ins~ad of adding the ~ry COtlStanls. Bank 4, position 6 is at stack position .45 (4 16 -1). Bank 3, position 5 is at stade position 131 (315 -4). Bank 3, position 2 isat st<>ek positiQn'28 lremembe:red). Summary n.e following two examples show "worst caset" COJ\vel"$ions, using no "shortcut" techniques (but illustrating I p~ that works reliably for all c.ards). To Convert from a Position to a Card Name Four brief menial steps will reveal the name of the card .t any specific position. For txilmplt, what is aud # 23! 1. Dttennine the Bank: R2<:all that positions 1-13 an- in Bank 1, 14-26in Dank 2. 27--J9in Bank 3, and 40-52 in Bank 4. Oml : 23 is in &nk 2. 1. Delennlne the position: Subtracting the corresponding Bank offsett lrom the position yields the !X'5ition within thl! Bank. TMurd is tht 10" OM in Bank 2 (23 -13J. 3. Determine the valut: The associated mirror-pair rule yields the card's value. Tilt 10" elml is Q T~. 4. Determine Ihe suit TIle card's basesui! is adjusted a.s specified by the Bank number. A Two's suit in Bank 2 isone greater than its ba:;e suit (Hearts), so it's thl! Two of Oubs. To Convert from a Cud Name to a Position Three simple slq>5 will take you (rom a card', namI! to its position in the pilck. Far f~t, whtrt is lire FiDt ~f SptUltJ? t. Determine the Rank: "The card's numeric value tells us its base suit; the relation to its actual $uit determines the Bank.. TIlt FiDt's 51/i! i5 Iht SIImf mlau, 015 ils Itc!st SlIil (Clubs}, so i' mllSl W in 81mA- 3. 2. Determine Ihe relative position: The associated mirror'pair rule yields the card's position within the Blink. II Fivt is tht J"; ami in Bank 3. 3, Determine the position: Adding the appropriate Bank offset to the position resuIts in the card's position. Tht Cflrd is al position 129 (26 + 3/.

Practice Here are a few more sample conversions. in both direction" using shortcu t!; where appropriate [non·shortCUI version in square brae~ : WIlt". is 1M Two of Htllrls? lhe Two's suit is the ",me as its base suit (Hearts); this is Bank I. A two is always in the 10'" position. thus it is the 10'" ca rd in the ded,. J.\IhQ/ CQrd ;5 II"' from the lop! The II'" po5ition is in Bank I, ilI1d refers to a Jack. III Bank I, a card's suit issimply its base ui~ so it's the Jack of Hearts. \o\Ihe~ is the Ten of DiQmonds? The Ten's suit is the sa!Tl(! colour as its base suit (Heart:s); this is Bank 3. A Ten is always In the 2"" position; in Bank 3, this is card 128 (remembered) [or 26 .. 2 .. 28). WIIQI CIIrd is at posiliml 1;457 The 4S*- card is the 6'" ca rd in Bank. 4 (415 .. I .. 6) [or 45 - 39 .. 6). The 6'" card is always a Nine. Ito Bank 4, a a rd's suit is one less than its base suit (Oubs,.ln this case~ so it's the Nirw of Hearts. "",t IT is llu Four of5".,dn? 1he Fou.r·ssuit is one greater than its base suit (Diamonds); this is Bank 2. As the four Is in the 13"' position, adding the Bank 2 offset (13) makes it card ~26. ""lilt is llu ~ CArd? The 31~ card is the ~ card In Bank 3 (3 11 .. 4 _ 5) [or 31- 26 .. 5). The 5" card is always a Three. In Bank 3, a card's suit is the ",me colour as its base suit (Oubs), so it's the"J"hm? oISpades.. hIM". i$ IM Fi~ofHnlrl"$7 The Five's suit is one less than its base suit (Oubs); this is Bank 4. As the Five is in the 3'" position. it is card '42 (413 - 1 .. 42) [or 39 .. 3 .. 42\. ""III' mrd is at position ' 52? The 52'" card is the 13'" card in 5imI<. 4 (remembered) [or 52- 39= 13]. The 13"' Cilrd is always a Four. Ito Bank 4, a card's suit is one Ies6 than its base suit (Oiamonds, In this case). so it's the Four of Clubs. 95

96 An Exercise Pllln For a more e>ctensive e~erci~ (and an e:<cellent w~y to become thoroughly fami1i~r with the stold;), .. rrmge an old deck of cards in stack order, and then number them (with a heavy dirk marlting pen) dearly on the backs. from I to 52. If you number them at both ends of the c;ud. as i\lustnt~, you can mix the cards more freely. and there will be 11'511 confusion with reversible digits such as (, and 9. Shuffle the cards. and then run through them. front and bad. 'Nhen looking at thO! face of any card, you should be able to de termine the numeric position wrilten on its back; when looking at the back (which give!llts stick position), you should be able to calculate the card's value and suit. Wilh a modest amount of ~laT practice, you shoold be able to do this quite rapidly. With lime Mod usage, you will find that the $lIck will become more and more truly memorized; eventually, you will Nautomatically'" know the Tlallll!/position a$SOCiatioM. Nonetheless, • gre .. t boenefit of Quid:Sl.>dc 3.0 is the reassurance of knowing that you can always (lIIOlI.tt those asso:]atiOflS whenever nece!l88ry. Thne Useful Tips Many mftllo rized deck effects entail the surreptitious (;QUnting of cards whll c thc participant deals them, in order to determine their identities. When USing this tedmique. it is more O!ffident to rount in ba tc:hes of thirt~n (i.e., when th" count reaches ~t hirt~nff, start over I gain wilh "or\('~. remembering that you are now in the rl@xt Bank). In this way, no subtraction will be neaossary to dl'lennine a particular card, you will instantly know its value, and almost III quickly it, suil. It should go wi!haut sayins that the use of a deo:eptive raise shuffle is of immeasurable usefulness whHt perfonnins with a staci<ed deck. For an appropriate recommendation. see ~ An Immoderate J:lecqltion~, elsewhere in this book. Fin.ally. uS(' a consistent method to keep track 01 )'OUr ta(k~ deck, toensure that yO\! ~n!using the corred one. and that it Is "ready 10 go~. [ keep mine in a rt>gular <:aId box, in the normal {act down position. [ mark the bo~ itself on the flap end, using two indelible dots; to me, this indicates s,1I£ka:I deck i"sidt. Should the stack become disturbed for Iny fflason. I return the deck to the bo~ in foet ~p condilion. as a reminder that 50me rearrange~nt is nea!ssaty before using the slack aglin.

An Ultra-Mental Update QuickStack3.0 can alsobe used in effects that require a partitiOllingof the deck into two Of more card groups. It rfOinfOla$ you r memory of the slack. and sometimes o ffers add itional benefits. A good example is Joe Berg's U"~·Mt"frl1IHd: (created in 1936, and commonly known u the /nvrsiblt D«k, after pn,os.entat;ions popularized by Eddie Fields and Don Alan). Instead of tM usual card pairings th.t total thirteen (th~ Kings being treated :>eparately), consider using QukkStack 3.0, with Banks 1 and 2 facing in one direction, matched with the cards from Banks 3 and 4 faring in the other (you can assemble this from a standard Ultra -Mental deck, or construct"" your own). To display a specific ca rd. simply find ils rolour-matched equivalent, and :>epa rate the card behind it. A Stay Stack Alternative Although I myself am more pa rtial to Ihl! tefTadistic organiza tion, Brian Marks hu observed that ir s not particularly diffiC1.llt to reverse banks three and four (as a singll! group).. yil!kling an easily- ",ml!mbe~ stay slack construction" as IoI:lows: 61. 104 ..... ,..,....., ...... _h <In:t. iI P""'J .. ,.,..'"'"-"'1. Ooot ...................... , "---t, '"""""" """ ooId .. ~,. .. 11>1«1 pri<nl1> Tc.oot. Il60 o.I<-1ooqoo<t. ~ .. ..,. . 001 modo! ... ppI, ..... ~ It. KtyIoo ...... ,. 1'1_ 1_ ,h<\t ·Oulli"ll. $p<.,-). Spo.,. r...... • d"'., ... ..t" obou< 1'1<., ; • • ""~ ,,, .. ,L.!«i ..., •. 0 .. ,,\ _"opnr; • W&h' b.>.",,·.<><I·to..h n""",,, h ... Iii<;"" I,..' ..... "'" p';",;", .... . . od). 1Joc..,.... ~".tKr.I'uo. U"",. fin,"" "",do: ",",,01"11. _"" ",_I, "" h;p..p.... ",.r..,.~ ........ "".""'PO'"I)' (.Ind I;n'"k,) 'PF"""" "" pIoy ....... bI< .oJ"";", (~",h .. ( .... 001 on r.,... h' ..... ,). An _ n(li<;, ,he 74 l.Wly G)LI< ~". " ,,],bI.. " ,m. '''Ivlr _1,.". r t...:. oJ<" '" ,I". In , .. ,~n' .. "''''''' Clod [rum , ... -10 f"';,.nd ..... ;, d'T 0«"" ~Iot;", I< In "'''''''' wi,b;" ,""".",. h"MlI ... (""~b ""nr lind '" hc <b ... ,) d.1\"m ""I)< ~11h't, (""" ,N., 0(. -p, . .. _Mh ........ 97

98 Optional Method for Bank 2/4 Suits Greg Ik>atty has p~ an alternative to the suil-determinlltion aSpKt of Quick$tack 3.0, in orde r to increase the suit randomness. [consider the origin.l distribution to be sufficiently random (and it aids withmanyeffectsthal .... lyon tetr8disticstacks), bUI if you would prefer it more so, and are willing to learn a slightly more complex algorithm, ~ 01\ the notion of majoc(5pac:1es &: HeaftS)l nd minor (Clubs &: DiAmOOd.s)suits, you may find it of va llK!. Just as the Bank3suil$ ffip~ 10 1he0ppo$ite suit of the same colour, Greg suggests that the Bank 2 suits "flip· to the corresponding (major or minor) suits, which are of the opposite colour. Similarly, the Bank 4 suits "flip~ to the "on-corresponding (major or minor) suits of the opposite colour. SpecifiCillly: ~nk): Suitt! Sl*Ies <; Hearts Clubs = D;~monds Blink 4 Suits Sl*Ies" DilImonds He~rts <; Clubs Here is the (revised) deck stack thai results from this modified I!gorithm (~ tha t Bank!; 1 and 3 remain the same; only Banks 2 and 4 an! changed): 7. 0. ~ K+ 3-fo g. A. Q+ 0 .. 2. J. e+ 4+ (Bank 1) n II. 5+ I .. 3+ 9. A. II .. 11 + 2. J. S. 4" (Bank2) 7. 11 + 5. n :5. 9. A .. Q. II. 2. Jt 8. 4. (8ank3) 7+ No 5. It :5. g. At Q. O. 2 .. J .. 8. 4. (a.nk ')

QuickStack 3.0 Summary Hete', a sImple, ,n·in-one-place SUIllmary of the QuickStad: 3.0 slac:k and the values required to perform the associated calculations. Mmkt a copy of illor re("rene(> while learning, 0, to arry with you if ~ed to !"!':fresh your memory. Bank 2 1 7. 7. 7. 7+ 2 10. 10. 10+ ~. 3 5. 5+ 5. 5. 4 K+ K. n K. 5 3. 3+ 3. 3. 6 9. 9+ 9. 9. 7 A. A. A. At 8 Q+ Q. Q. Q. 9 6. 6+ 6. 6. 10 Z. z. z+ z. 11 J. J. J+ J. 12 8+ 8. 8. 8. 13 4+ 26 4. 394. 524. suits: +1 >< -1 99

100 SnapS tack (A Painless Playing Olrd MemDeck) In ception Although the issue ill undeniably application-specific, a good argument (In ~ made for not worrying at all about the apparent randomness of a playing card stack. Proponents point out that Jay audiences seldom !MY much att~lion to card orderings, and that even" l'eallOnably skilled entertainer Ciln work with CilrdS in newdedi; order without anyone being the wiser, particularly with the judicious U!Ie 01 false shuffles. Whidl then raist!s the question; What would an optimll illgoritlunic memorW!d d ed(' st.od<. look like if one d idn' t care about a random ~arancdSn.ap5tack is my attempt to IJlswer tho! question. In truth. this WItS not originally created .s .. stand-alone !IOiution b.llhough it serves this purpose ""II for ~tultions w~ the card faces are not displayf!d). Rather, it began life as a component of The QStack". Along the way. however,l diS«lwrW that 1 had reinvented the major component of Michael Weber', "Card Kindergarten" s~tem .\I Comequently, I Mve choos<'n to des<:ribe it here au :oeparate item. The First Three Quarters SnlpStack is best expl ained in r;..,.() parts. The first is t!elTle y simp le, coru;iSling of the non<OUrt (i.e. uspot'" ) cards, which comprise 77% of the ded. lt looks like this: 6,. AI"-'" ;"~,11 ~ 'Sn'pS,,,,k' .ad "Cor<! 1:1"",~""'n-_dl< I.t«< (,.,." Mim..! ~'. 10000i~ Diffi<.lt 7ItI.." It';,h C."" uw ,.. "..u,) fOIl« I<ctu", ""'"-0,,, <" ..... Iy ,i",,;I., .. "", .. noalolo. ~ oh< arobtiolol", " ....... oJ ""'"",, thO II bn'Wl'.]Jln" In rl<"<. 10', kind of~. Mith •• f . _" .... oA<. .. """ "",","'." fo. "'~ ~ ......