996:
949:
902:
855:
808:
719:
693:
632:
578:
1031:
1024:
1017:
1010:
1003:
984:
977:
970:
963:
956:
937:
930:
923:
916:
909:
890:
883:
876:
869:
862:
843:
836:
829:
822:
815:
754:
747:
740:
733:
726:
707:
700:
686:
679:
672:
660:
653:
646:
639:
625:
613:
606:
599:
592:
585:
104:
36:
119:
A right-handed practitioner holds the cards from above in the left hand and from below in the right hand. The deck is separated into two preferably equal parts by simply lifting up half the cards with the right thumb slightly and pushing the left hand's packet forward away from the right hand. The
169:
An out-shuffle has the same result as removing the top and bottom cards, doing an in-shuffle on the remaining cards, and then replacing the top and bottom cards in their original positions. Repeated out-shuffles cannot reverse the order of the entire deck, only the middle n−2 cards. Mathematical
1894:
1285:
1393:
120:
two packets are often crossed and tapped against each other to align them. They are then pushed together on the short sides and bent either up or down. The cards will then alternately fall onto each other, ideally alternating one by one from each half, much like a
173:
An in-shuffle has the same result as adding one extraneous card at the top and one extraneous card at the bottom, doing an out-shuffle on the enlarged deck, and then removing the extraneous cards. Repeated in-shuffles can reverse the order of the deck.
135:, the above method was used, and he calls it the "faro dealer's shuffle". Maskelyne was the first to give clear instructions, but the shuffle was used and associated with faro earlier, as discovered mostly by the mathematician and magician
1723:
1712:
1160:
150:
A perfect faro shuffle, where the cards are perfectly alternated, requires the shuffler to cut the deck into two equal stacks and apply just the right pressure when pushing the half decks into each other.
96:, in which half of the deck is held in each hand with the thumbs inward, then cards are released by the thumbs so that they fall to the table interleaved. Diaconis, Graham, and Kantor also call this
1296:
1052:
discovered that a controlled series of in- and out-shuffles can be used to move the top card of the deck down into any desired position. The trick is to express the card's desired position as a
420:
322:
273:
469:
1063:). Shuffle in, out, in, out. Deal ten cards off the top of the deck; the eleventh will be your original card. Notice that it doesn't matter whether you express the number ten as 1010
2017:
1978:
1951:
1924:
1609:
1524:
1562:
1458:
1155:
1118:
1497:
1428:
3348:
1582:
365:
345:
218:
198:
111:
Mathematicians use the term "faro shuffle" to describe a precise rearrangement of a deck into two equal piles of 26 cards which are then interleaved perfectly.
3338:
3343:
1889:{\displaystyle {\mbox{sgn}}(\rho _{n})=(-1)^{\lfloor n/2\rfloor }={\begin{cases}+1&n\equiv 0,1{\pmod {4}}\\-1&n\equiv 2,3{\pmod {4}}\end{cases}}}
504:
57:
44:
3387:
511:
3633:
2541:
2341:
1617:
422:. For example, if one manages to perform eight out-shuffles in a row, then the deck of 52 cards will be restored to its original order, because
3286:
1280:{\displaystyle {\begin{pmatrix}1&2&3&4&\cdots &2n-1&2n\\1&n+1&2&n+2&\cdots &n&2n\end{pmatrix}}}
3746:
3764:
3728:
2889:
766:
The following shows the order of the deck after each out-shuffle. A deck of this size returns to its original order after 4 out-shuffles.
177:
If one can do perfect in-shuffles, then 26 shuffles will reverse the order of the deck and 26 more will restore it to its original order.
3668:
2480:
536:
The following shows the order of the deck after each in-shuffle. A deck of this size returns to its original order after 3 in-shuffles.
3324:
3184:
3012:
3104:
2247:
3737:
3309:
3304:
2982:
3626:
3219:
2832:
2633:
2512:
2507:
2495:
1388:{\displaystyle k\mapsto {\begin{cases}{\frac {k+1}{2}}&k\ {\text{odd}}\\n+{\frac {k}{2}}&k\ {\text{even}}\end{cases}}}
131:
ends with the cards in two equal piles that the dealer must combine to deal them for the next game. According to the magician
3795:
3719:
3402:
2729:
158:, while one that moves the original top card to second and the original bottom card to second from the bottom is known as an
3527:
3314:
2102:
3640:
3472:
2828:
2824:
3810:
3209:
3179:
2761:
2527:
2373:
2334:
995:
948:
901:
854:
807:
718:
692:
631:
577:
154:
A faro shuffle that leaves the original top card at the top and the original bottom card at the bottom is known as an
107:
Comparison of a perfect faro out-shuffle and in-shuffle, the numbers denoting each card's positions before the shuffle
3319:
3002:
2779:
1059:
For example, to move the top card down so that there are ten cards above it, express the number ten in binary (1010
2098:
1030:
1023:
1016:
1009:
1002:
983:
976:
969:
962:
955:
936:
929:
922:
915:
908:
889:
882:
875:
868:
861:
842:
835:
828:
821:
814:
753:
746:
739:
732:
725:
706:
699:
685:
678:
671:
659:
652:
645:
638:
624:
612:
605:
598:
591:
584:
497:=2, 4, 6, 8, 10, 12 ..., the number of in-shuffles needed are: 2, 4, 3, 6, 10, 12, 4, 8, 18, 6, 11, ... (sequence
49:
3412:
3064:
370:
278:
223:
3281:
3271:
3149:
3129:
2947:
2744:
425:
124:. A flourish can be added by springing the packets together by applying pressure and bending them from above.
1071:; preliminary out-shuffles will not affect the outcome because out-shuffles always keep the top card on top.
3805:
3276:
3124:
3074:
3054:
3661:
3598:
2485:
2327:
2967:
3773:
3700:
3417:
3392:
3154:
3028:
2876:
2688:
2673:
2638:
2558:
2474:
2358:
2140:
3692:
3483:
2724:
2710:
2698:
2678:
2628:
2490:
2435:
2275:
2212:
479:
132:
1794:
1311:
3800:
3619:
3377:
2884:
2693:
2447:
2430:
1983:
522:
3654:
3007:
2306:
483:
3514:
3509:
2218:
Sharps and Flats: A Complete
Revelation of the Secrets of Cheating at Games of Chance and Skill
1956:
1929:
1902:
1587:
1502:
3560:
3548:
3504:
3397:
3358:
3244:
3204:
3033:
2972:
2452:
2369:
2291:
2243:
2216:
2237:
1529:
3612:
3605:
3570:
3449:
3330:
3263:
3194:
3134:
2643:
2501:
2283:
2191:
2155:
1433:
1130:
1093:
128:
2176:
1470:
1401:
3234:
3229:
2927:
2563:
2440:
2392:
2172:
1084:
474:
In other words, the number of in-shuffles required to return a deck of cards of even size
471:. However, only 6 faro out-shuffles are required to restore the order of a 64-card deck.
2279:
3755:
3647:
3553:
3533:
3488:
3429:
3382:
3214:
3169:
3164:
2787:
2705:
2599:
2522:
2136:
2128:
1567:
350:
330:
275:. For example, 52 consecutive in-shuffles restore the order of a 52-card deck, because
203:
183:
136:
3789:
3478:
3456:
3444:
3299:
3199:
3144:
3139:
2987:
2952:
2856:
2851:
2808:
2769:
2739:
2734:
2423:
2418:
2387:
2382:
2160:
2132:
1053:
514:, it follows that there are infinitely many deck sizes which require the full set of
3493:
3434:
3224:
3119:
3114:
3049:
2997:
2846:
2813:
2792:
2397:
2350:
1049:
163:
93:
3059:
2287:
3685:
3519:
3466:
3461:
3407:
3189:
3079:
2957:
2841:
2517:
1080:
147:
The faro shuffle is a controlled shuffle that does not fully randomize a deck.
3575:
3565:
3439:
3239:
3109:
2932:
2864:
2613:
3538:
3363:
3159:
3099:
2942:
2683:
2457:
1707:{\displaystyle {\mbox{sgn}}(\rho _{n})=(-1)^{n+1}{\mbox{sgn}}(\rho _{n-1}).}
90:
2295:
103:
35:
2266:
Kolata, Gina (April 1982). "Perfect
Shuffles and Their Relation to Math".
1124:
is the permutation that splits the set into 2 piles and interleaves them:
521:
The analogous operation to an out-shuffle for an infinite sequence is the
17:
3174:
2977:
2622:
2606:
2592:
2305:
Jain, Peiyush (May 2008). "A simple in-place algorithm for in-shuffles".
3498:
3069:
2992:
2576:
2569:
2195:
1056:, and then do an in-shuffle for each 1 and an out-shuffle for each 0.
2962:
2894:
2656:
2649:
2585:
2552:
121:
2937:
2311:
162:. These names were coined by the magician and computer programmer
2716:
2319:
170:
theorems regarding faro shuffles tend to refer to out-shuffles.
2323:
2413:
29:
2239:
Magic Tricks, Card
Shuffling, and Dynamic Computer Memories
1882:
1381:
499:
2177:"The Cycles of the Multiway Perfect Shuffle Permutation"
1083:, a perfect shuffle can be considered an element of the
2184:
1728:
1673:
1622:
1169:
1986:
1959:
1932:
1905:
1726:
1620:
1590:
1570:
1532:
1505:
1473:
1436:
1404:
1299:
1163:
1133:
1096:
428:
373:
353:
333:
281:
226:
206:
186:
3677:
3591:
3584:
3371:
3357:
3262:
3253:
3092:
3042:
3021:
2920:
2911:
2875:
2822:
2801:
2778:
2760:
2753:
2666:
2540:
2466:
2406:
2368:
2357:
2011:
1972:
1945:
1918:
1888:
1706:
1603:
1576:
1556:
1518:
1491:
1452:
1422:
1387:
1279:
1149:
1112:
463:
414:
359:
347:perfect out-shuffles will restore the order of an
339:
316:
267:
212:
192:
533:For simplicity, we will use a deck of six cards.
200:perfect in-shuffles will restore the order of an
1430:-perfect shuffle permutation is the element of
3349:Worshipful Company of Makers of Playing Cards
2335:
8:
1781:
1767:
2242:. The Mathematical Association of America.
3588:
3368:
3344:Saga Arashiyama Museum of Arts and Culture
3259:
2917:
2757:
2365:
2342:
2328:
2320:
415:{\displaystyle 2^{k}\equiv 1{\pmod {n-1}}}
317:{\displaystyle 2^{52}\equiv 1{\pmod {53}}}
268:{\displaystyle 2^{k}\equiv 1{\pmod {n+1}}}
27:Perfectly interleaved playing card shuffle
2310:
2159:
2003:
1985:
1964:
1958:
1937:
1931:
1910:
1904:
1863:
1820:
1789:
1773:
1766:
1741:
1727:
1725:
1686:
1672:
1660:
1635:
1621:
1619:
1595:
1589:
1569:
1531:
1510:
1504:
1472:
1441:
1435:
1403:
1373:
1355:
1340:
1314:
1306:
1298:
1164:
1162:
1138:
1132:
1101:
1095:
464:{\displaystyle 2^{8}\equiv 1{\pmod {51}}}
445:
433:
427:
390:
378:
372:
352:
332:
298:
286:
280:
243:
231:
225:
205:
185:
772:
542:
102:
60:of all important aspects of the article.
3634:The Card Sharp with the Ace of Diamonds
2028:
3287:International Skat Players Association
2089:Diaconis, Graham, and Kantor 1983, 193
2035:Diaconis, Graham, and Kantor 1983, 188
56:Please consider expanding the lead to
3388:Blackstone's Card Trick Without Cards
2141:"The mathematics of perfect shuffles"
512:Artin's conjecture on primitive roots
7:
1899:The first few perfect shuffles are:
478:, to original order is given by the
3669:Violin and Playing Cards on a Table
1871:
1864:
1828:
1821:
453:
398:
306:
251:
3339:Musée Français de la Carte à Jouer
3325:International Playing-Card Society
3013:United States Playing Card Company
25:
3310:Fournier Museum of Playing Cards
3305:Cary Collection of Playing Cards
1029:
1022:
1015:
1008:
1001:
994:
982:
975:
968:
961:
954:
947:
935:
928:
921:
914:
907:
900:
888:
881:
874:
867:
860:
853:
841:
834:
827:
820:
813:
806:
752:
745:
738:
731:
724:
717:
705:
698:
691:
684:
677:
670:
658:
651:
644:
637:
630:
623:
611:
604:
597:
590:
583:
576:
493:For example, for a deck size of
34:
3627:Card Players in a Rich Interior
2148:Advances in Applied Mathematics
2099:Real v recreational mathematics
446:
391:
299:
244:
48:may be too short to adequately
1993:
1987:
1875:
1865:
1832:
1822:
1763:
1753:
1747:
1734:
1698:
1679:
1657:
1647:
1641:
1628:
1551:
1533:
1486:
1474:
1417:
1405:
1303:
1290:In other words, it is the map
457:
447:
408:
392:
310:
300:
261:
245:
58:provide an accessible overview
1:
3528:The Phantom of the Card Table
3315:German Doppelkopf Association
2983:Nürnberger-Spielkarten-Verlag
2221:. Longmans, Green and Company
2012:{\displaystyle (23)\in S_{4}}
1717:The sign is thus 4-periodic:
3747:Patience and solitaire games
3641:Cardplayers in a Sunlit Room
3473:The Expert at the Card Table
2288:10.1126/science.216.4545.505
2161:10.1016/0196-8858(83)90009-X
2114:Ellis, Fan, and Shallit 2002
1526:, is the composition of the
1464:piles and interleaves them.
3765:Tarot and Tarock card games
3729:Non trick-taking card games
3210:Richard Valentine Pitchford
3180:Master of the Playing Cards
3827:
3320:German Playing Card Museum
1499:-perfect shuffle, denoted
3714:
2236:Morris, S. Brent (1998).
1973:{\displaystyle \rho _{2}}
1946:{\displaystyle \rho _{1}}
1919:{\displaystyle \rho _{0}}
1604:{\displaystyle \rho _{n}}
1564:-perfect shuffle with an
1519:{\displaystyle \rho _{n}}
1460:that splits the set into
3282:International Skat Court
3272:British Skat Association
3738:Trick-taking card games
3277:German Skat Association
3055:Bielefelder Spielkarten
1584:-cycle, so the sign of
1557:{\displaystyle (2,n-1)}
3662:Still Life with a Poem
2865:Guru (circular whirls)
2013:
1974:
1947:
1920:
1890:
1708:
1605:
1578:
1558:
1520:
1493:
1454:
1453:{\displaystyle S_{kn}}
1424:
1389:
1281:
1151:
1150:{\displaystyle S_{2n}}
1114:
1113:{\displaystyle S_{2n}}
465:
416:
361:
341:
318:
269:
214:
194:
108:
100:, when used in magic.
3796:Card game terminology
3720:Historical card games
3701:Play Your Cards Right
3418:Twenty-One Card Trick
3393:The Circus Card Trick
3155:Johann Kaspar Hechtel
2481:Archaeology awareness
2475:Ambraser Hofjagdspiel
2014:
1980:is the transposition
1975:
1948:
1921:
1891:
1709:
1606:
1579:
1559:
1521:
1494:
1492:{\displaystyle (2,n)}
1455:
1425:
1423:{\displaystyle (k,n)}
1390:
1282:
1152:
1115:
466:
417:
362:
342:
319:
270:
215:
195:
106:
3484:History of cardistry
2968:J.O. Öberg & Son
2491:Flemish Hunting Deck
2171:Ellis, J.; Fan, H.;
1984:
1957:
1930:
1903:
1724:
1618:
1588:
1568:
1530:
1503:
1471:
1434:
1402:
1297:
1161:
1131:
1094:
1075:Group theory aspects
1044:As deck manipulation
480:multiplicative order
426:
371:
351:
331:
279:
224:
204:
184:
3678:Film and television
3620:The Card Players II
3378:The Acme of Control
2280:1982Sci...216..505K
2062:Maskelyne 1894, 204
1090:More generally, in
523:interleave sequence
3811:Permutation groups
3655:Dogs Playing Poker
3220:Johann Georg Rauch
3008:U.S. Games Systems
2370:Playing card suits
2196:10.46298/dmtcs.308
2080:Morris 1998, 11–12
2009:
1970:
1943:
1916:
1886:
1881:
1732:
1704:
1677:
1626:
1601:
1574:
1554:
1516:
1489:
1450:
1420:
1385:
1380:
1277:
1271:
1147:
1110:
461:
412:
357:
337:
314:
265:
210:
190:
109:
3783:
3782:
3710:
3709:
3561:Si Stebbins stack
3425:
3424:
3403:Out of This World
3398:The Four Burglars
3359:Card manipulation
3295:
3294:
3245:Fusajiro Yamauchi
3205:Ferdinand Piatnik
3088:
3087:
2907:
2906:
2634:Portuguese-suited
2536:
2535:
2513:Most-wanted Iraqi
2496:Hamas most wanted
2453:Curse of Scotland
2274:(4545): 505–506.
2105:, April 10, 2014.
1953:are trivial, and
1731:
1676:
1625:
1577:{\displaystyle n}
1398:Analogously, the
1376:
1372:
1363:
1343:
1339:
1330:
1037:
1036:
760:
759:
490: + 1).
360:{\displaystyle n}
340:{\displaystyle k}
213:{\displaystyle n}
193:{\displaystyle k}
75:
74:
16:(Redirected from
3818:
3778:
3772:
3769:
3763:
3760:
3754:
3751:
3745:
3742:
3736:
3733:
3727:
3724:
3718:
3613:The Card Players
3606:The Bezique Game
3589:
3571:Three-card monte
3450:Cards in the hat
3369:
3331:The Playing-Card
3260:
3195:Samuel J. Murray
3135:Thierry Depaulis
2918:
2802:German and Swiss
2758:
2564:Four-colour pack
2366:
2344:
2337:
2330:
2321:
2316:
2314:
2299:
2260:
2258:
2256:
2230:
2228:
2226:
2206:
2204:
2202:
2181:
2165:
2163:
2145:
2115:
2112:
2106:
2096:
2090:
2087:
2081:
2078:
2072:
2069:
2063:
2060:
2054:
2053:Morris 1998, 111
2051:
2045:
2042:
2036:
2033:
2018:
2016:
2015:
2010:
2008:
2007:
1979:
1977:
1976:
1971:
1969:
1968:
1952:
1950:
1949:
1944:
1942:
1941:
1925:
1923:
1922:
1917:
1915:
1914:
1895:
1893:
1892:
1887:
1885:
1884:
1878:
1835:
1785:
1784:
1777:
1746:
1745:
1733:
1729:
1713:
1711:
1710:
1705:
1697:
1696:
1678:
1674:
1671:
1670:
1640:
1639:
1627:
1623:
1610:
1608:
1607:
1602:
1600:
1599:
1583:
1581:
1580:
1575:
1563:
1561:
1560:
1555:
1525:
1523:
1522:
1517:
1515:
1514:
1498:
1496:
1495:
1490:
1459:
1457:
1456:
1451:
1449:
1448:
1429:
1427:
1426:
1421:
1394:
1392:
1391:
1386:
1384:
1383:
1377:
1374:
1370:
1364:
1356:
1344:
1341:
1337:
1331:
1326:
1315:
1286:
1284:
1283:
1278:
1276:
1275:
1156:
1154:
1153:
1148:
1146:
1145:
1119:
1117:
1116:
1111:
1109:
1108:
1033:
1026:
1019:
1012:
1005:
998:
986:
979:
972:
965:
958:
951:
939:
932:
925:
918:
911:
904:
892:
885:
878:
871:
864:
857:
845:
838:
831:
824:
817:
810:
773:
756:
749:
742:
735:
728:
721:
709:
702:
695:
688:
681:
674:
662:
655:
648:
641:
634:
627:
615:
608:
601:
594:
587:
580:
543:
502:
470:
468:
467:
462:
460:
438:
437:
421:
419:
418:
413:
411:
383:
382:
366:
364:
363:
358:
346:
344:
343:
338:
323:
321:
320:
315:
313:
291:
290:
274:
272:
271:
266:
264:
236:
235:
219:
217:
216:
211:
199:
197:
196:
191:
143:Perfect shuffles
87:dovetail shuffle
70:
67:
61:
38:
30:
21:
3826:
3825:
3821:
3820:
3819:
3817:
3816:
3815:
3786:
3785:
3784:
3779:
3776:
3770:
3767:
3761:
3758:
3752:
3749:
3743:
3740:
3734:
3731:
3725:
3722:
3716:
3706:
3673:
3580:
3421:
3361:
3353:
3291:
3255:
3249:
3235:Charles Troedel
3230:Howard Thurston
3150:Richard Harding
3084:
3065:Charles Goodall
3038:
3017:
2928:ASS Altenburger
2913:
2903:
2900:Tens of Myriads
2890:Strings of Cash
2877:Chinese (Money)
2871:
2818:
2797:
2774:
2749:
2662:
2543:
2532:
2462:
2441:Queen of spades
2402:
2360:
2353:
2348:
2304:
2265:
2254:
2252:
2250:
2235:
2224:
2222:
2213:Maskelyne, John
2211:
2200:
2198:
2179:
2170:
2143:
2129:Diaconis, Persi
2127:
2124:
2119:
2118:
2113:
2109:
2097:
2093:
2088:
2084:
2079:
2075:
2070:
2066:
2061:
2057:
2052:
2048:
2044:Morris 1998, 13
2043:
2039:
2034:
2030:
2025:
1999:
1982:
1981:
1960:
1955:
1954:
1933:
1928:
1927:
1906:
1901:
1900:
1880:
1879:
1846:
1837:
1836:
1803:
1790:
1762:
1737:
1722:
1721:
1682:
1656:
1631:
1616:
1615:
1591:
1586:
1585:
1566:
1565:
1528:
1527:
1506:
1501:
1500:
1469:
1468:
1437:
1432:
1431:
1400:
1399:
1379:
1378:
1365:
1346:
1345:
1332:
1316:
1307:
1295:
1294:
1270:
1269:
1261:
1256:
1251:
1240:
1235:
1224:
1218:
1217:
1209:
1195:
1190:
1185:
1180:
1175:
1165:
1159:
1158:
1134:
1129:
1128:
1122:perfect shuffle
1097:
1092:
1091:
1085:symmetric group
1077:
1070:
1066:
1062:
1046:
797:
780:
567:
550:
531:
498:
429:
424:
423:
374:
369:
368:
349:
348:
329:
328:
282:
277:
276:
227:
222:
221:
202:
201:
182:
181:
145:
117:
89:is a method of
71:
65:
62:
55:
43:This article's
39:
28:
23:
22:
15:
12:
11:
5:
3824:
3822:
3814:
3813:
3808:
3806:Card shuffling
3803:
3798:
3788:
3787:
3781:
3780:
3715:
3712:
3711:
3708:
3707:
3705:
3704:
3697:
3689:
3681:
3679:
3675:
3674:
3672:
3665:
3658:
3651:
3648:The Cardsharps
3644:
3637:
3630:
3623:
3616:
3609:
3602:
3595:
3593:
3586:
3582:
3581:
3579:
3578:
3573:
3568:
3563:
3558:
3557:
3556:
3551:
3546:
3536:
3534:Second dealing
3531:
3524:
3523:
3522:
3517:
3512:
3507:
3496:
3491:
3489:House of cards
3486:
3481:
3476:
3469:
3464:
3459:
3454:
3453:
3452:
3442:
3437:
3432:
3430:Bottom dealing
3426:
3423:
3422:
3420:
3415:
3410:
3405:
3400:
3395:
3390:
3385:
3383:Ambitious Card
3380:
3375:
3373:
3366:
3355:
3354:
3352:
3351:
3346:
3341:
3336:
3335:
3334:
3322:
3317:
3312:
3307:
3302:
3296:
3293:
3292:
3290:
3289:
3284:
3279:
3274:
3268:
3266:
3257:
3251:
3250:
3248:
3247:
3242:
3237:
3232:
3227:
3222:
3217:
3215:Franco Pratesi
3212:
3207:
3202:
3197:
3192:
3187:
3182:
3177:
3172:
3167:
3165:Sekiryo Kaneda
3162:
3157:
3152:
3147:
3142:
3137:
3132:
3127:
3122:
3117:
3112:
3107:
3102:
3096:
3094:
3093:Notable people
3090:
3089:
3086:
3085:
3083:
3082:
3077:
3072:
3067:
3062:
3057:
3052:
3046:
3044:
3040:
3039:
3037:
3036:
3031:
3025:
3023:
3019:
3018:
3016:
3015:
3010:
3005:
3000:
2995:
2990:
2985:
2980:
2975:
2970:
2965:
2960:
2955:
2950:
2945:
2940:
2935:
2930:
2924:
2922:
2915:
2909:
2908:
2905:
2904:
2902:
2901:
2898:
2892:
2887:
2881:
2879:
2873:
2872:
2870:
2869:
2868:
2867:
2859:
2854:
2849:
2844:
2838:
2836:
2820:
2819:
2817:
2816:
2811:
2805:
2803:
2799:
2798:
2796:
2795:
2790:
2784:
2782:
2776:
2775:
2773:
2772:
2766:
2764:
2755:
2751:
2750:
2748:
2747:
2742:
2737:
2732:
2727:
2722:
2721:
2720:
2713:
2703:
2702:
2701:
2696:
2691:
2681:
2676:
2670:
2668:
2664:
2663:
2661:
2660:
2653:
2646:
2641:
2636:
2631:
2626:
2619:
2618:
2617:
2610:
2603:
2600:Hyakunin Isshu
2596:
2582:
2581:
2580:
2566:
2561:
2556:
2548:
2546:
2538:
2537:
2534:
2533:
2531:
2530:
2528:Transformation
2525:
2523:Stuttgart pack
2520:
2515:
2510:
2508:Jerry's Nugget
2505:
2498:
2493:
2488:
2483:
2478:
2470:
2468:
2467:Specific decks
2464:
2463:
2461:
2460:
2455:
2450:
2445:
2444:
2443:
2433:
2428:
2427:
2426:
2421:
2410:
2408:
2404:
2403:
2401:
2400:
2395:
2390:
2385:
2379:
2377:
2363:
2355:
2354:
2349:
2347:
2346:
2339:
2332:
2324:
2318:
2317:
2301:
2300:
2262:
2261:
2248:
2232:
2231:
2208:
2207:
2167:
2166:
2154:(2): 175–196.
2123:
2120:
2117:
2116:
2107:
2091:
2082:
2073:
2071:Morris 1998, 8
2064:
2055:
2046:
2037:
2027:
2026:
2024:
2021:
2006:
2002:
1998:
1995:
1992:
1989:
1967:
1963:
1940:
1936:
1913:
1909:
1897:
1896:
1883:
1877:
1874:
1870:
1867:
1862:
1859:
1856:
1853:
1850:
1847:
1845:
1842:
1839:
1838:
1834:
1831:
1827:
1824:
1819:
1816:
1813:
1810:
1807:
1804:
1802:
1799:
1796:
1795:
1793:
1788:
1783:
1780:
1776:
1772:
1769:
1765:
1761:
1758:
1755:
1752:
1749:
1744:
1740:
1736:
1715:
1714:
1703:
1700:
1695:
1692:
1689:
1685:
1681:
1669:
1666:
1663:
1659:
1655:
1652:
1649:
1646:
1643:
1638:
1634:
1630:
1598:
1594:
1573:
1553:
1550:
1547:
1544:
1541:
1538:
1535:
1513:
1509:
1488:
1485:
1482:
1479:
1476:
1447:
1444:
1440:
1419:
1416:
1413:
1410:
1407:
1396:
1395:
1382:
1369:
1366:
1362:
1359:
1354:
1351:
1348:
1347:
1336:
1333:
1329:
1325:
1322:
1319:
1313:
1312:
1310:
1305:
1302:
1288:
1287:
1274:
1268:
1265:
1262:
1260:
1257:
1255:
1252:
1250:
1247:
1244:
1241:
1239:
1236:
1234:
1231:
1228:
1225:
1223:
1220:
1219:
1216:
1213:
1210:
1208:
1205:
1202:
1199:
1196:
1194:
1191:
1189:
1186:
1184:
1181:
1179:
1176:
1174:
1171:
1170:
1168:
1144:
1141:
1137:
1107:
1104:
1100:
1076:
1073:
1068:
1064:
1060:
1045:
1042:
1041:
1040:
1039:
1038:
1035:
1034:
1027:
1020:
1013:
1006:
999:
992:
988:
987:
980:
973:
966:
959:
952:
945:
941:
940:
933:
926:
919:
912:
905:
898:
894:
893:
886:
879:
872:
865:
858:
851:
847:
846:
839:
832:
825:
818:
811:
804:
800:
799:
794:
791:
788:
785:
782:
777:
764:
763:
762:
761:
758:
757:
750:
743:
736:
729:
722:
715:
711:
710:
703:
696:
689:
682:
675:
668:
664:
663:
656:
649:
642:
635:
628:
621:
617:
616:
609:
602:
595:
588:
581:
574:
570:
569:
564:
561:
558:
555:
552:
547:
530:
527:
459:
456:
452:
449:
444:
441:
436:
432:
410:
407:
404:
401:
397:
394:
389:
386:
381:
377:
367:-card deck if
356:
336:
312:
309:
305:
302:
297:
294:
289:
285:
263:
260:
257:
254:
250:
247:
242:
239:
234:
230:
220:-card deck if
209:
189:
144:
141:
137:Persi Diaconis
133:John Maskelyne
116:
113:
85:(British), or
73:
72:
52:the key points
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3823:
3812:
3809:
3807:
3804:
3802:
3799:
3797:
3794:
3793:
3791:
3775:
3766:
3757:
3748:
3739:
3730:
3721:
3713:
3703:
3702:
3698:
3695:
3694:
3693:Playing Cards
3690:
3688:
3687:
3683:
3682:
3680:
3676:
3671:
3670:
3666:
3664:
3663:
3659:
3657:
3656:
3652:
3650:
3649:
3645:
3643:
3642:
3638:
3636:
3635:
3631:
3629:
3628:
3624:
3622:
3621:
3617:
3615:
3614:
3610:
3608:
3607:
3603:
3601:
3600:
3596:
3594:
3590:
3587:
3585:Art and media
3583:
3577:
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3555:
3552:
3550:
3547:
3545:
3542:
3541:
3540:
3537:
3535:
3532:
3530:
3529:
3525:
3521:
3518:
3516:
3513:
3511:
3508:
3506:
3503:
3502:
3500:
3497:
3495:
3492:
3490:
3487:
3485:
3482:
3480:
3479:Herrmann pass
3477:
3475:
3474:
3470:
3468:
3465:
3463:
3460:
3458:
3457:Cardistry-Con
3455:
3451:
3448:
3447:
3446:
3445:Card throwing
3443:
3441:
3438:
3436:
3433:
3431:
3428:
3427:
3419:
3416:
3414:
3411:
3409:
3406:
3404:
3401:
3399:
3396:
3394:
3391:
3389:
3386:
3384:
3381:
3379:
3376:
3374:
3370:
3367:
3365:
3360:
3356:
3350:
3347:
3345:
3342:
3340:
3337:
3333:
3332:
3328:
3327:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3303:
3301:
3300:52 Plus Joker
3298:
3297:
3288:
3285:
3283:
3280:
3278:
3275:
3273:
3270:
3269:
3267:
3265:
3261:
3258:
3256:organisations
3252:
3246:
3243:
3241:
3238:
3236:
3233:
3231:
3228:
3226:
3223:
3221:
3218:
3216:
3213:
3211:
3208:
3206:
3203:
3201:
3200:David Parlett
3198:
3196:
3193:
3191:
3188:
3186:
3183:
3181:
3178:
3176:
3173:
3171:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3151:
3148:
3146:
3145:Lennart Green
3143:
3141:
3140:S. W. Erdnase
3138:
3136:
3133:
3131:
3128:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3108:
3106:
3103:
3101:
3098:
3097:
3095:
3091:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3047:
3045:
3041:
3035:
3032:
3030:
3027:
3026:
3024:
3020:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2989:
2988:Oishi Tengudo
2986:
2984:
2981:
2979:
2976:
2974:
2971:
2969:
2966:
2964:
2961:
2959:
2956:
2954:
2953:France Cartes
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2925:
2923:
2921:Manufacturers
2919:
2916:
2912:Manufacturers
2910:
2899:
2896:
2893:
2891:
2888:
2886:
2883:
2882:
2880:
2878:
2874:
2866:
2863:
2862:
2860:
2858:
2855:
2853:
2850:
2848:
2845:
2843:
2840:
2839:
2837:
2834:
2830:
2826:
2821:
2815:
2812:
2810:
2807:
2806:
2804:
2800:
2794:
2791:
2789:
2786:
2785:
2783:
2781:
2777:
2771:
2768:
2767:
2765:
2763:
2759:
2756:
2752:
2746:
2743:
2741:
2738:
2736:
2735:Stripped deck
2733:
2731:
2728:
2726:
2723:
2719:
2718:
2714:
2712:
2709:
2708:
2707:
2704:
2700:
2697:
2695:
2692:
2690:
2687:
2686:
2685:
2682:
2680:
2677:
2675:
2672:
2671:
2669:
2665:
2659:
2658:
2654:
2652:
2651:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2624:
2620:
2616:
2615:
2611:
2609:
2608:
2604:
2602:
2601:
2597:
2595:
2594:
2590:
2589:
2588:
2587:
2583:
2579:
2578:
2574:
2573:
2572:
2571:
2567:
2565:
2562:
2560:
2557:
2555:
2554:
2550:
2549:
2547:
2545:
2539:
2529:
2526:
2524:
2521:
2519:
2516:
2514:
2511:
2509:
2506:
2504:
2503:
2502:Hofämterspiel
2499:
2497:
2494:
2492:
2489:
2487:
2484:
2482:
2479:
2477:
2476:
2472:
2471:
2469:
2465:
2459:
2456:
2454:
2451:
2449:
2446:
2442:
2439:
2438:
2437:
2434:
2432:
2429:
2425:
2424:Ace of hearts
2422:
2420:
2419:Ace of spades
2417:
2416:
2415:
2412:
2411:
2409:
2405:
2399:
2396:
2394:
2391:
2389:
2386:
2384:
2381:
2380:
2378:
2375:
2371:
2367:
2364:
2362:
2356:
2352:
2351:Playing cards
2345:
2340:
2338:
2333:
2331:
2326:
2325:
2322:
2313:
2308:
2303:
2302:
2297:
2293:
2289:
2285:
2281:
2277:
2273:
2269:
2264:
2263:
2251:
2249:0-883-85527-5
2245:
2241:
2240:
2234:
2233:
2220:
2219:
2214:
2210:
2209:
2197:
2193:
2189:
2185:
2178:
2174:
2169:
2168:
2162:
2157:
2153:
2149:
2142:
2138:
2137:Kantor, W. M.
2134:
2133:Graham, R. L.
2130:
2126:
2125:
2121:
2111:
2108:
2104:
2103:Peter Cameron
2100:
2095:
2092:
2086:
2083:
2077:
2074:
2068:
2065:
2059:
2056:
2050:
2047:
2041:
2038:
2032:
2029:
2022:
2020:
2004:
2000:
1996:
1990:
1965:
1961:
1938:
1934:
1911:
1907:
1872:
1868:
1860:
1857:
1854:
1851:
1848:
1843:
1840:
1829:
1825:
1817:
1814:
1811:
1808:
1805:
1800:
1797:
1791:
1786:
1778:
1774:
1770:
1759:
1756:
1750:
1742:
1738:
1720:
1719:
1718:
1701:
1693:
1690:
1687:
1683:
1667:
1664:
1661:
1653:
1650:
1644:
1636:
1632:
1614:
1613:
1612:
1596:
1592:
1571:
1548:
1545:
1542:
1539:
1536:
1511:
1507:
1483:
1480:
1477:
1465:
1463:
1445:
1442:
1438:
1414:
1411:
1408:
1367:
1360:
1357:
1352:
1349:
1334:
1327:
1323:
1320:
1317:
1308:
1300:
1293:
1292:
1291:
1272:
1266:
1263:
1258:
1253:
1248:
1245:
1242:
1237:
1232:
1229:
1226:
1221:
1214:
1211:
1206:
1203:
1200:
1197:
1192:
1187:
1182:
1177:
1172:
1166:
1142:
1139:
1135:
1127:
1126:
1125:
1123:
1105:
1102:
1098:
1088:
1086:
1082:
1074:
1072:
1057:
1055:
1054:binary number
1051:
1043:
1032:
1028:
1025:
1021:
1018:
1014:
1011:
1007:
1004:
1000:
997:
993:
990:
989:
985:
981:
978:
974:
971:
967:
964:
960:
957:
953:
950:
946:
943:
942:
938:
934:
931:
927:
924:
920:
917:
913:
910:
906:
903:
899:
896:
895:
891:
887:
884:
880:
877:
873:
870:
866:
863:
859:
856:
852:
849:
848:
844:
840:
837:
833:
830:
826:
823:
819:
816:
812:
809:
805:
802:
801:
795:
792:
789:
786:
783:
778:
775:
774:
771:
770:
769:
768:
767:
755:
751:
748:
744:
741:
737:
734:
730:
727:
723:
720:
716:
713:
712:
708:
704:
701:
697:
694:
690:
687:
683:
680:
676:
673:
669:
666:
665:
661:
657:
654:
650:
647:
643:
640:
636:
633:
629:
626:
622:
619:
618:
614:
610:
607:
603:
600:
596:
593:
589:
586:
582:
579:
575:
572:
571:
565:
562:
559:
556:
553:
548:
545:
544:
541:
540:
539:
538:
537:
534:
528:
526:
524:
519:
517:
513:
510:According to
508:
506:
501:
496:
491:
489:
485:
481:
477:
472:
454:
450:
442:
439:
434:
430:
405:
402:
399:
395:
387:
384:
379:
375:
354:
334:
325:
307:
303:
295:
292:
287:
283:
258:
255:
252:
248:
240:
237:
232:
228:
207:
187:
178:
175:
171:
167:
165:
161:
157:
152:
148:
142:
140:
138:
134:
130:
125:
123:
114:
112:
105:
101:
99:
98:the technique
95:
94:playing cards
92:
88:
84:
83:weave shuffle
80:
69:
59:
53:
51:
46:
41:
37:
32:
31:
19:
3777:}}
3774:Occult tarot
3771:{{
3768:}}
3762:{{
3759:}}
3753:{{
3750:}}
3744:{{
3741:}}
3735:{{
3732:}}
3726:{{
3723:}}
3717:{{
3699:
3691:
3684:
3667:
3660:
3653:
3646:
3639:
3632:
3625:
3618:
3611:
3604:
3599:The Acrobats
3597:
3543:
3526:
3494:One-way deck
3471:
3435:Card marking
3413:Spelling Bee
3329:
3225:Juan Tamariz
3130:Dan and Dave
3120:Derren Brown
3115:David Blaine
3050:Aspioti-ELKA
2998:Ravensburger
2715:
2655:
2648:
2621:
2612:
2605:
2598:
2591:
2584:
2575:
2568:
2551:
2500:
2473:
2361:52-card deck
2271:
2267:
2253:. Retrieved
2238:
2223:. Retrieved
2217:
2199:. Retrieved
2187:
2183:
2151:
2147:
2110:
2094:
2085:
2076:
2067:
2058:
2049:
2040:
2031:
1898:
1716:
1466:
1461:
1397:
1289:
1121:
1089:
1078:
1058:
1050:Alex Elmsley
1047:
765:
535:
532:
520:
515:
509:
494:
492:
487:
475:
473:
327:In general,
326:
180:In general,
179:
176:
172:
168:
164:Alex Elmsley
159:
155:
153:
149:
146:
126:
118:
110:
97:
86:
82:
81:(American),
79:faro shuffle
78:
76:
66:October 2018
63:
47:
45:lead section
3686:Card Sharks
3576:Trick decks
3467:Double lift
3408:Rising Card
3190:Anton Moser
3185:John McLeod
3170:René Lavand
3125:Lewis Cohen
3105:Hubert Auer
3080:Waddingtons
3075:Lewis Cohen
2958:F.X. Schmid
2754:Other suits
2542:Other packs
2518:Politicards
2190:: 169–180.
2173:Shallit, J.
1081:mathematics
1067:or 00001010
156:out-shuffle
115:Description
3801:Card magic
3790:Categories
3566:Spoke card
3515:mechanic's
3510:magician's
3501:and grips
3440:Card sharp
3254:Groups and
3240:Dai Vernon
3110:Bryan Berg
2933:Cartamundi
2914:and brands
2897:of Strings
2833:Portuguese
2684:Court card
2644:Tarot pack
2614:uta-garuta
2122:References
518:shuffles.
160:in-shuffle
127:A game of
18:In shuffle
3592:Paintings
3549:Gilbreath
3539:Shuffling
3505:gambler's
3364:cardistry
3160:Ricky Jay
3100:Lee Asher
3060:C.L. Wüst
2943:Dal Negro
2861:Japanese
2730:Nicknames
2544:and decks
2458:Beer card
2359:Standard
2312:0805.1598
1997:∈
1962:ρ
1935:ρ
1908:ρ
1852:≡
1841:−
1809:≡
1782:⌋
1768:⌊
1757:−
1739:ρ
1691:−
1684:ρ
1651:−
1633:ρ
1593:ρ
1546:−
1508:ρ
1304:↦
1254:⋯
1204:−
1193:⋯
1048:Magician
440:≡
403:−
385:≡
293:≡
238:≡
91:shuffling
50:summarize
3175:Ed Marlo
2978:Nintendo
2948:Fournier
2706:Pip card
2623:Kvitlech
2607:kabufuda
2593:hanafuda
2486:Charruan
2393:Diamonds
2296:17735734
2215:(1894).
2175:(2002).
2139:(1983).
3462:Cutting
3070:Dondorf
3043:Defunct
3034:Grimaud
3029:Bicycle
2993:Piatnik
2973:Modiano
2895:Myriads
2829:Spanish
2825:Italian
2823:Latin (
2788:Shields
2745:Unicode
2639:Russian
2577:ganjapa
2570:Ganjifa
2559:Chinese
2276:Bibcode
2268:Science
529:Example
503:in the
500:A002326
3696:(1896)
3554:Zarrow
3520:Tenkai
3372:Tricks
3022:Brands
2963:Gemaco
2857:Swords
2852:Batons
2809:Acorns
2770:Leaves
2762:German
2689:knight
2674:Banner
2657:Zi pai
2650:Tujeon
2629:Polish
2586:Karuta
2553:As-Nas
2388:Hearts
2383:Spades
2374:French
2294:
2255:26 Dec
2246:
2225:26 Dec
2201:26 Dec
1371:
1338:
1120:, the
803:Start
796:Bottom
573:Start
566:Bottom
484:modulo
122:zipper
3756:Poker
3499:Palms
3003:Trefl
2938:Copag
2847:Coins
2814:Bells
2793:Roses
2780:Swiss
2740:Talon
2725:Joker
2711:deuce
2699:Unter
2679:Blank
2667:Cards
2436:Queen
2407:Ranks
2398:Clubs
2307:arXiv
2180:(PDF)
2144:(PDF)
2023:Notes
798:Card
781:Card
776:Step
568:Card
551:Card
546:Step
482:of 2
3544:faro
3362:and
3264:Skat
2885:Cash
2842:Cups
2717:Weli
2694:Ober
2448:Jack
2431:King
2292:PMID
2257:2013
2244:ISBN
2227:2013
2203:2013
1926:and
1611:is:
1467:The
1375:even
505:OEIS
129:Faro
77:The
2414:Ace
2284:doi
2272:216
2192:doi
2156:doi
1869:mod
1826:mod
1730:sgn
1675:sgn
1624:sgn
1342:odd
1079:In
779:Top
549:Top
507:).
451:mod
396:mod
304:mod
249:mod
3792::
2290:.
2282:.
2270:.
2186:.
2182:.
2150:.
2146:.
2135:;
2131:;
2101:,
2019:.
1991:23
1087:.
991:4
944:3
897:2
850:1
793:5
790:4
787:3
784:2
714:3
667:2
620:1
563:5
560:4
557:3
554:2
525:.
455:51
324:.
308:53
288:52
166:.
139:.
2835:)
2831:/
2827:/
2376:)
2372:(
2343:e
2336:t
2329:v
2315:.
2309::
2298:.
2286::
2278::
2259:.
2229:.
2205:.
2194::
2188:5
2164:.
2158::
2152:4
2005:4
2001:S
1994:)
1988:(
1966:2
1939:1
1912:0
1876:)
1873:4
1866:(
1861:3
1858:,
1855:2
1849:n
1844:1
1833:)
1830:4
1823:(
1818:1
1815:,
1812:0
1806:n
1801:1
1798:+
1792:{
1787:=
1779:2
1775:/
1771:n
1764:)
1760:1
1754:(
1751:=
1748:)
1743:n
1735:(
1702:.
1699:)
1694:1
1688:n
1680:(
1668:1
1665:+
1662:n
1658:)
1654:1
1648:(
1645:=
1642:)
1637:n
1629:(
1597:n
1572:n
1552:)
1549:1
1543:n
1540:,
1537:2
1534:(
1512:n
1487:)
1484:n
1481:,
1478:2
1475:(
1462:k
1446:n
1443:k
1439:S
1418:)
1415:n
1412:,
1409:k
1406:(
1368:k
1361:2
1358:k
1353:+
1350:n
1335:k
1328:2
1324:1
1321:+
1318:k
1309:{
1301:k
1273:)
1267:n
1264:2
1259:n
1249:2
1246:+
1243:n
1238:2
1233:1
1230:+
1227:n
1222:1
1215:n
1212:2
1207:1
1201:n
1198:2
1188:4
1183:3
1178:2
1173:1
1167:(
1157:=
1143:n
1140:2
1136:S
1106:n
1103:2
1099:S
1069:2
1065:2
1061:2
516:n
495:n
488:n
486:(
476:n
458:)
448:(
443:1
435:8
431:2
409:)
406:1
400:n
393:(
388:1
380:k
376:2
355:n
335:k
311:)
301:(
296:1
284:2
262:)
259:1
256:+
253:n
246:(
241:1
233:k
229:2
208:n
188:k
68:)
64:(
54:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
