Exhibit

Rarest hands.

Deal the top five cards of a freshly shuffled deck as a poker hand. Almost always it is nothing much. This room holds the shuffles where it was four of a kind or better, ranked rarest first.

What is ranked

The poker rank of the top five cards, evaluated as a standard five-card hand. Only four of a kind, straight flushes and royal flushes qualify. Ties are ordered by archive number, oldest first.

How rare

Of all possible decks, about one in 3,914 opens with four of a kind or better: 664 of the 2,598,960 possible five-card hands.

The record

Royal flush

Shuffle #35,419, recorded April 28, 2025. 3,659 shuffles have qualified so far.

RankShuffleHandShuffledEra
401#803,305Four of a kindMay 8, 20252025 engine
402#805,887Four of a kindMay 8, 20252025 engine
403#809,922Four of a kindMay 8, 20252025 engine
404#810,227Four of a kindMay 8, 20252025 engine
405#817,653Four of a kindMay 8, 20252025 engine
406#820,323Four of a kindMay 8, 20252025 engine
407#824,300Four of a kindMay 8, 20252025 engine
408#828,770Four of a kindMay 9, 20252025 engine
409#846,820Four of a kindMay 9, 20252025 engine
410#852,634Four of a kindMay 9, 20252025 engine
411#856,182Four of a kindMay 9, 20252025 engine
412#860,300Four of a kindMay 9, 20252025 engine
413#861,203Four of a kindMay 9, 20252025 engine
414#865,191Four of a kindMay 9, 20252025 engine
415#878,068Four of a kindMay 9, 20252025 engine
416#880,764Four of a kindMay 9, 20252025 engine
417#883,697Four of a kindMay 9, 20252025 engine
418#884,560Four of a kindMay 9, 20252025 engine
419#888,862Four of a kindMay 9, 20252025 engine
420#891,076Four of a kindMay 9, 20252025 engine
421#891,136Four of a kindMay 9, 20252025 engine
422#893,291Four of a kindMay 9, 20252025 engine
423#893,803Four of a kindMay 9, 20252025 engine
424#895,801Four of a kindMay 9, 20252025 engine
425#901,818Four of a kindMay 9, 20252025 engine
426#902,662Four of a kindMay 9, 20252025 engine
427#908,788Four of a kindMay 9, 20252025 engine
428#914,267Four of a kindMay 10, 20252025 engine
429#919,875Four of a kindMay 10, 20252025 engine
430#922,332Four of a kindMay 10, 20252025 engine
431#926,921Four of a kindMay 10, 20252025 engine
432#931,039Four of a kindMay 10, 20252025 engine
433#932,503Four of a kindMay 10, 20252025 engine
434#933,273Four of a kindMay 10, 20252025 engine
435#935,602Four of a kindMay 10, 20252025 engine
436#938,392Four of a kindMay 10, 20252025 engine
437#938,665Four of a kindMay 10, 20252025 engine
438#939,271Four of a kindMay 10, 20252025 engine
439#939,812Four of a kindMay 10, 20252025 engine
440#945,097Four of a kindMay 10, 20252025 engine
441#946,338Four of a kindMay 10, 20252025 engine
442#965,310Four of a kindMay 10, 20252025 engine
443#971,879Four of a kindMay 10, 20252025 engine
444#972,557Four of a kindMay 10, 20252025 engine
445#973,054Four of a kindMay 10, 20252025 engine
446#975,040Four of a kindMay 10, 20252025 engine
447#986,583Four of a kindMay 10, 20252025 engine
448#996,763Four of a kindMay 11, 20252025 engine
449#998,932Four of a kindMay 11, 20252025 engine
450#999,036Four of a kindMay 11, 20252025 engine
451#1,003,012Four of a kindMay 11, 20252025 engine
452#1,003,044Four of a kindMay 11, 20252025 engine
453#1,005,008Four of a kindMay 11, 20252025 engine
454#1,007,292Four of a kindMay 11, 20252025 engine
455#1,009,826Four of a kindMay 11, 20252025 engine
456#1,019,814Four of a kindMay 11, 20252025 engine
457#1,023,678Four of a kindMay 11, 20252025 engine
458#1,036,291Four of a kindMay 11, 20252025 engine
459#1,038,889Four of a kindMay 11, 20252025 engine
460#1,040,107Four of a kindMay 11, 20252025 engine
461#1,041,526Four of a kindMay 11, 20252025 engine
462#1,043,668Four of a kindMay 11, 20252025 engine
463#1,059,106Four of a kindMay 11, 20252025 engine
464#1,059,432Four of a kindMay 11, 20252025 engine
465#1,063,154Four of a kindMay 11, 20252025 engine
466#1,064,069Four of a kindMay 11, 20252025 engine
467#1,064,094Four of a kindMay 11, 20252025 engine
468#1,073,588Four of a kindMay 11, 20252025 engine
469#1,073,806Four of a kindMay 11, 20252025 engine
470#1,080,543Four of a kindMay 11, 20252025 engine
471#1,083,109Four of a kindMay 12, 20252025 engine
472#1,086,467Four of a kindMay 12, 20252025 engine
473#1,091,842Four of a kindMay 12, 20252025 engine
474#1,093,471Four of a kindMay 12, 20252025 engine
475#1,097,658Four of a kindMay 12, 20252025 engine
476#1,100,415Four of a kindMay 12, 20252025 engine
477#1,102,463Four of a kindMay 12, 20252025 engine
478#1,105,338Four of a kindMay 12, 20252025 engine
479#1,107,752Four of a kindMay 12, 20252025 engine
480#1,111,577Four of a kindMay 12, 20252025 engine
481#1,112,297Four of a kindMay 12, 20252025 engine
482#1,116,629Four of a kindMay 12, 20252025 engine
483#1,117,412Four of a kindMay 12, 20252025 engine
484#1,119,807Four of a kindMay 12, 20252025 engine
485#1,127,706Four of a kindMay 12, 20252025 engine
486#1,128,802Four of a kindMay 12, 20252025 engine
487#1,131,373Four of a kindMay 12, 20252025 engine
488#1,131,600Four of a kindMay 12, 20252025 engine
489#1,133,515Four of a kindMay 12, 20252025 engine
490#1,133,622Four of a kindMay 12, 20252025 engine
491#1,136,020Four of a kindMay 12, 20252025 engine
492#1,154,462Four of a kindMay 12, 20252025 engine
493#1,155,891Four of a kindMay 12, 20252025 engine
494#1,159,051Four of a kindMay 12, 20252025 engine
495#1,166,267Four of a kindMay 12, 20252025 engine
496#1,167,911Four of a kindMay 13, 20252025 engine
497#1,170,648Four of a kindMay 13, 20252025 engine
498#1,173,323Four of a kindMay 13, 20252025 engine
499#1,176,949Four of a kindMay 13, 20252025 engine
500#1,177,322Four of a kindMay 13, 20252025 engine

The counts behind that probability are the classical poker enumeration, re-verified in this project by evaluating all 2,598,960 hands. The math pages cover why a deck has so many orderings that even a royal flush on top has turned up here more than once.