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
501#1,181,393Four of a kindMay 13, 20252025 engine
502#1,186,449Four of a kindMay 13, 20252025 engine
503#1,194,332Four of a kindMay 13, 20252025 engine
504#1,202,000Four of a kindMay 13, 20252025 engine
505#1,202,399Four of a kindMay 13, 20252025 engine
506#1,202,403Four of a kindMay 13, 20252025 engine
507#1,203,716Four of a kindMay 13, 20252025 engine
508#1,212,431Four of a kindMay 13, 20252025 engine
509#1,220,385Four of a kindMay 13, 20252025 engine
510#1,227,304Four of a kindMay 13, 20252025 engine
511#1,229,685Four of a kindMay 13, 20252025 engine
512#1,233,870Four of a kindMay 13, 20252025 engine
513#1,234,425Four of a kindMay 13, 20252025 engine
514#1,245,423Four of a kindMay 13, 20252025 engine
515#1,246,144Four of a kindMay 13, 20252025 engine
516#1,251,959Four of a kindMay 13, 20252025 engine
517#1,253,477Four of a kindMay 14, 20252025 engine
518#1,254,338Four of a kindMay 14, 20252025 engine
519#1,255,301Four of a kindMay 14, 20252025 engine
520#1,255,975Four of a kindMay 14, 20252025 engine
521#1,261,785Four of a kindMay 14, 20252025 engine
522#1,265,278Four of a kindMay 14, 20252025 engine
523#1,267,191Four of a kindMay 14, 20252025 engine
524#1,274,440Four of a kindMay 14, 20252025 engine
525#1,277,812Four of a kindMay 14, 20252025 engine
526#1,280,937Four of a kindMay 14, 20252025 engine
527#1,282,104Four of a kindMay 14, 20252025 engine
528#1,282,390Four of a kindMay 14, 20252025 engine
529#1,293,114Four of a kindMay 14, 20252025 engine
530#1,296,500Four of a kindMay 14, 20252025 engine
531#1,303,117Four of a kindMay 14, 20252025 engine
532#1,303,332Four of a kindMay 14, 20252025 engine
533#1,308,882Four of a kindMay 14, 20252025 engine
534#1,310,626Four of a kindMay 14, 20252025 engine
535#1,312,527Four of a kindMay 14, 20252025 engine
536#1,314,803Four of a kindMay 14, 20252025 engine
537#1,316,402Four of a kindMay 14, 20252025 engine
538#1,318,823Four of a kindMay 14, 20252025 engine
539#1,324,189Four of a kindMay 14, 20252025 engine
540#1,343,916Four of a kindMay 15, 20252025 engine
541#1,346,344Four of a kindMay 15, 20252025 engine
542#1,354,109Four of a kindMay 15, 20252025 engine
543#1,356,843Four of a kindMay 15, 20252025 engine
544#1,358,161Four of a kindMay 15, 20252025 engine
545#1,358,499Four of a kindMay 15, 20252025 engine
546#1,359,639Four of a kindMay 15, 20252025 engine
547#1,363,193Four of a kindMay 15, 20252025 engine
548#1,365,061Four of a kindMay 15, 20252025 engine
549#1,372,562Four of a kindMay 15, 20252025 engine
550#1,372,772Four of a kindMay 15, 20252025 engine
551#1,376,685Four of a kindMay 15, 20252025 engine
552#1,379,122Four of a kindMay 15, 20252025 engine
553#1,379,170Four of a kindMay 15, 20252025 engine
554#1,386,525Four of a kindMay 15, 20252025 engine
555#1,388,173Four of a kindMay 15, 20252025 engine
556#1,388,347Four of a kindMay 15, 20252025 engine
557#1,390,154Four of a kindMay 15, 20252025 engine
558#1,396,172Four of a kindMay 15, 20252025 engine
559#1,397,986Four of a kindMay 15, 20252025 engine
560#1,407,348Four of a kindMay 15, 20252025 engine
561#1,427,555Four of a kindMay 16, 20252025 engine
562#1,433,585Four of a kindMay 16, 20252025 engine
563#1,439,306Four of a kindMay 16, 20252025 engine
564#1,442,466Four of a kindMay 16, 20252025 engine
565#1,442,559Four of a kindMay 16, 20252025 engine
566#1,443,110Four of a kindMay 16, 20252025 engine
567#1,443,739Four of a kindMay 16, 20252025 engine
568#1,445,004Four of a kindMay 16, 20252025 engine
569#1,450,201Four of a kindMay 16, 20252025 engine
570#1,450,274Four of a kindMay 16, 20252025 engine
571#1,455,666Four of a kindMay 16, 20252025 engine
572#1,458,934Four of a kindMay 16, 20252025 engine
573#1,459,058Four of a kindMay 16, 20252025 engine
574#1,462,947Four of a kindMay 16, 20252025 engine
575#1,462,948Four of a kindMay 16, 20252025 engine
576#1,465,152Four of a kindMay 16, 20252025 engine
577#1,467,327Four of a kindMay 16, 20252025 engine
578#1,469,572Four of a kindMay 16, 20252025 engine
579#1,485,053Four of a kindMay 16, 20252025 engine
580#1,506,428Four of a kindMay 16, 20252025 engine
581#1,537,725Four of a kindMay 17, 20252025 engine
582#1,544,697Four of a kindMay 17, 20252025 engine
583#1,545,627Four of a kindMay 17, 20252025 engine
584#1,552,021Four of a kindMay 17, 20252025 engine
585#1,557,785Four of a kindMay 17, 20252025 engine
586#1,565,413Four of a kindMay 17, 20252025 engine
587#1,572,278Four of a kindMay 17, 20252025 engine
588#1,579,907Four of a kindMay 17, 20252025 engine
589#1,587,605Four of a kindMay 17, 20252025 engine
590#1,592,232Four of a kindMay 17, 20252025 engine
591#1,592,897Four of a kindMay 17, 20252025 engine
592#1,593,720Four of a kindMay 18, 20252025 engine
593#1,598,616Four of a kindMay 18, 20252025 engine
594#1,607,755Four of a kindMay 18, 20252025 engine
595#1,607,756Four of a kindMay 18, 20252025 engine
596#1,616,170Four of a kindMay 18, 20252025 engine
597#1,617,027Four of a kindMay 18, 20252025 engine
598#1,619,103Four of a kindMay 18, 20252025 engine
599#1,621,914Four of a kindMay 18, 20252025 engine
600#1,626,121Four of a kindMay 18, 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.