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. 3,663 shuffles have qualified so far.

RankShuffleHandShuffledEra
701#2,095,510Four of a kindMay 24, 20252025 engine
702#2,097,957Four of a kindMay 24, 20252025 engine
703#2,100,807Four of a kindMay 24, 20252025 engine
704#2,104,286Four of a kindMay 24, 20252025 engine
705#2,110,304Four of a kindMay 24, 20252025 engine
706#2,115,085Four of a kindMay 24, 20252025 engine
707#2,115,607Four of a kindMay 24, 20252025 engine
708#2,115,958Four of a kindMay 24, 20252025 engine
709#2,116,061Four of a kindMay 24, 20252025 engine
710#2,125,634Four of a kindMay 24, 20252025 engine
711#2,135,143Four of a kindMay 24, 20252025 engine
712#2,135,475Four of a kindMay 24, 20252025 engine
713#2,136,298Four of a kindMay 24, 20252025 engine
714#2,137,557Four of a kindMay 24, 20252025 engine
715#2,140,655Four of a kindMay 24, 20252025 engine
716#2,145,778Four of a kindMay 24, 20252025 engine
717#2,149,983Four of a kindMay 24, 20252025 engine
718#2,156,128Four of a kindMay 24, 20252025 engine
719#2,159,887Four of a kindMay 24, 20252025 engine
720#2,163,348Four of a kindMay 24, 20252025 engine
721#2,163,886Four of a kindMay 24, 20252025 engine
722#2,164,317Four of a kindMay 24, 20252025 engine
723#2,165,612Four of a kindMay 24, 20252025 engine
724#2,166,977Four of a kindMay 24, 20252025 engine
725#2,170,540Four of a kindMay 24, 20252025 engine
726#2,176,545Four of a kindMay 24, 20252025 engine
727#2,178,578Four of a kindMay 24, 20252025 engine
728#2,182,200Four of a kindMay 25, 20252025 engine
729#2,194,472Four of a kindMay 25, 20252025 engine
730#2,200,312Four of a kindMay 25, 20252025 engine
731#2,207,600Four of a kindMay 25, 20252025 engine
732#2,214,114Four of a kindMay 25, 20252025 engine
733#2,216,538Four of a kindMay 25, 20252025 engine
734#2,217,091Four of a kindMay 25, 20252025 engine
735#2,218,209Four of a kindMay 25, 20252025 engine
736#2,218,835Four of a kindMay 25, 20252025 engine
737#2,228,048Four of a kindMay 25, 20252025 engine
738#2,229,343Four of a kindMay 25, 20252025 engine
739#2,230,714Four of a kindMay 25, 20252025 engine
740#2,231,936Four of a kindMay 25, 20252025 engine
741#2,240,957Four of a kindMay 25, 20252025 engine
742#2,243,575Four of a kindMay 25, 20252025 engine
743#2,244,602Four of a kindMay 25, 20252025 engine
744#2,246,100Four of a kindMay 25, 20252025 engine
745#2,249,644Four of a kindMay 25, 20252025 engine
746#2,252,404Four of a kindMay 25, 20252025 engine
747#2,252,686Four of a kindMay 25, 20252025 engine
748#2,254,673Four of a kindMay 25, 20252025 engine
749#2,255,147Four of a kindMay 25, 20252025 engine
750#2,262,695Four of a kindMay 25, 20252025 engine
751#2,267,720Four of a kindMay 26, 20252025 engine
752#2,268,183Four of a kindMay 26, 20252025 engine
753#2,268,659Four of a kindMay 26, 20252025 engine
754#2,269,574Four of a kindMay 26, 20252025 engine
755#2,283,089Four of a kindMay 26, 20252025 engine
756#2,293,213Four of a kindMay 26, 20252025 engine
757#2,297,349Four of a kindMay 26, 20252025 engine
758#2,297,621Four of a kindMay 26, 20252025 engine
759#2,299,182Four of a kindMay 26, 20252025 engine
760#2,304,139Four of a kindMay 26, 20252025 engine
761#2,312,249Four of a kindMay 26, 20252025 engine
762#2,312,586Four of a kindMay 26, 20252025 engine
763#2,314,133Four of a kindMay 26, 20252025 engine
764#2,321,551Four of a kindMay 26, 20252025 engine
765#2,326,780Four of a kindMay 26, 20252025 engine
766#2,329,085Four of a kindMay 26, 20252025 engine
767#2,335,743Four of a kindMay 26, 20252025 engine
768#2,338,030Four of a kindMay 26, 20252025 engine
769#2,344,960Four of a kindMay 26, 20252025 engine
770#2,347,713Four of a kindMay 26, 20252025 engine
771#2,352,240Four of a kindMay 27, 20252025 engine
772#2,354,251Four of a kindMay 27, 20252025 engine
773#2,355,367Four of a kindMay 27, 20252025 engine
774#2,356,613Four of a kindMay 27, 20252025 engine
775#2,364,679Four of a kindMay 27, 20252025 engine
776#2,370,510Four of a kindMay 27, 20252025 engine
777#2,384,012Four of a kindMay 27, 20252025 engine
778#2,386,928Four of a kindMay 27, 20252025 engine
779#2,397,147Four of a kindMay 27, 20252025 engine
780#2,416,467Four of a kindMay 27, 20252025 engine
781#2,417,275Four of a kindMay 27, 20252025 engine
782#2,419,834Four of a kindMay 27, 20252025 engine
783#2,423,164Four of a kindMay 27, 20252025 engine
784#2,424,350Four of a kindMay 27, 20252025 engine
785#2,426,122Four of a kindMay 27, 20252025 engine
786#2,426,410Four of a kindMay 27, 20252025 engine
787#2,428,008Four of a kindMay 27, 20252025 engine
788#2,428,589Four of a kindMay 27, 20252025 engine
789#2,430,152Four of a kindMay 27, 20252025 engine
790#2,436,518Four of a kindMay 28, 20252025 engine
791#2,453,878Four of a kindMay 28, 20252025 engine
792#2,456,485Four of a kindMay 28, 20252025 engine
793#2,456,940Four of a kindMay 28, 20252025 engine
794#2,461,785Four of a kindMay 28, 20252025 engine
795#2,467,900Four of a kindMay 28, 20252025 engine
796#2,469,955Four of a kindMay 28, 20252025 engine
797#2,473,850Four of a kindMay 28, 20252025 engine
798#2,475,560Four of a kindMay 28, 20252025 engine
799#2,479,326Four of a kindMay 28, 20252025 engine
800#2,480,879Four of a kindMay 28, 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.