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
801#2,487,854Four of a kindMay 28, 20252025 engine
802#2,493,302Four of a kindMay 28, 20252025 engine
803#2,502,178Four of a kindMay 28, 20252025 engine
804#2,502,414Four of a kindMay 28, 20252025 engine
805#2,504,329Four of a kindMay 28, 20252025 engine
806#2,513,202Four of a kindMay 28, 20252025 engine
807#2,515,030Four of a kindMay 28, 20252025 engine
808#2,515,412Four of a kindMay 28, 20252025 engine
809#2,528,857Four of a kindMay 29, 20252025 engine
810#2,539,095Four of a kindMay 29, 20252025 engine
811#2,551,484Four of a kindMay 29, 20252025 engine
812#2,552,233Four of a kindMay 29, 20252025 engine
813#2,554,513Four of a kindMay 29, 20252025 engine
814#2,556,185Four of a kindMay 29, 20252025 engine
815#2,576,688Four of a kindMay 29, 20252025 engine
816#2,580,838Four of a kindMay 29, 20252025 engine
817#2,581,073Four of a kindMay 29, 20252025 engine
818#2,585,287Four of a kindMay 29, 20252025 engine
819#2,591,281Four of a kindMay 29, 20252025 engine
820#2,594,630Four of a kindMay 29, 20252025 engine
821#2,595,941Four of a kindMay 29, 20252025 engine
822#2,605,235Four of a kindMay 30, 20252025 engine
823#2,606,360Four of a kindMay 30, 20252025 engine
824#2,612,613Four of a kindMay 30, 20252025 engine
825#2,613,379Four of a kindMay 30, 20252025 engine
826#2,624,352Four of a kindMay 30, 20252025 engine
827#2,626,020Four of a kindMay 30, 20252025 engine
828#2,629,145Four of a kindMay 30, 20252025 engine
829#2,632,626Four of a kindMay 30, 20252025 engine
830#2,635,058Four of a kindMay 30, 20252025 engine
831#2,641,889Four of a kindMay 30, 20252025 engine
832#2,648,185Four of a kindMay 30, 20252025 engine
833#2,655,514Four of a kindMay 30, 20252025 engine
834#2,657,646Four of a kindMay 30, 20252025 engine
835#2,663,981Four of a kindMay 30, 20252025 engine
836#2,666,450Four of a kindMay 30, 20252025 engine
837#2,666,651Four of a kindMay 30, 20252025 engine
838#2,667,668Four of a kindMay 30, 20252025 engine
839#2,668,788Four of a kindMay 30, 20252025 engine
840#2,669,521Four of a kindMay 30, 20252025 engine
841#2,675,670Four of a kindMay 30, 20252025 engine
842#2,681,494Four of a kindMay 30, 20252025 engine
843#2,685,744Four of a kindMay 30, 20252025 engine
844#2,699,015Four of a kindMay 31, 20252025 engine
845#2,709,113Four of a kindMay 31, 20252025 engine
846#2,710,005Four of a kindMay 31, 20252025 engine
847#2,712,893Four of a kindMay 31, 20252025 engine
848#2,721,037Four of a kindMay 31, 20252025 engine
849#2,731,404Four of a kindMay 31, 20252025 engine
850#2,732,202Four of a kindMay 31, 20252025 engine
851#2,733,571Four of a kindMay 31, 20252025 engine
852#2,734,266Four of a kindMay 31, 20252025 engine
853#2,741,245Four of a kindMay 31, 20252025 engine
854#2,747,541Four of a kindMay 31, 20252025 engine
855#2,749,356Four of a kindMay 31, 20252025 engine
856#2,750,722Four of a kindMay 31, 20252025 engine
857#2,751,108Four of a kindMay 31, 20252025 engine
858#2,756,524Four of a kindMay 31, 20252025 engine
859#2,757,515Four of a kindMay 31, 20252025 engine
860#2,761,954Four of a kindMay 31, 20252025 engine
861#2,764,163Four of a kindMay 31, 20252025 engine
862#2,770,540Four of a kindJune 1, 20252025 engine
863#2,773,725Four of a kindJune 1, 20252025 engine
864#2,775,198Four of a kindJune 1, 20252025 engine
865#2,778,803Four of a kindJune 1, 20252025 engine
866#2,802,123Four of a kindJune 1, 20252025 engine
867#2,815,815Four of a kindJune 1, 20252025 engine
868#2,816,358Four of a kindJune 1, 20252025 engine
869#2,820,253Four of a kindJune 1, 20252025 engine
870#2,823,249Four of a kindJune 1, 20252025 engine
871#2,824,544Four of a kindJune 1, 20252025 engine
872#2,830,210Four of a kindJune 1, 20252025 engine
873#2,835,352Four of a kindJune 1, 20252025 engine
874#2,836,336Four of a kindJune 1, 20252025 engine
875#2,839,465Four of a kindJune 1, 20252025 engine
876#2,839,973Four of a kindJune 1, 20252025 engine
877#2,842,289Four of a kindJune 1, 20252025 engine
878#2,849,823Four of a kindJune 1, 20252025 engine
879#2,854,808Four of a kindJune 2, 20252025 engine
880#2,855,820Four of a kindJune 2, 20252025 engine
881#2,866,581Four of a kindJune 2, 20252025 engine
882#2,868,683Four of a kindJune 2, 20252025 engine
883#2,870,314Four of a kindJune 2, 20252025 engine
884#2,876,149Four of a kindJune 2, 20252025 engine
885#2,878,709Four of a kindJune 2, 20252025 engine
886#2,886,695Four of a kindJune 2, 20252025 engine
887#2,887,136Four of a kindJune 2, 20252025 engine
888#2,890,498Four of a kindJune 2, 20252025 engine
889#2,898,066Four of a kindJune 2, 20252025 engine
890#2,898,553Four of a kindJune 2, 20252025 engine
891#2,900,641Four of a kindJune 2, 20252025 engine
892#2,906,076Four of a kindJune 2, 20252025 engine
893#2,914,978Four of a kindJune 2, 20252025 engine
894#2,921,842Four of a kindJune 2, 20252025 engine
895#2,935,726Four of a kindJune 2, 20252025 engine
896#2,950,793Four of a kindJune 3, 20252025 engine
897#2,958,081Four of a kindJune 3, 20252025 engine
898#2,959,317Four of a kindJune 3, 20252025 engine
899#2,971,734Four of a kindJune 3, 20252025 engine
900#2,978,398Four of a kindJune 3, 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.