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. 3,662 shuffles have qualified so far.

RankShuffleHandShuffledEra
601#1,638,664Four of a kindMay 18, 20252025 engine
602#1,640,465Four of a kindMay 18, 20252025 engine
603#1,648,714Four of a kindMay 18, 20252025 engine
604#1,648,850Four of a kindMay 18, 20252025 engine
605#1,649,001Four of a kindMay 18, 20252025 engine
606#1,650,456Four of a kindMay 18, 20252025 engine
607#1,653,670Four of a kindMay 18, 20252025 engine
608#1,654,168Four of a kindMay 18, 20252025 engine
609#1,657,182Four of a kindMay 18, 20252025 engine
610#1,660,774Four of a kindMay 18, 20252025 engine
611#1,668,815Four of a kindMay 18, 20252025 engine
612#1,671,209Four of a kindMay 18, 20252025 engine
613#1,676,238Four of a kindMay 18, 20252025 engine
614#1,696,670Four of a kindMay 19, 20252025 engine
615#1,701,422Four of a kindMay 19, 20252025 engine
616#1,704,507Four of a kindMay 19, 20252025 engine
617#1,708,724Four of a kindMay 19, 20252025 engine
618#1,711,081Four of a kindMay 19, 20252025 engine
619#1,716,403Four of a kindMay 19, 20252025 engine
620#1,718,940Four of a kindMay 19, 20252025 engine
621#1,724,688Four of a kindMay 19, 20252025 engine
622#1,727,727Four of a kindMay 19, 20252025 engine
623#1,730,861Four of a kindMay 19, 20252025 engine
624#1,731,742Four of a kindMay 19, 20252025 engine
625#1,738,594Four of a kindMay 19, 20252025 engine
626#1,739,162Four of a kindMay 19, 20252025 engine
627#1,741,050Four of a kindMay 19, 20252025 engine
628#1,744,390Four of a kindMay 19, 20252025 engine
629#1,745,969Four of a kindMay 19, 20252025 engine
630#1,749,061Four of a kindMay 19, 20252025 engine
631#1,749,185Four of a kindMay 19, 20252025 engine
632#1,752,741Four of a kindMay 19, 20252025 engine
633#1,756,609Four of a kindMay 19, 20252025 engine
634#1,762,841Four of a kindMay 19, 20252025 engine
635#1,770,010Four of a kindMay 20, 20252025 engine
636#1,779,429Four of a kindMay 20, 20252025 engine
637#1,787,584Four of a kindMay 20, 20252025 engine
638#1,787,919Four of a kindMay 20, 20252025 engine
639#1,792,796Four of a kindMay 20, 20252025 engine
640#1,799,264Four of a kindMay 20, 20252025 engine
641#1,805,997Four of a kindMay 20, 20252025 engine
642#1,811,243Four of a kindMay 20, 20252025 engine
643#1,811,379Four of a kindMay 20, 20252025 engine
644#1,812,919Four of a kindMay 20, 20252025 engine
645#1,814,740Four of a kindMay 20, 20252025 engine
646#1,817,400Four of a kindMay 20, 20252025 engine
647#1,818,350Four of a kindMay 20, 20252025 engine
648#1,822,669Four of a kindMay 20, 20252025 engine
649#1,826,950Four of a kindMay 20, 20252025 engine
650#1,827,055Four of a kindMay 20, 20252025 engine
651#1,834,248Four of a kindMay 20, 20252025 engine
652#1,848,070Four of a kindMay 20, 20252025 engine
653#1,860,817Four of a kindMay 21, 20252025 engine
654#1,863,847Four of a kindMay 21, 20252025 engine
655#1,870,061Four of a kindMay 21, 20252025 engine
656#1,872,292Four of a kindMay 21, 20252025 engine
657#1,895,116Four of a kindMay 21, 20252025 engine
658#1,904,216Four of a kindMay 21, 20252025 engine
659#1,908,143Four of a kindMay 21, 20252025 engine
660#1,912,322Four of a kindMay 21, 20252025 engine
661#1,912,984Four of a kindMay 21, 20252025 engine
662#1,918,975Four of a kindMay 21, 20252025 engine
663#1,921,025Four of a kindMay 21, 20252025 engine
664#1,928,418Four of a kindMay 21, 20252025 engine
665#1,929,727Four of a kindMay 21, 20252025 engine
666#1,933,475Four of a kindMay 21, 20252025 engine
667#1,940,258Four of a kindMay 22, 20252025 engine
668#1,940,433Four of a kindMay 22, 20252025 engine
669#1,941,967Four of a kindMay 22, 20252025 engine
670#1,946,497Four of a kindMay 22, 20252025 engine
671#1,950,098Four of a kindMay 22, 20252025 engine
672#1,957,693Four of a kindMay 22, 20252025 engine
673#1,957,883Four of a kindMay 22, 20252025 engine
674#1,957,988Four of a kindMay 22, 20252025 engine
675#1,959,036Four of a kindMay 22, 20252025 engine
676#1,959,514Four of a kindMay 22, 20252025 engine
677#1,962,277Four of a kindMay 22, 20252025 engine
678#1,963,921Four of a kindMay 22, 20252025 engine
679#1,967,004Four of a kindMay 22, 20252025 engine
680#1,968,231Four of a kindMay 22, 20252025 engine
681#1,981,544Four of a kindMay 22, 20252025 engine
682#1,984,794Four of a kindMay 22, 20252025 engine
683#1,988,051Four of a kindMay 22, 20252025 engine
684#1,991,769Four of a kindMay 22, 20252025 engine
685#1,992,109Four of a kindMay 22, 20252025 engine
686#1,998,885Four of a kindMay 22, 20252025 engine
687#2,004,427Four of a kindMay 22, 20252025 engine
688#2,005,255Four of a kindMay 22, 20252025 engine
689#2,011,391Four of a kindMay 23, 20252025 engine
690#2,018,935Four of a kindMay 23, 20252025 engine
691#2,024,482Four of a kindMay 23, 20252025 engine
692#2,043,925Four of a kindMay 23, 20252025 engine
693#2,043,954Four of a kindMay 23, 20252025 engine
694#2,047,524Four of a kindMay 23, 20252025 engine
695#2,059,557Four of a kindMay 23, 20252025 engine
696#2,075,526Four of a kindMay 23, 20252025 engine
697#2,075,942Four of a kindMay 23, 20252025 engine
698#2,087,478Four of a kindMay 23, 20252025 engine
699#2,093,044Four of a kindMay 23, 20252025 engine
700#2,094,594Four of a kindMay 23, 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.