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. 3,687 shuffles have qualified so far.

RankShuffleHandShuffledEra
2,501#9,547,326Four of a kindAugust 20, 20252025 engine
2,502#9,561,572Four of a kindAugust 20, 20252025 engine
2,503#9,562,838Four of a kindAugust 20, 20252025 engine
2,504#9,564,086Four of a kindAugust 20, 20252025 engine
2,505#9,564,321Four of a kindAugust 20, 20252025 engine
2,506#9,565,977Four of a kindAugust 20, 20252025 engine
2,507#9,566,213Four of a kindAugust 20, 20252025 engine
2,508#9,571,964Four of a kindAugust 20, 20252025 engine
2,509#9,573,907Four of a kindAugust 20, 20252025 engine
2,510#9,574,288Four of a kindAugust 20, 20252025 engine
2,511#9,574,707Four of a kindAugust 20, 20252025 engine
2,512#9,579,516Four of a kindAugust 20, 20252025 engine
2,513#9,579,814Four of a kindAugust 20, 20252025 engine
2,514#9,581,263Four of a kindAugust 20, 20252025 engine
2,515#9,596,856Four of a kindAugust 20, 20252025 engine
2,516#9,599,882Four of a kindAugust 20, 20252025 engine
2,517#9,601,519Four of a kindAugust 20, 20252025 engine
2,518#9,609,719Four of a kindAugust 20, 20252025 engine
2,519#9,612,328Four of a kindAugust 20, 20252025 engine
2,520#9,615,982Four of a kindAugust 20, 20252025 engine
2,521#9,617,685Four of a kindAugust 20, 20252025 engine
2,522#9,622,274Four of a kindAugust 21, 20252025 engine
2,523#9,624,443Four of a kindAugust 21, 20252025 engine
2,524#9,627,631Four of a kindAugust 21, 20252025 engine
2,525#9,631,450Four of a kindAugust 21, 20252025 engine
2,526#9,634,844Four of a kindAugust 21, 20252025 engine
2,527#9,635,146Four of a kindAugust 21, 20252025 engine
2,528#9,637,990Four of a kindAugust 21, 20252025 engine
2,529#9,644,016Four of a kindAugust 21, 20252025 engine
2,530#9,645,108Four of a kindAugust 21, 20252025 engine
2,531#9,645,510Four of a kindAugust 21, 20252025 engine
2,532#9,657,592Four of a kindAugust 21, 20252025 engine
2,533#9,659,293Four of a kindAugust 21, 20252025 engine
2,534#9,662,698Four of a kindAugust 21, 20252025 engine
2,535#9,680,567Four of a kindAugust 21, 20252025 engine
2,536#9,680,893Four of a kindAugust 21, 20252025 engine
2,537#9,690,427Four of a kindAugust 21, 20252025 engine
2,538#9,693,681Four of a kindAugust 21, 20252025 engine
2,539#9,693,865Four of a kindAugust 21, 20252025 engine
2,540#9,701,794Four of a kindAugust 21, 20252025 engine
2,541#9,704,365Four of a kindAugust 22, 20252025 engine
2,542#9,705,315Four of a kindAugust 22, 20252025 engine
2,543#9,705,408Four of a kindAugust 22, 20252025 engine
2,544#9,708,042Four of a kindAugust 22, 20252025 engine
2,545#9,708,057Four of a kindAugust 22, 20252025 engine
2,546#9,713,720Four of a kindAugust 22, 20252025 engine
2,547#9,714,517Four of a kindAugust 22, 20252025 engine
2,548#9,722,481Four of a kindAugust 22, 20252025 engine
2,549#9,734,356Four of a kindAugust 22, 20252025 engine
2,550#9,744,984Four of a kindAugust 22, 20252025 engine
2,551#9,746,493Four of a kindAugust 22, 20252025 engine
2,552#9,749,082Four of a kindAugust 22, 20252025 engine
2,553#9,754,644Four of a kindAugust 22, 20252025 engine
2,554#9,756,316Four of a kindAugust 22, 20252025 engine
2,555#9,757,587Four of a kindAugust 22, 20252025 engine
2,556#9,757,637Four of a kindAugust 22, 20252025 engine
2,557#9,762,136Four of a kindAugust 22, 20252025 engine
2,558#9,768,892Four of a kindAugust 22, 20252025 engine
2,559#9,770,998Four of a kindAugust 22, 20252025 engine
2,560#9,774,051Four of a kindAugust 22, 20252025 engine
2,561#9,776,458Four of a kindAugust 22, 20252025 engine
2,562#9,777,489Four of a kindAugust 22, 20252025 engine
2,563#9,778,429Four of a kindAugust 22, 20252025 engine
2,564#9,781,095Four of a kindAugust 22, 20252025 engine
2,565#9,781,567Four of a kindAugust 22, 20252025 engine
2,566#9,781,722Four of a kindAugust 22, 20252025 engine
2,567#9,786,529Four of a kindAugust 22, 20252025 engine
2,568#9,787,830Four of a kindAugust 23, 20252025 engine
2,569#9,792,269Four of a kindAugust 23, 20252025 engine
2,570#9,793,887Four of a kindAugust 23, 20252025 engine
2,571#9,794,082Four of a kindAugust 23, 20252025 engine
2,572#9,796,243Four of a kindAugust 23, 20252025 engine
2,573#9,803,558Four of a kindAugust 23, 20252025 engine
2,574#9,806,146Four of a kindAugust 23, 20252025 engine
2,575#9,810,032Four of a kindAugust 23, 20252025 engine
2,576#9,814,433Four of a kindAugust 23, 20252025 engine
2,577#9,815,106Four of a kindAugust 23, 20252025 engine
2,578#9,816,269Four of a kindAugust 23, 20252025 engine
2,579#9,817,439Four of a kindAugust 23, 20252025 engine
2,580#9,818,688Four of a kindAugust 23, 20252025 engine
2,581#9,828,139Four of a kindAugust 23, 20252025 engine
2,582#9,830,557Four of a kindAugust 23, 20252025 engine
2,583#9,832,340Four of a kindAugust 23, 20252025 engine
2,584#9,842,670Four of a kindAugust 23, 20252025 engine
2,585#9,846,661Four of a kindAugust 23, 20252025 engine
2,586#9,848,984Four of a kindAugust 23, 20252025 engine
2,587#9,850,601Four of a kindAugust 23, 20252025 engine
2,588#9,854,903Four of a kindAugust 23, 20252025 engine
2,589#9,857,295Four of a kindAugust 23, 20252025 engine
2,590#9,862,321Four of a kindAugust 23, 20252025 engine
2,591#9,862,975Four of a kindAugust 23, 20252025 engine
2,592#9,869,703Four of a kindAugust 23, 20252025 engine
2,593#9,871,930Four of a kindAugust 23, 20252025 engine
2,594#9,876,916Four of a kindAugust 24, 20252025 engine
2,595#9,882,468Four of a kindAugust 24, 20252025 engine
2,596#9,883,749Four of a kindAugust 24, 20252025 engine
2,597#9,885,677Four of a kindAugust 24, 20252025 engine
2,598#9,891,415Four of a kindAugust 24, 20252025 engine
2,599#9,894,154Four of a kindAugust 24, 20252025 engine
2,600#9,894,708Four of a kindAugust 24, 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.