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. 3,666 shuffles have qualified so far.

RankShuffleHandShuffledEra
1,001#3,346,038Four of a kindJune 7, 20252025 engine
1,002#3,349,027Four of a kindJune 7, 20252025 engine
1,003#3,351,728Four of a kindJune 7, 20252025 engine
1,004#3,354,060Four of a kindJune 7, 20252025 engine
1,005#3,358,417Four of a kindJune 7, 20252025 engine
1,006#3,360,183Four of a kindJune 7, 20252025 engine
1,007#3,360,521Four of a kindJune 7, 20252025 engine
1,008#3,364,731Four of a kindJune 8, 20252025 engine
1,009#3,365,206Four of a kindJune 8, 20252025 engine
1,010#3,366,232Four of a kindJune 8, 20252025 engine
1,011#3,383,570Four of a kindJune 8, 20252025 engine
1,012#3,385,929Four of a kindJune 8, 20252025 engine
1,013#3,388,841Four of a kindJune 8, 20252025 engine
1,014#3,392,589Four of a kindJune 8, 20252025 engine
1,015#3,399,318Four of a kindJune 8, 20252025 engine
1,016#3,400,661Four of a kindJune 8, 20252025 engine
1,017#3,409,707Four of a kindJune 8, 20252025 engine
1,018#3,409,975Four of a kindJune 8, 20252025 engine
1,019#3,410,455Four of a kindJune 8, 20252025 engine
1,020#3,412,260Four of a kindJune 8, 20252025 engine
1,021#3,421,984Four of a kindJune 8, 20252025 engine
1,022#3,425,573Four of a kindJune 8, 20252025 engine
1,023#3,428,381Four of a kindJune 8, 20252025 engine
1,024#3,429,245Four of a kindJune 8, 20252025 engine
1,025#3,433,933Four of a kindJune 8, 20252025 engine
1,026#3,434,575Four of a kindJune 8, 20252025 engine
1,027#3,442,337Four of a kindJune 8, 20252025 engine
1,028#3,444,541Four of a kindJune 8, 20252025 engine
1,029#3,446,319Four of a kindJune 9, 20252025 engine
1,030#3,451,182Four of a kindJune 9, 20252025 engine
1,031#3,452,783Four of a kindJune 9, 20252025 engine
1,032#3,453,327Four of a kindJune 9, 20252025 engine
1,033#3,454,548Four of a kindJune 9, 20252025 engine
1,034#3,455,947Four of a kindJune 9, 20252025 engine
1,035#3,457,489Four of a kindJune 9, 20252025 engine
1,036#3,459,429Four of a kindJune 9, 20252025 engine
1,037#3,461,015Four of a kindJune 9, 20252025 engine
1,038#3,461,273Four of a kindJune 9, 20252025 engine
1,039#3,464,518Four of a kindJune 9, 20252025 engine
1,040#3,465,759Four of a kindJune 9, 20252025 engine
1,041#3,466,391Four of a kindJune 9, 20252025 engine
1,042#3,496,299Four of a kindJune 9, 20252025 engine
1,043#3,496,326Four of a kindJune 9, 20252025 engine
1,044#3,496,607Four of a kindJune 9, 20252025 engine
1,045#3,496,617Four of a kindJune 9, 20252025 engine
1,046#3,498,440Four of a kindJune 9, 20252025 engine
1,047#3,500,140Four of a kindJune 9, 20252025 engine
1,048#3,501,884Four of a kindJune 9, 20252025 engine
1,049#3,504,141Four of a kindJune 9, 20252025 engine
1,050#3,505,826Four of a kindJune 9, 20252025 engine
1,051#3,507,200Four of a kindJune 9, 20252025 engine
1,052#3,515,261Four of a kindJune 9, 20252025 engine
1,053#3,516,246Four of a kindJune 9, 20252025 engine
1,054#3,526,824Four of a kindJune 9, 20252025 engine
1,055#3,538,687Four of a kindJune 10, 20252025 engine
1,056#3,541,308Four of a kindJune 10, 20252025 engine
1,057#3,549,069Four of a kindJune 10, 20252025 engine
1,058#3,549,958Four of a kindJune 10, 20252025 engine
1,059#3,551,084Four of a kindJune 10, 20252025 engine
1,060#3,551,425Four of a kindJune 10, 20252025 engine
1,061#3,554,961Four of a kindJune 10, 20252025 engine
1,062#3,555,427Four of a kindJune 10, 20252025 engine
1,063#3,557,214Four of a kindJune 10, 20252025 engine
1,064#3,566,702Four of a kindJune 10, 20252025 engine
1,065#3,574,214Four of a kindJune 10, 20252025 engine
1,066#3,575,075Four of a kindJune 10, 20252025 engine
1,067#3,575,369Four of a kindJune 10, 20252025 engine
1,068#3,575,983Four of a kindJune 10, 20252025 engine
1,069#3,578,870Four of a kindJune 10, 20252025 engine
1,070#3,586,168Four of a kindJune 10, 20252025 engine
1,071#3,588,143Four of a kindJune 10, 20252025 engine
1,072#3,590,871Four of a kindJune 10, 20252025 engine
1,073#3,593,514Four of a kindJune 10, 20252025 engine
1,074#3,600,737Four of a kindJune 10, 20252025 engine
1,075#3,604,597Four of a kindJune 10, 20252025 engine
1,076#3,608,704Four of a kindJune 10, 20252025 engine
1,077#3,613,639Four of a kindJune 10, 20252025 engine
1,078#3,616,049Four of a kindJune 11, 20252025 engine
1,079#3,636,694Four of a kindJune 11, 20252025 engine
1,080#3,638,737Four of a kindJune 11, 20252025 engine
1,081#3,640,520Four of a kindJune 11, 20252025 engine
1,082#3,643,595Four of a kindJune 11, 20252025 engine
1,083#3,646,349Four of a kindJune 11, 20252025 engine
1,084#3,647,252Four of a kindJune 11, 20252025 engine
1,085#3,649,656Four of a kindJune 11, 20252025 engine
1,086#3,650,604Four of a kindJune 11, 20252025 engine
1,087#3,657,394Four of a kindJune 11, 20252025 engine
1,088#3,657,893Four of a kindJune 11, 20252025 engine
1,089#3,667,727Four of a kindJune 11, 20252025 engine
1,090#3,672,651Four of a kindJune 11, 20252025 engine
1,091#3,682,023Four of a kindJune 11, 20252025 engine
1,092#3,688,648Four of a kindJune 11, 20252025 engine
1,093#3,688,986Four of a kindJune 11, 20252025 engine
1,094#3,694,954Four of a kindJune 11, 20252025 engine
1,095#3,705,869Four of a kindJune 12, 20252025 engine
1,096#3,707,703Four of a kindJune 12, 20252025 engine
1,097#3,708,021Four of a kindJune 12, 20252025 engine
1,098#3,709,259Four of a kindJune 12, 20252025 engine
1,099#3,715,852Four of a kindJune 12, 20252025 engine
1,100#3,717,057Four of a kindJune 12, 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.