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. 3,671 shuffles have qualified so far.

RankShuffleHandShuffledEra
1,301#4,548,357Four of a kindJune 22, 20252025 engine
1,302#4,552,728Four of a kindJune 22, 20252025 engine
1,303#4,564,305Four of a kindJune 22, 20252025 engine
1,304#4,565,400Four of a kindJune 22, 20252025 engine
1,305#4,566,798Four of a kindJune 22, 20252025 engine
1,306#4,570,865Four of a kindJune 22, 20252025 engine
1,307#4,573,245Four of a kindJune 22, 20252025 engine
1,308#4,592,197Four of a kindJune 22, 20252025 engine
1,309#4,592,433Four of a kindJune 22, 20252025 engine
1,310#4,595,695Four of a kindJune 22, 20252025 engine
1,311#4,595,947Four of a kindJune 22, 20252025 engine
1,312#4,596,552Four of a kindJune 22, 20252025 engine
1,313#4,596,715Four of a kindJune 22, 20252025 engine
1,314#4,600,213Four of a kindJune 22, 20252025 engine
1,315#4,602,122Four of a kindJune 22, 20252025 engine
1,316#4,604,615Four of a kindJune 22, 20252025 engine
1,317#4,616,498Four of a kindJune 22, 20252025 engine
1,318#4,620,347Four of a kindJune 22, 20252025 engine
1,319#4,620,691Four of a kindJune 22, 20252025 engine
1,320#4,623,721Four of a kindJune 22, 20252025 engine
1,321#4,624,833Four of a kindJune 22, 20252025 engine
1,322#4,630,052Four of a kindJune 23, 20252025 engine
1,323#4,637,761Four of a kindJune 23, 20252025 engine
1,324#4,644,188Four of a kindJune 23, 20252025 engine
1,325#4,648,283Four of a kindJune 23, 20252025 engine
1,326#4,651,494Four of a kindJune 23, 20252025 engine
1,327#4,660,106Four of a kindJune 23, 20252025 engine
1,328#4,661,097Four of a kindJune 23, 20252025 engine
1,329#4,666,662Four of a kindJune 23, 20252025 engine
1,330#4,672,707Four of a kindJune 23, 20252025 engine
1,331#4,674,020Four of a kindJune 23, 20252025 engine
1,332#4,679,203Four of a kindJune 23, 20252025 engine
1,333#4,680,351Four of a kindJune 23, 20252025 engine
1,334#4,680,997Four of a kindJune 23, 20252025 engine
1,335#4,683,864Four of a kindJune 23, 20252025 engine
1,336#4,698,569Four of a kindJune 23, 20252025 engine
1,337#4,699,533Four of a kindJune 23, 20252025 engine
1,338#4,706,995Four of a kindJune 23, 20252025 engine
1,339#4,711,180Four of a kindJune 23, 20252025 engine
1,340#4,714,314Four of a kindJune 24, 20252025 engine
1,341#4,715,499Four of a kindJune 24, 20252025 engine
1,342#4,717,103Four of a kindJune 24, 20252025 engine
1,343#4,724,496Four of a kindJune 24, 20252025 engine
1,344#4,727,376Four of a kindJune 24, 20252025 engine
1,345#4,727,838Four of a kindJune 24, 20252025 engine
1,346#4,729,325Four of a kindJune 24, 20252025 engine
1,347#4,732,420Four of a kindJune 24, 20252025 engine
1,348#4,737,397Four of a kindJune 24, 20252025 engine
1,349#4,744,957Four of a kindJune 24, 20252025 engine
1,350#4,746,496Four of a kindJune 24, 20252025 engine
1,351#4,749,514Four of a kindJune 24, 20252025 engine
1,352#4,752,749Four of a kindJune 24, 20252025 engine
1,353#4,755,762Four of a kindJune 24, 20252025 engine
1,354#4,763,914Four of a kindJune 24, 20252025 engine
1,355#4,766,457Four of a kindJune 24, 20252025 engine
1,356#4,778,271Four of a kindJune 24, 20252025 engine
1,357#4,780,745Four of a kindJune 24, 20252025 engine
1,358#4,784,263Four of a kindJune 24, 20252025 engine
1,359#4,784,445Four of a kindJune 24, 20252025 engine
1,360#4,793,629Four of a kindJune 24, 20252025 engine
1,361#4,795,718Four of a kindJune 24, 20252025 engine
1,362#4,798,038Four of a kindJune 25, 20252025 engine
1,363#4,798,750Four of a kindJune 25, 20252025 engine
1,364#4,811,196Four of a kindJune 25, 20252025 engine
1,365#4,815,771Four of a kindJune 25, 20252025 engine
1,366#4,825,569Four of a kindJune 25, 20252025 engine
1,367#4,827,180Four of a kindJune 25, 20252025 engine
1,368#4,828,122Four of a kindJune 25, 20252025 engine
1,369#4,831,584Four of a kindJune 25, 20252025 engine
1,370#4,832,522Four of a kindJune 25, 20252025 engine
1,371#4,835,134Four of a kindJune 25, 20252025 engine
1,372#4,837,059Four of a kindJune 25, 20252025 engine
1,373#4,839,710Four of a kindJune 25, 20252025 engine
1,374#4,843,526Four of a kindJune 25, 20252025 engine
1,375#4,849,872Four of a kindJune 25, 20252025 engine
1,376#4,854,702Four of a kindJune 25, 20252025 engine
1,377#4,858,429Four of a kindJune 25, 20252025 engine
1,378#4,865,391Four of a kindJune 25, 20252025 engine
1,379#4,879,210Four of a kindJune 25, 20252025 engine
1,380#4,882,603Four of a kindJune 26, 20252025 engine
1,381#4,886,975Four of a kindJune 26, 20252025 engine
1,382#4,887,902Four of a kindJune 26, 20252025 engine
1,383#4,895,184Four of a kindJune 26, 20252025 engine
1,384#4,911,680Four of a kindJune 26, 20252025 engine
1,385#4,912,423Four of a kindJune 26, 20252025 engine
1,386#4,918,260Four of a kindJune 26, 20252025 engine
1,387#4,924,307Four of a kindJune 26, 20252025 engine
1,388#4,935,150Four of a kindJune 26, 20252025 engine
1,389#4,939,313Four of a kindJune 26, 20252025 engine
1,390#4,951,227Four of a kindJune 26, 20252025 engine
1,391#4,952,390Four of a kindJune 26, 20252025 engine
1,392#4,952,666Four of a kindJune 26, 20252025 engine
1,393#4,962,282Four of a kindJune 26, 20252025 engine
1,394#4,967,514Four of a kindJune 27, 20252025 engine
1,395#4,969,166Four of a kindJune 27, 20252025 engine
1,396#4,969,334Four of a kindJune 27, 20252025 engine
1,397#4,978,544Four of a kindJune 27, 20252025 engine
1,398#4,981,139Four of a kindJune 27, 20252025 engine
1,399#4,981,361Four of a kindJune 27, 20252025 engine
1,400#4,993,386Four of a kindJune 27, 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.