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. 3,669 shuffles have qualified so far.

RankShuffleHandShuffledEra
1,201#4,129,002Four of a kindJune 17, 20252025 engine
1,202#4,130,059Four of a kindJune 17, 20252025 engine
1,203#4,132,177Four of a kindJune 17, 20252025 engine
1,204#4,144,013Four of a kindJune 17, 20252025 engine
1,205#4,152,199Four of a kindJune 17, 20252025 engine
1,206#4,157,978Four of a kindJune 17, 20252025 engine
1,207#4,176,652Four of a kindJune 17, 20252025 engine
1,208#4,183,775Four of a kindJune 17, 20252025 engine
1,209#4,192,509Four of a kindJune 17, 20252025 engine
1,210#4,197,333Four of a kindJune 17, 20252025 engine
1,211#4,197,996Four of a kindJune 17, 20252025 engine
1,212#4,199,185Four of a kindJune 17, 20252025 engine
1,213#4,205,120Four of a kindJune 18, 20252025 engine
1,214#4,210,475Four of a kindJune 18, 20252025 engine
1,215#4,217,409Four of a kindJune 18, 20252025 engine
1,216#4,218,666Four of a kindJune 18, 20252025 engine
1,217#4,222,719Four of a kindJune 18, 20252025 engine
1,218#4,223,537Four of a kindJune 18, 20252025 engine
1,219#4,225,935Four of a kindJune 18, 20252025 engine
1,220#4,229,789Four of a kindJune 18, 20252025 engine
1,221#4,246,392Four of a kindJune 18, 20252025 engine
1,222#4,250,766Four of a kindJune 18, 20252025 engine
1,223#4,250,982Four of a kindJune 18, 20252025 engine
1,224#4,257,405Four of a kindJune 18, 20252025 engine
1,225#4,258,871Four of a kindJune 18, 20252025 engine
1,226#4,267,644Four of a kindJune 18, 20252025 engine
1,227#4,269,804Four of a kindJune 18, 20252025 engine
1,228#4,271,274Four of a kindJune 18, 20252025 engine
1,229#4,271,716Four of a kindJune 18, 20252025 engine
1,230#4,272,125Four of a kindJune 18, 20252025 engine
1,231#4,273,676Four of a kindJune 18, 20252025 engine
1,232#4,275,424Four of a kindJune 18, 20252025 engine
1,233#4,276,120Four of a kindJune 18, 20252025 engine
1,234#4,277,023Four of a kindJune 18, 20252025 engine
1,235#4,283,427Four of a kindJune 18, 20252025 engine
1,236#4,289,523Four of a kindJune 19, 20252025 engine
1,237#4,290,907Four of a kindJune 19, 20252025 engine
1,238#4,295,659Four of a kindJune 19, 20252025 engine
1,239#4,296,022Four of a kindJune 19, 20252025 engine
1,240#4,298,166Four of a kindJune 19, 20252025 engine
1,241#4,305,303Four of a kindJune 19, 20252025 engine
1,242#4,310,740Four of a kindJune 19, 20252025 engine
1,243#4,319,125Four of a kindJune 19, 20252025 engine
1,244#4,328,451Four of a kindJune 19, 20252025 engine
1,245#4,328,862Four of a kindJune 19, 20252025 engine
1,246#4,332,912Four of a kindJune 19, 20252025 engine
1,247#4,347,343Four of a kindJune 19, 20252025 engine
1,248#4,348,960Four of a kindJune 19, 20252025 engine
1,249#4,361,045Four of a kindJune 19, 20252025 engine
1,250#4,362,145Four of a kindJune 19, 20252025 engine
1,251#4,364,526Four of a kindJune 19, 20252025 engine
1,252#4,364,699Four of a kindJune 19, 20252025 engine
1,253#4,367,866Four of a kindJune 19, 20252025 engine
1,254#4,374,081Four of a kindJune 20, 20252025 engine
1,255#4,376,576Four of a kindJune 20, 20252025 engine
1,256#4,380,440Four of a kindJune 20, 20252025 engine
1,257#4,380,514Four of a kindJune 20, 20252025 engine
1,258#4,381,594Four of a kindJune 20, 20252025 engine
1,259#4,389,987Four of a kindJune 20, 20252025 engine
1,260#4,394,744Four of a kindJune 20, 20252025 engine
1,261#4,395,216Four of a kindJune 20, 20252025 engine
1,262#4,396,644Four of a kindJune 20, 20252025 engine
1,263#4,402,005Four of a kindJune 20, 20252025 engine
1,264#4,404,612Four of a kindJune 20, 20252025 engine
1,265#4,408,247Four of a kindJune 20, 20252025 engine
1,266#4,414,638Four of a kindJune 20, 20252025 engine
1,267#4,415,054Four of a kindJune 20, 20252025 engine
1,268#4,422,636Four of a kindJune 20, 20252025 engine
1,269#4,433,030Four of a kindJune 20, 20252025 engine
1,270#4,444,506Four of a kindJune 20, 20252025 engine
1,271#4,447,789Four of a kindJune 20, 20252025 engine
1,272#4,453,323Four of a kindJune 20, 20252025 engine
1,273#4,455,998Four of a kindJune 20, 20252025 engine
1,274#4,462,538Four of a kindJune 21, 20252025 engine
1,275#4,470,283Four of a kindJune 21, 20252025 engine
1,276#4,474,981Four of a kindJune 21, 20252025 engine
1,277#4,477,809Four of a kindJune 21, 20252025 engine
1,278#4,478,337Four of a kindJune 21, 20252025 engine
1,279#4,492,771Four of a kindJune 21, 20252025 engine
1,280#4,495,950Four of a kindJune 21, 20252025 engine
1,281#4,498,381Four of a kindJune 21, 20252025 engine
1,282#4,503,655Four of a kindJune 21, 20252025 engine
1,283#4,505,688Four of a kindJune 21, 20252025 engine
1,284#4,506,068Four of a kindJune 21, 20252025 engine
1,285#4,507,131Four of a kindJune 21, 20252025 engine
1,286#4,511,396Four of a kindJune 21, 20252025 engine
1,287#4,511,653Four of a kindJune 21, 20252025 engine
1,288#4,512,536Four of a kindJune 21, 20252025 engine
1,289#4,512,612Four of a kindJune 21, 20252025 engine
1,290#4,513,713Four of a kindJune 21, 20252025 engine
1,291#4,516,433Four of a kindJune 21, 20252025 engine
1,292#4,521,094Four of a kindJune 21, 20252025 engine
1,293#4,529,081Four of a kindJune 21, 20252025 engine
1,294#4,533,165Four of a kindJune 21, 20252025 engine
1,295#4,536,922Four of a kindJune 21, 20252025 engine
1,296#4,539,133Four of a kindJune 21, 20252025 engine
1,297#4,543,518Four of a kindJune 22, 20252025 engine
1,298#4,546,193Four of a kindJune 22, 20252025 engine
1,299#4,546,507Four of a kindJune 22, 20252025 engine
1,300#4,548,356Four of a kindJune 22, 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.