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. 3,664 shuffles have qualified so far.

RankShuffleHandShuffledEra
901#2,978,527Four of a kindJune 3, 20252025 engine
902#2,983,686Four of a kindJune 3, 20252025 engine
903#2,984,153Four of a kindJune 3, 20252025 engine
904#2,988,886Four of a kindJune 3, 20252025 engine
905#2,999,309Four of a kindJune 3, 20252025 engine
906#3,006,197Four of a kindJune 3, 20252025 engine
907#3,020,016Four of a kindJune 3, 20252025 engine
908#3,020,170Four of a kindJune 3, 20252025 engine
909#3,026,164Four of a kindJune 4, 20252025 engine
910#3,027,755Four of a kindJune 4, 20252025 engine
911#3,028,400Four of a kindJune 4, 20252025 engine
912#3,033,170Four of a kindJune 4, 20252025 engine
913#3,034,904Four of a kindJune 4, 20252025 engine
914#3,037,025Four of a kindJune 4, 20252025 engine
915#3,037,026Four of a kindJune 4, 20252025 engine
916#3,038,859Four of a kindJune 4, 20252025 engine
917#3,040,558Four of a kindJune 4, 20252025 engine
918#3,041,572Four of a kindJune 4, 20252025 engine
919#3,042,352Four of a kindJune 4, 20252025 engine
920#3,045,396Four of a kindJune 4, 20252025 engine
921#3,046,512Four of a kindJune 4, 20252025 engine
922#3,053,367Four of a kindJune 4, 20252025 engine
923#3,055,273Four of a kindJune 4, 20252025 engine
924#3,059,578Four of a kindJune 4, 20252025 engine
925#3,060,111Four of a kindJune 4, 20252025 engine
926#3,060,712Four of a kindJune 4, 20252025 engine
927#3,063,810Four of a kindJune 4, 20252025 engine
928#3,065,714Four of a kindJune 4, 20252025 engine
929#3,068,169Four of a kindJune 4, 20252025 engine
930#3,068,219Four of a kindJune 4, 20252025 engine
931#3,069,670Four of a kindJune 4, 20252025 engine
932#3,069,726Four of a kindJune 4, 20252025 engine
933#3,078,383Four of a kindJune 4, 20252025 engine
934#3,078,646Four of a kindJune 4, 20252025 engine
935#3,078,647Four of a kindJune 4, 20252025 engine
936#3,081,013Four of a kindJune 4, 20252025 engine
937#3,084,127Four of a kindJune 4, 20252025 engine
938#3,085,183Four of a kindJune 4, 20252025 engine
939#3,086,990Four of a kindJune 4, 20252025 engine
940#3,089,055Four of a kindJune 4, 20252025 engine
941#3,089,331Four of a kindJune 4, 20252025 engine
942#3,106,956Four of a kindJune 4, 20252025 engine
943#3,113,337Four of a kindJune 5, 20252025 engine
944#3,124,173Four of a kindJune 5, 20252025 engine
945#3,129,003Four of a kindJune 5, 20252025 engine
946#3,130,692Four of a kindJune 5, 20252025 engine
947#3,131,701Four of a kindJune 5, 20252025 engine
948#3,131,881Four of a kindJune 5, 20252025 engine
949#3,141,026Four of a kindJune 5, 20252025 engine
950#3,143,545Four of a kindJune 5, 20252025 engine
951#3,148,328Four of a kindJune 5, 20252025 engine
952#3,163,563Four of a kindJune 5, 20252025 engine
953#3,164,741Four of a kindJune 5, 20252025 engine
954#3,169,479Four of a kindJune 5, 20252025 engine
955#3,176,205Four of a kindJune 5, 20252025 engine
956#3,180,010Four of a kindJune 5, 20252025 engine
957#3,185,882Four of a kindJune 5, 20252025 engine
958#3,187,740Four of a kindJune 5, 20252025 engine
959#3,189,495Four of a kindJune 5, 20252025 engine
960#3,198,033Four of a kindJune 6, 20252025 engine
961#3,200,193Four of a kindJune 6, 20252025 engine
962#3,205,491Four of a kindJune 6, 20252025 engine
963#3,209,064Four of a kindJune 6, 20252025 engine
964#3,210,027Four of a kindJune 6, 20252025 engine
965#3,215,444Four of a kindJune 6, 20252025 engine
966#3,216,781Four of a kindJune 6, 20252025 engine
967#3,217,251Four of a kindJune 6, 20252025 engine
968#3,222,915Four of a kindJune 6, 20252025 engine
969#3,226,341Four of a kindJune 6, 20252025 engine
970#3,235,204Four of a kindJune 6, 20252025 engine
971#3,243,591Four of a kindJune 6, 20252025 engine
972#3,245,788Four of a kindJune 6, 20252025 engine
973#3,258,951Four of a kindJune 6, 20252025 engine
974#3,261,583Four of a kindJune 6, 20252025 engine
975#3,265,075Four of a kindJune 6, 20252025 engine
976#3,266,117Four of a kindJune 6, 20252025 engine
977#3,267,135Four of a kindJune 6, 20252025 engine
978#3,267,380Four of a kindJune 6, 20252025 engine
979#3,268,881Four of a kindJune 6, 20252025 engine
980#3,272,505Four of a kindJune 6, 20252025 engine
981#3,276,056Four of a kindJune 6, 20252025 engine
982#3,280,858Four of a kindJune 7, 20252025 engine
983#3,281,460Four of a kindJune 7, 20252025 engine
984#3,289,582Four of a kindJune 7, 20252025 engine
985#3,295,133Four of a kindJune 7, 20252025 engine
986#3,297,160Four of a kindJune 7, 20252025 engine
987#3,298,216Four of a kindJune 7, 20252025 engine
988#3,305,139Four of a kindJune 7, 20252025 engine
989#3,311,190Four of a kindJune 7, 20252025 engine
990#3,315,965Four of a kindJune 7, 20252025 engine
991#3,318,594Four of a kindJune 7, 20252025 engine
992#3,319,382Four of a kindJune 7, 20252025 engine
993#3,327,907Four of a kindJune 7, 20252025 engine
994#3,331,571Four of a kindJune 7, 20252025 engine
995#3,335,627Four of a kindJune 7, 20252025 engine
996#3,336,157Four of a kindJune 7, 20252025 engine
997#3,338,627Four of a kindJune 7, 20252025 engine
998#3,339,500Four of a kindJune 7, 20252025 engine
999#3,342,201Four of a kindJune 7, 20252025 engine
1,000#3,343,845Four of a kindJune 7, 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.