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. 3,676 shuffles have qualified so far.

RankShuffleHandShuffledEra
1,901#7,058,346Four of a kindJuly 21, 20252025 engine
1,902#7,061,411Four of a kindJuly 21, 20252025 engine
1,903#7,061,637Four of a kindJuly 21, 20252025 engine
1,904#7,066,416Four of a kindJuly 21, 20252025 engine
1,905#7,072,516Four of a kindJuly 21, 20252025 engine
1,906#7,088,516Four of a kindJuly 22, 20252025 engine
1,907#7,088,716Four of a kindJuly 22, 20252025 engine
1,908#7,090,722Four of a kindJuly 22, 20252025 engine
1,909#7,104,051Four of a kindJuly 22, 20252025 engine
1,910#7,127,299Four of a kindJuly 22, 20252025 engine
1,911#7,129,046Four of a kindJuly 22, 20252025 engine
1,912#7,149,153Four of a kindJuly 22, 20252025 engine
1,913#7,160,249Four of a kindJuly 22, 20252025 engine
1,914#7,165,338Four of a kindJuly 22, 20252025 engine
1,915#7,167,350Four of a kindJuly 23, 20252025 engine
1,916#7,167,381Four of a kindJuly 23, 20252025 engine
1,917#7,171,680Four of a kindJuly 23, 20252025 engine
1,918#7,175,115Four of a kindJuly 23, 20252025 engine
1,919#7,184,107Four of a kindJuly 23, 20252025 engine
1,920#7,186,086Four of a kindJuly 23, 20252025 engine
1,921#7,187,184Four of a kindJuly 23, 20252025 engine
1,922#7,187,452Four of a kindJuly 23, 20252025 engine
1,923#7,192,930Four of a kindJuly 23, 20252025 engine
1,924#7,196,568Four of a kindJuly 23, 20252025 engine
1,925#7,198,187Four of a kindJuly 23, 20252025 engine
1,926#7,212,267Four of a kindJuly 23, 20252025 engine
1,927#7,221,577Four of a kindJuly 23, 20252025 engine
1,928#7,221,733Four of a kindJuly 23, 20252025 engine
1,929#7,223,045Four of a kindJuly 23, 20252025 engine
1,930#7,233,834Four of a kindJuly 23, 20252025 engine
1,931#7,235,227Four of a kindJuly 23, 20252025 engine
1,932#7,236,193Four of a kindJuly 23, 20252025 engine
1,933#7,242,041Four of a kindJuly 23, 20252025 engine
1,934#7,243,530Four of a kindJuly 23, 20252025 engine
1,935#7,245,020Four of a kindJuly 23, 20252025 engine
1,936#7,245,687Four of a kindJuly 23, 20252025 engine
1,937#7,248,924Four of a kindJuly 23, 20252025 engine
1,938#7,248,925Four of a kindJuly 23, 20252025 engine
1,939#7,259,554Four of a kindJuly 24, 20252025 engine
1,940#7,259,885Four of a kindJuly 24, 20252025 engine
1,941#7,268,350Four of a kindJuly 24, 20252025 engine
1,942#7,269,318Four of a kindJuly 24, 20252025 engine
1,943#7,270,580Four of a kindJuly 24, 20252025 engine
1,944#7,272,598Four of a kindJuly 24, 20252025 engine
1,945#7,293,721Four of a kindJuly 24, 20252025 engine
1,946#7,294,638Four of a kindJuly 24, 20252025 engine
1,947#7,294,940Four of a kindJuly 24, 20252025 engine
1,948#7,300,866Four of a kindJuly 24, 20252025 engine
1,949#7,308,130Four of a kindJuly 24, 20252025 engine
1,950#7,314,688Four of a kindJuly 24, 20252025 engine
1,951#7,327,167Four of a kindJuly 24, 20252025 engine
1,952#7,327,305Four of a kindJuly 24, 20252025 engine
1,953#7,329,288Four of a kindJuly 24, 20252025 engine
1,954#7,341,140Four of a kindJuly 25, 20252025 engine
1,955#7,343,482Four of a kindJuly 25, 20252025 engine
1,956#7,344,116Four of a kindJuly 25, 20252025 engine
1,957#7,344,623Four of a kindJuly 25, 20252025 engine
1,958#7,352,098Four of a kindJuly 25, 20252025 engine
1,959#7,352,476Four of a kindJuly 25, 20252025 engine
1,960#7,357,538Four of a kindJuly 25, 20252025 engine
1,961#7,359,194Four of a kindJuly 25, 20252025 engine
1,962#7,361,413Four of a kindJuly 25, 20252025 engine
1,963#7,368,468Four of a kindJuly 25, 20252025 engine
1,964#7,370,704Four of a kindJuly 25, 20252025 engine
1,965#7,371,667Four of a kindJuly 25, 20252025 engine
1,966#7,384,220Four of a kindJuly 25, 20252025 engine
1,967#7,391,017Four of a kindJuly 25, 20252025 engine
1,968#7,400,737Four of a kindJuly 25, 20252025 engine
1,969#7,401,566Four of a kindJuly 25, 20252025 engine
1,970#7,408,937Four of a kindJuly 25, 20252025 engine
1,971#7,412,545Four of a kindJuly 25, 20252025 engine
1,972#7,414,252Four of a kindJuly 25, 20252025 engine
1,973#7,421,607Four of a kindJuly 26, 20252025 engine
1,974#7,426,604Four of a kindJuly 26, 20252025 engine
1,975#7,429,822Four of a kindJuly 26, 20252025 engine
1,976#7,431,733Four of a kindJuly 26, 20252025 engine
1,977#7,432,448Four of a kindJuly 26, 20252025 engine
1,978#7,432,551Four of a kindJuly 26, 20252025 engine
1,979#7,433,097Four of a kindJuly 26, 20252025 engine
1,980#7,435,316Four of a kindJuly 26, 20252025 engine
1,981#7,436,143Four of a kindJuly 26, 20252025 engine
1,982#7,439,859Four of a kindJuly 26, 20252025 engine
1,983#7,446,624Four of a kindJuly 26, 20252025 engine
1,984#7,446,958Four of a kindJuly 26, 20252025 engine
1,985#7,456,564Four of a kindJuly 26, 20252025 engine
1,986#7,458,597Four of a kindJuly 26, 20252025 engine
1,987#7,459,011Four of a kindJuly 26, 20252025 engine
1,988#7,463,402Four of a kindJuly 26, 20252025 engine
1,989#7,463,932Four of a kindJuly 26, 20252025 engine
1,990#7,464,101Four of a kindJuly 26, 20252025 engine
1,991#7,464,351Four of a kindJuly 26, 20252025 engine
1,992#7,464,968Four of a kindJuly 26, 20252025 engine
1,993#7,472,141Four of a kindJuly 26, 20252025 engine
1,994#7,483,346Four of a kindJuly 26, 20252025 engine
1,995#7,487,284Four of a kindJuly 26, 20252025 engine
1,996#7,493,620Four of a kindJuly 26, 20252025 engine
1,997#7,495,309Four of a kindJuly 26, 20252025 engine
1,998#7,495,697Four of a kindJuly 26, 20252025 engine
1,999#7,498,078Four of a kindJuly 26, 20252025 engine
2,000#7,500,043Four of a kindJuly 26, 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.