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.
| Rank | Shuffle | Hand | Shuffled | Era |
|---|---|---|---|---|
| 1,801 | #6,689,447 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,802 | #6,697,007 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,803 | #6,701,078 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,804 | #6,701,622 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,805 | #6,705,109 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,806 | #6,708,096 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,807 | #6,709,383 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,808 | #6,711,512 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,809 | #6,714,870 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,810 | #6,718,530 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,811 | #6,718,861 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,812 | #6,726,988 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,813 | #6,730,209 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,814 | #6,737,951 | Four of a kind | July 17, 2025 | 2025 engine |
| 1,815 | #6,745,547 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,816 | #6,746,489 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,817 | #6,756,439 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,818 | #6,756,820 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,819 | #6,758,810 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,820 | #6,759,176 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,821 | #6,763,229 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,822 | #6,765,604 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,823 | #6,769,631 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,824 | #6,771,101 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,825 | #6,772,351 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,826 | #6,773,157 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,827 | #6,776,118 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,828 | #6,792,263 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,829 | #6,794,766 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,830 | #6,798,089 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,831 | #6,800,149 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,832 | #6,800,892 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,833 | #6,809,194 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,834 | #6,820,743 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,835 | #6,821,580 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,836 | #6,825,125 | Four of a kind | July 18, 2025 | 2025 engine |
| 1,837 | #6,827,576 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,838 | #6,831,135 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,839 | #6,837,735 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,840 | #6,837,798 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,841 | #6,843,236 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,842 | #6,843,439 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,843 | #6,851,208 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,844 | #6,852,944 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,845 | #6,854,955 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,846 | #6,860,750 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,847 | #6,861,493 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,848 | #6,869,104 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,849 | #6,874,036 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,850 | #6,875,483 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,851 | #6,877,908 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,852 | #6,878,361 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,853 | #6,879,898 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,854 | #6,895,363 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,855 | #6,898,642 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,856 | #6,899,372 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,857 | #6,900,690 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,858 | #6,902,466 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,859 | #6,905,736 | Four of a kind | July 19, 2025 | 2025 engine |
| 1,860 | #6,914,764 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,861 | #6,927,516 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,862 | #6,929,351 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,863 | #6,934,346 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,864 | #6,934,413 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,865 | #6,937,816 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,866 | #6,939,231 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,867 | #6,942,647 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,868 | #6,944,964 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,869 | #6,949,635 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,870 | #6,953,160 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,871 | #6,961,261 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,872 | #6,971,653 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,873 | #6,972,853 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,874 | #6,972,930 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,875 | #6,976,354 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,876 | #6,976,554 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,877 | #6,978,268 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,878 | #6,979,021 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,879 | #6,983,236 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,880 | #6,984,220 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,881 | #6,989,754 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,882 | #6,991,167 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,883 | #6,993,400 | Four of a kind | July 20, 2025 | 2025 engine |
| 1,884 | #7,003,685 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,885 | #7,005,078 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,886 | #7,006,301 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,887 | #7,014,914 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,888 | #7,015,384 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,889 | #7,023,790 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,890 | #7,031,100 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,891 | #7,034,231 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,892 | #7,037,456 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,893 | #7,039,699 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,894 | #7,039,873 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,895 | #7,040,305 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,896 | #7,045,242 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,897 | #7,054,821 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,898 | #7,055,260 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,899 | #7,057,563 | Four of a kind | July 21, 2025 | 2025 engine |
| 1,900 | #7,058,146 | Four of a kind | July 21, 2025 | 2025 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.