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. 3,667 shuffles have qualified so far.

RankShuffleHandShuffledEra
1,101#3,717,202Four of a kindJune 12, 20252025 engine
1,102#3,731,124Four of a kindJune 12, 20252025 engine
1,103#3,731,492Four of a kindJune 12, 20252025 engine
1,104#3,735,615Four of a kindJune 12, 20252025 engine
1,105#3,736,012Four of a kindJune 12, 20252025 engine
1,106#3,737,960Four of a kindJune 12, 20252025 engine
1,107#3,742,979Four of a kindJune 12, 20252025 engine
1,108#3,752,863Four of a kindJune 12, 20252025 engine
1,109#3,760,447Four of a kindJune 12, 20252025 engine
1,110#3,763,771Four of a kindJune 12, 20252025 engine
1,111#3,768,609Four of a kindJune 12, 20252025 engine
1,112#3,771,119Four of a kindJune 12, 20252025 engine
1,113#3,772,783Four of a kindJune 12, 20252025 engine
1,114#3,775,418Four of a kindJune 12, 20252025 engine
1,115#3,776,226Four of a kindJune 12, 20252025 engine
1,116#3,778,591Four of a kindJune 12, 20252025 engine
1,117#3,803,040Four of a kindJune 13, 20252025 engine
1,118#3,804,245Four of a kindJune 13, 20252025 engine
1,119#3,816,438Four of a kindJune 13, 20252025 engine
1,120#3,827,771Four of a kindJune 13, 20252025 engine
1,121#3,828,646Four of a kindJune 13, 20252025 engine
1,122#3,831,124Four of a kindJune 13, 20252025 engine
1,123#3,834,775Four of a kindJune 13, 20252025 engine
1,124#3,841,400Four of a kindJune 13, 20252025 engine
1,125#3,848,743Four of a kindJune 13, 20252025 engine
1,126#3,864,728Four of a kindJune 13, 20252025 engine
1,127#3,867,736Four of a kindJune 14, 20252025 engine
1,128#3,868,290Four of a kindJune 14, 20252025 engine
1,129#3,876,738Four of a kindJune 14, 20252025 engine
1,130#3,879,647Four of a kindJune 14, 20252025 engine
1,131#3,881,835Four of a kindJune 14, 20252025 engine
1,132#3,884,235Four of a kindJune 14, 20252025 engine
1,133#3,897,855Four of a kindJune 14, 20252025 engine
1,134#3,898,567Four of a kindJune 14, 20252025 engine
1,135#3,901,010Four of a kindJune 14, 20252025 engine
1,136#3,901,591Four of a kindJune 14, 20252025 engine
1,137#3,905,197Four of a kindJune 14, 20252025 engine
1,138#3,908,134Four of a kindJune 14, 20252025 engine
1,139#3,908,733Four of a kindJune 14, 20252025 engine
1,140#3,909,854Four of a kindJune 14, 20252025 engine
1,141#3,914,249Four of a kindJune 14, 20252025 engine
1,142#3,918,788Four of a kindJune 14, 20252025 engine
1,143#3,919,999Four of a kindJune 14, 20252025 engine
1,144#3,921,366Four of a kindJune 14, 20252025 engine
1,145#3,924,780Four of a kindJune 14, 20252025 engine
1,146#3,932,745Four of a kindJune 14, 20252025 engine
1,147#3,938,197Four of a kindJune 14, 20252025 engine
1,148#3,938,960Four of a kindJune 14, 20252025 engine
1,149#3,939,637Four of a kindJune 14, 20252025 engine
1,150#3,939,686Four of a kindJune 14, 20252025 engine
1,151#3,943,253Four of a kindJune 14, 20252025 engine
1,152#3,944,352Four of a kindJune 14, 20252025 engine
1,153#3,945,043Four of a kindJune 14, 20252025 engine
1,154#3,946,536Four of a kindJune 14, 20252025 engine
1,155#3,947,061Four of a kindJune 14, 20252025 engine
1,156#3,949,374Four of a kindJune 14, 20252025 engine
1,157#3,949,462Four of a kindJune 14, 20252025 engine
1,158#3,951,085Four of a kindJune 14, 20252025 engine
1,159#3,951,383Four of a kindJune 14, 20252025 engine
1,160#3,954,889Four of a kindJune 15, 20252025 engine
1,161#3,960,321Four of a kindJune 15, 20252025 engine
1,162#3,977,896Four of a kindJune 15, 20252025 engine
1,163#3,979,719Four of a kindJune 15, 20252025 engine
1,164#3,983,173Four of a kindJune 15, 20252025 engine
1,165#3,985,270Four of a kindJune 15, 20252025 engine
1,166#3,994,104Four of a kindJune 15, 20252025 engine
1,167#3,998,793Four of a kindJune 15, 20252025 engine
1,168#3,999,110Four of a kindJune 15, 20252025 engine
1,169#4,006,769Four of a kindJune 15, 20252025 engine
1,170#4,012,194Four of a kindJune 15, 20252025 engine
1,171#4,018,079Four of a kindJune 15, 20252025 engine
1,172#4,019,182Four of a kindJune 15, 20252025 engine
1,173#4,024,281Four of a kindJune 15, 20252025 engine
1,174#4,024,632Four of a kindJune 15, 20252025 engine
1,175#4,027,963Four of a kindJune 15, 20252025 engine
1,176#4,034,554Four of a kindJune 15, 20252025 engine
1,177#4,038,644Four of a kindJune 16, 20252025 engine
1,178#4,043,451Four of a kindJune 16, 20252025 engine
1,179#4,044,001Four of a kindJune 16, 20252025 engine
1,180#4,049,982Four of a kindJune 16, 20252025 engine
1,181#4,050,475Four of a kindJune 16, 20252025 engine
1,182#4,050,544Four of a kindJune 16, 20252025 engine
1,183#4,055,335Four of a kindJune 16, 20252025 engine
1,184#4,071,002Four of a kindJune 16, 20252025 engine
1,185#4,072,030Four of a kindJune 16, 20252025 engine
1,186#4,075,226Four of a kindJune 16, 20252025 engine
1,187#4,090,599Four of a kindJune 16, 20252025 engine
1,188#4,091,775Four of a kindJune 16, 20252025 engine
1,189#4,092,773Four of a kindJune 16, 20252025 engine
1,190#4,094,191Four of a kindJune 16, 20252025 engine
1,191#4,097,508Four of a kindJune 16, 20252025 engine
1,192#4,102,859Four of a kindJune 16, 20252025 engine
1,193#4,106,143Four of a kindJune 16, 20252025 engine
1,194#4,110,704Four of a kindJune 16, 20252025 engine
1,195#4,111,854Four of a kindJune 16, 20252025 engine
1,196#4,112,395Four of a kindJune 16, 20252025 engine
1,197#4,117,203Four of a kindJune 16, 20252025 engine
1,198#4,125,511Four of a kindJune 17, 20252025 engine
1,199#4,126,472Four of a kindJune 17, 20252025 engine
1,200#4,128,399Four of a kindJune 17, 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.