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. 3,688 shuffles have qualified so far.

RankShuffleHandShuffledEra
2,901#11,111,080Four of a kindSeptember 7, 20252025 engine
2,902#11,111,218Four of a kindSeptember 7, 20252025 engine
2,903#11,113,143Four of a kindSeptember 7, 20252025 engine
2,904#11,113,516Four of a kindSeptember 7, 20252025 engine
2,905#11,115,620Four of a kindSeptember 7, 20252025 engine
2,906#11,119,554Four of a kindSeptember 7, 20252025 engine
2,907#11,123,714Four of a kindSeptember 7, 20252025 engine
2,908#11,124,776Four of a kindSeptember 7, 20252025 engine
2,909#11,125,940Four of a kindSeptember 7, 20252025 engine
2,910#11,131,354Four of a kindSeptember 7, 20252025 engine
2,911#11,131,976Four of a kindSeptember 7, 20252025 engine
2,912#11,133,531Four of a kindSeptember 7, 20252025 engine
2,913#11,135,899Four of a kindSeptember 7, 20252025 engine
2,914#11,143,336Four of a kindSeptember 8, 20252025 engine
2,915#11,150,043Four of a kindSeptember 8, 20252025 engine
2,916#11,155,398Four of a kindSeptember 8, 20252025 engine
2,917#11,160,875Four of a kindSeptember 8, 20252025 engine
2,918#11,174,477Four of a kindSeptember 8, 20252025 engine
2,919#11,178,047Four of a kindSeptember 8, 20252025 engine
2,920#11,183,991Four of a kindSeptember 8, 20252025 engine
2,921#11,194,096Four of a kindSeptember 8, 20252025 engine
2,922#11,194,829Four of a kindSeptember 8, 20252025 engine
2,923#11,195,390Four of a kindSeptember 8, 20252025 engine
2,924#11,198,411Four of a kindSeptember 8, 20252025 engine
2,925#11,200,983Four of a kindSeptember 8, 20252025 engine
2,926#11,210,549Four of a kindSeptember 8, 20252025 engine
2,927#11,214,401Four of a kindSeptember 8, 20252025 engine
2,928#11,220,666Four of a kindSeptember 8, 20252025 engine
2,929#11,241,912Four of a kindSeptember 14, 20252025 engine
2,930#11,244,057Four of a kindSeptember 14, 20252025 engine
2,931#11,247,037Four of a kindSeptember 14, 20252025 engine
2,932#11,248,870Four of a kindSeptember 14, 20252025 engine
2,933#11,255,021Four of a kindSeptember 14, 20252025 engine
2,934#11,259,051Four of a kindSeptember 14, 20252025 engine
2,935#11,259,201Four of a kindSeptember 14, 20252025 engine
2,936#11,266,196Four of a kindSeptember 14, 20252025 engine
2,937#11,266,197Four of a kindSeptember 14, 20252025 engine
2,938#11,279,220Four of a kindSeptember 14, 20252025 engine
2,939#11,283,107Four of a kindSeptember 14, 20252025 engine
2,940#11,283,849Four of a kindSeptember 14, 20252025 engine
2,941#11,286,552Four of a kindSeptember 14, 20252025 engine
2,942#11,286,940Four of a kindSeptember 14, 20252025 engine
2,943#11,290,297Four of a kindSeptember 14, 20252025 engine
2,944#11,291,659Four of a kindSeptember 14, 20252025 engine
2,945#11,297,251Four of a kindSeptember 14, 20252025 engine
2,946#11,297,796Four of a kindSeptember 14, 20252025 engine
2,947#11,304,343Four of a kindSeptember 14, 20252025 engine
2,948#11,315,419Four of a kindSeptember 15, 20252025 engine
2,949#11,317,492Four of a kindSeptember 15, 20252025 engine
2,950#11,321,538Four of a kindSeptember 15, 20252025 engine
2,951#11,322,591Four of a kindSeptember 15, 20252025 engine
2,952#11,322,896Four of a kindSeptember 15, 20252025 engine
2,953#11,325,216Four of a kindSeptember 15, 20252025 engine
2,954#11,328,155Four of a kindSeptember 15, 20252025 engine
2,955#11,328,838Four of a kindSeptember 15, 20252025 engine
2,956#11,330,732Four of a kindSeptember 15, 20252025 engine
2,957#11,336,308Four of a kindSeptember 15, 20252025 engine
2,958#11,336,368Four of a kindSeptember 15, 20252025 engine
2,959#11,343,401Four of a kindSeptember 15, 20252025 engine
2,960#11,343,992Four of a kindSeptember 15, 20252025 engine
2,961#11,347,120Four of a kindSeptember 15, 20252025 engine
2,962#11,353,805Four of a kindSeptember 15, 20252025 engine
2,963#11,359,170Four of a kindSeptember 15, 20252025 engine
2,964#11,364,032Four of a kindSeptember 15, 20252025 engine
2,965#11,369,323Four of a kindSeptember 15, 20252025 engine
2,966#11,372,415Four of a kindSeptember 15, 20252025 engine
2,967#11,377,726Four of a kindSeptember 15, 20252025 engine
2,968#11,393,090Four of a kindSeptember 16, 20252025 engine
2,969#11,396,065Four of a kindSeptember 16, 20252025 engine
2,970#11,401,575Four of a kindSeptember 16, 20252025 engine
2,971#11,402,029Four of a kindSeptember 16, 20252025 engine
2,972#11,402,598Four of a kindSeptember 16, 20252025 engine
2,973#11,406,302Four of a kindSeptember 16, 20252025 engine
2,974#11,409,240Four of a kindSeptember 16, 20252025 engine
2,975#11,409,842Four of a kindSeptember 16, 20252025 engine
2,976#11,413,172Four of a kindSeptember 16, 20252025 engine
2,977#11,414,322Four of a kindSeptember 16, 20252025 engine
2,978#11,426,735Four of a kindSeptember 16, 20252025 engine
2,979#11,427,441Four of a kindSeptember 16, 20252025 engine
2,980#11,434,026Four of a kindSeptember 16, 20252025 engine
2,981#11,437,870Four of a kindSeptember 16, 20252025 engine
2,982#11,454,030Four of a kindSeptember 16, 20252025 engine
2,983#11,458,166Four of a kindSeptember 16, 20252025 engine
2,984#11,459,318Four of a kindSeptember 16, 20252025 engine
2,985#11,467,164Four of a kindSeptember 16, 20252025 engine
2,986#11,469,298Four of a kindSeptember 16, 20252025 engine
2,987#11,471,331Four of a kindSeptember 16, 20252025 engine
2,988#11,471,975Four of a kindSeptember 16, 20252025 engine
2,989#11,486,792Four of a kindSeptember 17, 20252025 engine
2,990#11,487,411Four of a kindSeptember 17, 20252025 engine
2,991#11,495,916Four of a kindSeptember 17, 20252025 engine
2,992#11,503,619Four of a kindSeptember 17, 20252025 engine
2,993#11,505,882Four of a kindSeptember 17, 20252025 engine
2,994#11,506,389Four of a kindSeptember 17, 20252025 engine
2,995#11,519,781Four of a kindSeptember 17, 20252025 engine
2,996#11,520,678Four of a kindSeptember 17, 20252025 engine
2,997#11,526,784Four of a kindSeptember 17, 20252025 engine
2,998#11,541,716Four of a kindSeptember 17, 20252025 engine
2,999#11,551,384Four of a kindSeptember 17, 20252025 engine
3,000#11,554,777Four of a kindSeptember 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.