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. 3,687 shuffles have qualified so far.

RankShuffleHandShuffledEra
2,601#9,897,833Four of a kindAugust 24, 20252025 engine
2,602#9,900,448Four of a kindAugust 24, 20252025 engine
2,603#9,900,923Four of a kindAugust 24, 20252025 engine
2,604#9,901,206Four of a kindAugust 24, 20252025 engine
2,605#9,908,076Four of a kindAugust 24, 20252025 engine
2,606#9,909,236Four of a kindAugust 24, 20252025 engine
2,607#9,909,320Four of a kindAugust 24, 20252025 engine
2,608#9,914,833Four of a kindAugust 24, 20252025 engine
2,609#9,934,666Four of a kindAugust 24, 20252025 engine
2,610#9,938,312Four of a kindAugust 24, 20252025 engine
2,611#9,939,144Four of a kindAugust 24, 20252025 engine
2,612#9,939,789Four of a kindAugust 24, 20252025 engine
2,613#9,945,506Four of a kindAugust 24, 20252025 engine
2,614#9,945,833Four of a kindAugust 24, 20252025 engine
2,615#9,946,014Four of a kindAugust 24, 20252025 engine
2,616#9,946,803Four of a kindAugust 24, 20252025 engine
2,617#9,957,306Four of a kindAugust 25, 20252025 engine
2,618#9,959,049Four of a kindAugust 25, 20252025 engine
2,619#9,962,410Four of a kindAugust 25, 20252025 engine
2,620#9,962,501Four of a kindAugust 25, 20252025 engine
2,621#9,967,967Four of a kindAugust 25, 20252025 engine
2,622#9,968,196Four of a kindAugust 25, 20252025 engine
2,623#9,970,121Four of a kindAugust 25, 20252025 engine
2,624#9,973,039Four of a kindAugust 25, 20252025 engine
2,625#9,983,736Four of a kindAugust 25, 20252025 engine
2,626#9,984,254Four of a kindAugust 25, 20252025 engine
2,627#9,984,950Four of a kindAugust 25, 20252025 engine
2,628#9,989,647Four of a kindAugust 25, 20252025 engine
2,629#9,992,848Four of a kindAugust 25, 20252025 engine
2,630#9,994,794Four of a kindAugust 25, 20252025 engine
2,631#9,997,556Four of a kindAugust 25, 20252025 engine
2,632#10,001,468Four of a kindAugust 25, 20252025 engine
2,633#10,005,902Four of a kindAugust 25, 20252025 engine
2,634#10,005,903Four of a kindAugust 25, 20252025 engine
2,635#10,007,256Four of a kindAugust 25, 20252025 engine
2,636#10,015,481Four of a kindAugust 25, 20252025 engine
2,637#10,015,759Four of a kindAugust 25, 20252025 engine
2,638#10,019,894Four of a kindAugust 25, 20252025 engine
2,639#10,025,781Four of a kindAugust 25, 20252025 engine
2,640#10,026,620Four of a kindAugust 25, 20252025 engine
2,641#10,034,823Four of a kindAugust 25, 20252025 engine
2,642#10,035,209Four of a kindAugust 25, 20252025 engine
2,643#10,046,279Four of a kindAugust 26, 20252025 engine
2,644#10,048,295Four of a kindAugust 26, 20252025 engine
2,645#10,051,814Four of a kindAugust 26, 20252025 engine
2,646#10,059,915Four of a kindAugust 26, 20252025 engine
2,647#10,067,385Four of a kindAugust 26, 20252025 engine
2,648#10,069,275Four of a kindAugust 26, 20252025 engine
2,649#10,069,666Four of a kindAugust 26, 20252025 engine
2,650#10,071,190Four of a kindAugust 26, 20252025 engine
2,651#10,073,063Four of a kindAugust 26, 20252025 engine
2,652#10,091,817Four of a kindAugust 26, 20252025 engine
2,653#10,101,503Four of a kindAugust 26, 20252025 engine
2,654#10,106,490Four of a kindAugust 26, 20252025 engine
2,655#10,109,038Four of a kindAugust 26, 20252025 engine
2,656#10,117,704Four of a kindAugust 26, 20252025 engine
2,657#10,128,773Four of a kindAugust 27, 20252025 engine
2,658#10,128,882Four of a kindAugust 27, 20252025 engine
2,659#10,133,287Four of a kindAugust 27, 20252025 engine
2,660#10,141,615Four of a kindAugust 27, 20252025 engine
2,661#10,150,800Four of a kindAugust 27, 20252025 engine
2,662#10,153,320Four of a kindAugust 27, 20252025 engine
2,663#10,153,989Four of a kindAugust 27, 20252025 engine
2,664#10,161,175Four of a kindAugust 27, 20252025 engine
2,665#10,173,755Four of a kindAugust 27, 20252025 engine
2,666#10,184,457Four of a kindAugust 27, 20252025 engine
2,667#10,187,767Four of a kindAugust 27, 20252025 engine
2,668#10,197,164Four of a kindAugust 27, 20252025 engine
2,669#10,201,453Four of a kindAugust 27, 20252025 engine
2,670#10,212,304Four of a kindAugust 28, 20252025 engine
2,671#10,219,302Four of a kindAugust 28, 20252025 engine
2,672#10,224,305Four of a kindAugust 28, 20252025 engine
2,673#10,224,981Four of a kindAugust 28, 20252025 engine
2,674#10,225,826Four of a kindAugust 28, 20252025 engine
2,675#10,225,849Four of a kindAugust 28, 20252025 engine
2,676#10,227,694Four of a kindAugust 28, 20252025 engine
2,677#10,232,673Four of a kindAugust 28, 20252025 engine
2,678#10,233,968Four of a kindAugust 28, 20252025 engine
2,679#10,234,154Four of a kindAugust 28, 20252025 engine
2,680#10,240,901Four of a kindAugust 28, 20252025 engine
2,681#10,252,642Four of a kindAugust 28, 20252025 engine
2,682#10,257,501Four of a kindAugust 28, 20252025 engine
2,683#10,257,801Four of a kindAugust 28, 20252025 engine
2,684#10,263,882Four of a kindAugust 28, 20252025 engine
2,685#10,269,925Four of a kindAugust 28, 20252025 engine
2,686#10,275,186Four of a kindAugust 28, 20252025 engine
2,687#10,279,785Four of a kindAugust 28, 20252025 engine
2,688#10,284,109Four of a kindAugust 28, 20252025 engine
2,689#10,284,424Four of a kindAugust 28, 20252025 engine
2,690#10,287,059Four of a kindAugust 28, 20252025 engine
2,691#10,290,942Four of a kindAugust 28, 20252025 engine
2,692#10,295,629Four of a kindAugust 29, 20252025 engine
2,693#10,309,220Four of a kindAugust 29, 20252025 engine
2,694#10,313,837Four of a kindAugust 29, 20252025 engine
2,695#10,323,675Four of a kindAugust 29, 20252025 engine
2,696#10,324,303Four of a kindAugust 29, 20252025 engine
2,697#10,326,787Four of a kindAugust 29, 20252025 engine
2,698#10,329,026Four of a kindAugust 29, 20252025 engine
2,699#10,342,025Four of a kindAugust 29, 20252025 engine
2,700#10,342,922Four of a kindAugust 29, 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.