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
2,701#10,349,810Four of a kindAugust 29, 20252025 engine
2,702#10,363,616Four of a kindAugust 29, 20252025 engine
2,703#10,367,393Four of a kindAugust 29, 20252025 engine
2,704#10,375,076Four of a kindAugust 29, 20252025 engine
2,705#10,379,254Four of a kindAugust 29, 20252025 engine
2,706#10,379,812Four of a kindAugust 30, 20252025 engine
2,707#10,382,881Four of a kindAugust 30, 20252025 engine
2,708#10,387,503Four of a kindAugust 30, 20252025 engine
2,709#10,390,624Four of a kindAugust 30, 20252025 engine
2,710#10,397,644Four of a kindAugust 30, 20252025 engine
2,711#10,398,427Four of a kindAugust 30, 20252025 engine
2,712#10,398,532Four of a kindAugust 30, 20252025 engine
2,713#10,398,567Four of a kindAugust 30, 20252025 engine
2,714#10,399,967Four of a kindAugust 30, 20252025 engine
2,715#10,400,554Four of a kindAugust 30, 20252025 engine
2,716#10,413,518Four of a kindAugust 30, 20252025 engine
2,717#10,413,595Four of a kindAugust 30, 20252025 engine
2,718#10,416,763Four of a kindAugust 30, 20252025 engine
2,719#10,423,548Four of a kindAugust 30, 20252025 engine
2,720#10,435,745Four of a kindAugust 30, 20252025 engine
2,721#10,440,465Four of a kindAugust 30, 20252025 engine
2,722#10,445,326Four of a kindAugust 30, 20252025 engine
2,723#10,450,745Four of a kindAugust 30, 20252025 engine
2,724#10,458,751Four of a kindAugust 30, 20252025 engine
2,725#10,462,391Four of a kindAugust 30, 20252025 engine
2,726#10,465,208Four of a kindAugust 31, 20252025 engine
2,727#10,476,305Four of a kindAugust 31, 20252025 engine
2,728#10,478,143Four of a kindAugust 31, 20252025 engine
2,729#10,480,410Four of a kindAugust 31, 20252025 engine
2,730#10,486,719Four of a kindAugust 31, 20252025 engine
2,731#10,486,760Four of a kindAugust 31, 20252025 engine
2,732#10,494,416Four of a kindAugust 31, 20252025 engine
2,733#10,497,838Four of a kindAugust 31, 20252025 engine
2,734#10,500,619Four of a kindAugust 31, 20252025 engine
2,735#10,509,433Four of a kindAugust 31, 20252025 engine
2,736#10,514,989Four of a kindAugust 31, 20252025 engine
2,737#10,516,650Four of a kindAugust 31, 20252025 engine
2,738#10,518,273Four of a kindAugust 31, 20252025 engine
2,739#10,519,123Four of a kindAugust 31, 20252025 engine
2,740#10,520,000Four of a kindAugust 31, 20252025 engine
2,741#10,526,823Four of a kindAugust 31, 20252025 engine
2,742#10,535,290Four of a kindAugust 31, 20252025 engine
2,743#10,535,935Four of a kindAugust 31, 20252025 engine
2,744#10,537,019Four of a kindAugust 31, 20252025 engine
2,745#10,537,519Four of a kindAugust 31, 20252025 engine
2,746#10,539,380Four of a kindAugust 31, 20252025 engine
2,747#10,540,508Four of a kindAugust 31, 20252025 engine
2,748#10,540,621Four of a kindAugust 31, 20252025 engine
2,749#10,540,622Four of a kindAugust 31, 20252025 engine
2,750#10,544,945Four of a kindAugust 31, 20252025 engine
2,751#10,544,946Four of a kindAugust 31, 20252025 engine
2,752#10,545,867Four of a kindAugust 31, 20252025 engine
2,753#10,550,122Four of a kindSeptember 1, 20252025 engine
2,754#10,556,566Four of a kindSeptember 1, 20252025 engine
2,755#10,561,622Four of a kindSeptember 1, 20252025 engine
2,756#10,562,894Four of a kindSeptember 1, 20252025 engine
2,757#10,567,058Four of a kindSeptember 1, 20252025 engine
2,758#10,567,299Four of a kindSeptember 1, 20252025 engine
2,759#10,570,271Four of a kindSeptember 1, 20252025 engine
2,760#10,582,066Four of a kindSeptember 1, 20252025 engine
2,761#10,584,989Four of a kindSeptember 1, 20252025 engine
2,762#10,585,250Four of a kindSeptember 1, 20252025 engine
2,763#10,585,724Four of a kindSeptember 1, 20252025 engine
2,764#10,586,175Four of a kindSeptember 1, 20252025 engine
2,765#10,587,566Four of a kindSeptember 1, 20252025 engine
2,766#10,589,943Four of a kindSeptember 1, 20252025 engine
2,767#10,598,016Four of a kindSeptember 1, 20252025 engine
2,768#10,599,227Four of a kindSeptember 1, 20252025 engine
2,769#10,600,696Four of a kindSeptember 1, 20252025 engine
2,770#10,601,628Four of a kindSeptember 1, 20252025 engine
2,771#10,608,308Four of a kindSeptember 1, 20252025 engine
2,772#10,608,543Four of a kindSeptember 1, 20252025 engine
2,773#10,615,004Four of a kindSeptember 1, 20252025 engine
2,774#10,618,108Four of a kindSeptember 1, 20252025 engine
2,775#10,621,488Four of a kindSeptember 1, 20252025 engine
2,776#10,626,871Four of a kindSeptember 1, 20252025 engine
2,777#10,627,336Four of a kindSeptember 1, 20252025 engine
2,778#10,631,881Four of a kindSeptember 1, 20252025 engine
2,779#10,636,847Four of a kindSeptember 2, 20252025 engine
2,780#10,652,993Four of a kindSeptember 2, 20252025 engine
2,781#10,656,663Four of a kindSeptember 2, 20252025 engine
2,782#10,663,825Four of a kindSeptember 2, 20252025 engine
2,783#10,665,326Four of a kindSeptember 2, 20252025 engine
2,784#10,667,627Four of a kindSeptember 2, 20252025 engine
2,785#10,667,958Four of a kindSeptember 2, 20252025 engine
2,786#10,668,095Four of a kindSeptember 2, 20252025 engine
2,787#10,668,508Four of a kindSeptember 2, 20252025 engine
2,788#10,677,410Four of a kindSeptember 2, 20252025 engine
2,789#10,679,582Four of a kindSeptember 2, 20252025 engine
2,790#10,682,394Four of a kindSeptember 2, 20252025 engine
2,791#10,683,257Four of a kindSeptember 2, 20252025 engine
2,792#10,691,025Four of a kindSeptember 2, 20252025 engine
2,793#10,692,583Four of a kindSeptember 2, 20252025 engine
2,794#10,693,383Four of a kindSeptember 2, 20252025 engine
2,795#10,704,427Four of a kindSeptember 2, 20252025 engine
2,796#10,705,567Four of a kindSeptember 2, 20252025 engine
2,797#10,706,294Four of a kindSeptember 2, 20252025 engine
2,798#10,706,708Four of a kindSeptember 2, 20252025 engine
2,799#10,711,301Four of a kindSeptember 2, 20252025 engine
2,800#10,711,774Four of a kindSeptember 2, 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.