In Gin-Rummy, in the start of a round players draw 10 cards.
What is the probability to draw 10 cards such that all the cards are part of some meld?
Board & Card Games Stack Exchange is a question and answer site for people who like playing board games, designing board games or modifying the rules of existing board games. It only takes a minute to sign up.Sign up to join this community
Three Independent sources counted about 136,694 Gin hands, out of 15.8B possible 10-cards hands.
2+2 forum post: 1 in ~118,000. Using brute force which checked for Gin each of the 15.8B hands.
Rulemonger's analysis: 136,694 in 15,820,024,220 or 1 in ~115733
How to Win at Gin Rummy: 1 in ~117,000, according to the book How to Win at Gin Rummy: Playing for Fun and Profit which state that there are 136,694 Gin hands out of 15,820,024,220 hands. See page 65:
EDIT: this count is flawed, it doesn't recognize sets of three that include a spade. The correct number is given in the accepted answer. When the code is corrected, it gives the 136,694 unique gin hands, matching the accepted answer.