Define a legal Solitaire-type move within a group of face-up playing cards as moving one card to partially cover a stationary card provided that the stationary card:

1) has numeric value exactly one larger than the card to be moved; and

2) is of a color opposite to that of the card to be moved.

Note that Jack, Queen and King have numeric values of 11, 12 and 13 respectively and Ace only has the value of 1.

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From 52 cards, 8 cards are randomly chosen and are laid out face up in a row. In this simplified game, the other 44 cards are discarded. What is the probability that no legal Solitaire-type move is possible for a:

a) Standard Deck, 2 suits are red and 2 suits are black.

b) One-Suit Deck: what if the 52 cards are all one suit, 4 complete sets of Ace through King, and the "opposite color" requirement is removed?

Consider an infinite deck so that each card is independent of the others, the probability is exactly

Posted by Jer on 2021-01-18 14:51:32