> > > In Citadels there are 8 character cards, one of which > is the King. At the beginning of each turn they are > shuffled and two cards are put placed face up and one > face down, the remaining 5 cards enter distribution > to the players. If the king appears as a face up card > then the process must be restarted and repeated until > the King is not a face up card. The question is, what > is the chance that the king will be the face down > card?
The 8 character cards contain 1 King.
In any valid deal, the King is not one of the 2 face up cards. Therefore it must be 1 of the other 6 cards.
1 of those 6 cards is facing down.
Therefore the probability is 1/6 that the face down card is the King.