My initial game set-up: All players must NOT begin by holding a matching pair of cards where there are as many initial pairs possible as there are players.

For example, in a four-player game there are 4 pairs in a total of 8 cards such as 2 jacks, 2 queens, 2 kings, and 2 aces. Initially, all 8 cards are dealt to the four players. I need to begin the game where NO player has two-of-a-kind. In a four-player game, I believe the chances of this happening randomly are 1 in 4. That is... 3*2*1 or six valid combinations (where no pairs exist) in a total of 4*3*2*1 or 24 total combinations. For five players, the chances are one in five. For six players, one in six, etc.

The only mechanism that I can think of to appropriately distribute these eight cards unknowingly to all players and to avoid any pairs, is to deal the cards, then shuffle and re-deal them if a pair is formed. In a typical four-player game, this would often require re-dealing these cards 4 or more times before any play begins.

My questions are: Have I calculated the odds correctly? Is there a better mechanism for distributing these cards appropriately? And, if not, is this set-up mechanism overly complicated?

Thank you in advance for your thoughts.

jf

seo -

Thanks for your reply.

There is an additional requirement that I did not mention in the first post, so let me elaborate. The game concept has one discrete set of cards dealt, then the second set. The first four cards are individual character cards. The second set of cards represent a relationship that the character has to another character. I need to avoid the situation where someone is assigned as having a relationship to oneself.

So, I believe I am stuck with the situation of having to re-deal the second set of four cards until no one has a relationship card matching their character card.

Thanks.

jf