[pzhon]

[ QUOTE ]
Now I wonder if I know what you meant by "cycle 3 suits."

[/ QUOTE ]
There are 8 ways to cycle 3 suits. One of them is described by [img]/images/graemlins/spade.gif[/img] -> [img]/images/graemlins/heart.gif[/img] -> [img]/images/graemlins/diamond.gif[/img] -> [img]/images/graemlins/spade.gif[/img]. That means the new matchup has a [img]/images/graemlins/heart.gif[/img] where the original matchup had a [img]/images/graemlins/spade.gif[/img], a [img]/images/graemlins/diamond.gif[/img] where the original had a [img]/images/graemlins/heart.gif[/img], and a [img]/images/graemlins/spade.gif[/img] in place of every [img]/images/graemlins/diamond.gif[/img]. Every [img]/images/graemlins/club.gif[/img] stays the same.

This is how the permutations of {[img]/images/graemlins/spade.gif[/img], [img]/images/graemlins/heart.gif[/img], [img]/images/graemlins/diamond.gif[/img], [img]/images/graemlins/club.gif[/img]} act on a deck of cards or the set of pairs of hands. The 24 permutations of the suits have the structure of a group. The action on the set of pairs of hands has the structure of a group action.