Round robins are in a nut shell, a cooperative method of trading postcards with a group of people.
To work sucessfully, one person will lead the round robin. The leader will make a list of all the people who are wanting to participate in it.
The leader will also write the mailing address list of all the people in the group and the wants list with the names of the people.
The leader make circulate a sheet with all these details listed on it.

Below is an example of how a round robin sheet will look:

Name of the round robin: Disney
Postcards: 10 mint continental
Type: General
The rules: of the round robin, what must be adhered to by all participants; they are regulated by the leader.
Next on this list is the names of all the participants
For example:
The members name .......?.......
The members mailing address .......?.......
The members want list or preferences.......?.......
Then the next member is listed here and so on. The list contiues with all of the members being listed. 

Most times there will be a minimum of about six members involved in a round robin and member who is number six in the robin is usually the leader, as the leader is the one who started the robin.
The leader will start the round robin off by checking the participants list to see what member number one on the robin list, had asked for as their preferences in postcards. The leader will then place the first agreed ten mint continental postcards that suit the preference of member number one, in an envelope and then initial his/her name on the list to say that they have put in their ten cards. The leader will then pass or mail the envelope to member number one on the round robin list.

When member number one receives the postcards from the leader, he or she will pick out of the pile of cards, how ever many cards that they want and then he or she will replace the same amount of cards that they took from the pile with the exact same amount of replacement cards, adhereing of course to the list rules and what the tastes are of the next member in the list. Member number one will then intial his/her name off the list and then send the cards forward on the list to the next member, number two!

The list and postcards envelope will continue on to all of the members on the participants list. Once the sheet passed every member and has found its way back to the leader. The leader can finally now select the cards that he/she wants and then replace the ones that he/she took and if there are any cards still there from the original cards that he or she put in, it is then up to the leader to replace those cards with fresh ones, as no one obviously wants them. Once this is done and the leader has intialed their name off the list again, it is then time to resend the list and postcards back to the first member, just as before.

As to how many times the round robin is executed, that is basically the groups choice that is usually agreed on from the start, but can be discussed by correspondance between a fully functioning round robin, as the greater the number of people in the group, the bigger the variety of postcards will become available, so whether the round robin does the loop of the postcard group twice over or ten times over, its entirely a groups decision.