The number of hosts is not alway a multiple of the number of courses/meals (mostly 3). In those cases the courses are not equally divided, resulting in different numbers of guests. To spare the host with the main course the goal is to take care that the number of maincourses is always equal of bigger than the number of the other courses (first course or dessert).
Problem: average table occupation
Below in the third column the formula for the average table occupation. At a Rdinner for couples where every couple is serving a course, the average occupation is always 6 (incl.host), so 2 couples as guests. When the number of hosts is not a multiple of the number of courses, than the number of guests will vary (plus/minus 1 couple).
The number of guests will increase if participants are exempted of a course. The risk of meeting each other twice is than also increasing. That risk can be calculated with Q (see formula). The break lies with Q=1. Below 1 no solution.