Keith,

I have a program that will look at all possible schedules and find a "most balanced" one. The criteria involves measuring the number of times each pair plays together, with "more balanced" being regarded as better. The program has run for the past few days, and just finished. It eventually looked at almost 2 billion candidate schedules; the rest were eliminated because the could not be "best". Here is the best schedule it found, according to the criteria used. The way to read it is that the positions are the players, and the numbers are the groups. For example, on day 0 the groups are 1, 2, 3, 4; 5, 6, 7, 8; 9, 10

Day 0 : (0, 0, 0, 0, 1, 1, 1, 1, 2, 2)
Day 1 : (0, 0, 1, 1, 0, 0, 1, 2, 1, 2)
Day 2 : (0, 1, 0, 1, 0, 1, 2, 0, 2, 1)
Day 3 : (0, 1, 1, 2, 2, 0, 0, 1, 1, 0)
Day 4 : (0, 1, 2, 0, 1, 2, 1, 0, 0, 1)

Hope it helps.
--Victoria