I would never recommend three-player Cosmic when another choice is available ... so I say definitely three games of 5 players if you have exactly 15. If a 16th shows up, then four games of 4 players would also work.
Consider having two rounds before the finals rather than just one. Nobody like showing up to a tournament and only getting to play one game. Back in the Eon days there was a scoring system for determining who advanced, in which you get more points for a solo win. Here they are, but you'll have to do a little translation (from tokens, bases, challenges, etc. to ships, colonies, encounters, etc.).
II. TOURNAMENT RULES
The official [Eon] Cosmic Encounter Rules are designed to
allow tournament play within a relatively defined time
frame. A point system is used to end the first and
second round games in 50 minutes, preventing them
from being prolonged as players struggle for solo victories.
Divide players into four player games. This round will
have two games. Each game will last for 50 minutes.
The first game in this round will use the basic Cosmic
Encounter set only. At the end of 50 minutes, end all
games, distribute the game points, have the players
switch around so that they are in new groups and
begin the second game. All players advance to the
second game. The second game will add in Expansion
Set one, two and three. End the game after 50
minutes and total each player’s points from game
one and game two.
ADVANCEMENT TO ROUND 2
To advance to round 2 a player must score high
enough to make the cut off. Scores are totaled from
game one and game two. The cut off is figured by
taking the top scoring players in multiples of four until
you have about half of the original players.
There will be one game in round two. Divide the players
into four player games. The game will last for 50 minutes.
Add in Expansion Sets four, six, seven and eight.
Victory points are figured by the same system, but players
do not carry their round one points over into this
round. All players are starting from zero points.
ADVANCEMENT TO FINALS
The top six players, based on the points earned in round
two only, advance to the finals.
One game, no time limit. Add Expansion Sets five and
nine. No points are used, the regular winner(s) are the
VICTORY POINT SYSTEM
The victory point system is used in round one and round
two. At the end of 50 minutes each player gets:
• 1 point for every home planet base (5 possible)
• 2 points for every foreign planet base (10 possible)
• 6 points in the pot divided among the winners.
Example: A player who won alone, and who still had all
home bases would have 21 points (5 for home bases +
10 for foreign bases + 6 from the pot).
RANKING THE FINALISTS
After the winner(s) are determined, the other finalists
can be ranked by adding the total points earned in
Round 1 and Round 2 for each player. The player with
the high total is ranked second, the next high third and
If there is a multiple player win the finals, players may
elect to play off. In this case the winners start a new
game. The winners of that game again start a new
game until there is only one winner. This process continues
even if a two player game is necessary.
The following Aliens are not used during Round 1 or
Round 2: Filth, Schizoid, Terrorist. In the finals however,
there are no exclusions (except as defined by statements
on the power cards, hexes etc. “Do not use with