Number of allowed games
The number of games you may play in parallel is limited by the number of valid games you have played so far.
As a newcomer (no completed games yet), you may play only 6 games at the same time. Therefore, newcomers may enroll in 5-player and 7-player, but not in 9-player tournaments (because the latter have 8 games per player).
The more valid games you have played, the more games (and tournaments) you may play in parallel. The general formula is simple:
AG = MIN + NVG (with upper limit)
Here, AG is the number of allowed parallel games and NVG is the number of valid games you have played so far.
Important: The game limits determine if you may enroll in new tournaments. But they have no influence on already running games. If your number of running games exceeds these game limits, don't worry - simply play your games to their regular end.
Minimum value and upper limit
The minimum value and the upper limit of this formula depend on your membership state.
Only very engaged players can manage to play (and complete!) many games. I advise "normal" players to play no more than 10-20 games in parallel. As a start, one tournament (with up to 6 games) is enough.
Hint. The above formulas are applied to members, too. This means that you cannot play 40 (or 80) games immediately. You have to finish valid games until you reach these upper limits.
Example for guests
A new player enrolls for a 5-player tournament. Then, he has 4 running games. Since the game limit is 6, he cannot enroll in another tournament.
After finishing the first game regularily, he has 3 running games and his game limit is 7. The difference 7-3=4 is enough to enroll in another 5-player tournament.
But if he waits until another game is over, he has 2 running games and his game limit increased to 8. Because the difference is now 8-2=6, he may even enroll in a 7-player tournament.
Example for members
A guest player has already finished 6 valid games. His game allowance is therefore 6+6=12 games. However, he has 10 games running and cannot enroll in a new tournament.
He purchases the standard PlayChess membership for 6 months.
This increases his number of allowed games to 12+6=18 games, allowing him to enroll in another 9-player tournament.
I am a new member. Why can't I play the full 40 games in parallel?