Twelve matches at once
The limit on open matches, and why a friend can appear greyed out.
You can have twelve online matches running at once (supporters: 25). A match frees its slot when it finishes or is declined.
When you're full
The New match button says so. Tap it to see your open matches, pick the ones to end, delete them, and you're back on New match with room to start one.
Screenshot to comematch-limit-button.png
Bot games are free
Practice matches against the bot don't use a slot — you can always play one, however busy your list is.
Invitations count too
A match someone else started with you fills a slot exactly like one you started. If your list feels full without you having done anything, that's why.