YIKES!!! nope, can't tell at all actually. I'll be surprised if you know 
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Ok, here's how I understand it.
I can play in as many Official Chess.com tournaments as I like. (they're the ones with the little green pawn next to them)
Then I can join join 10 member tournaments.
As soon as one of these tournaments complete, I can join another, and this tournament disappears from my current tournament list.
But, also, as soon as I get eliminated from a tournament, I can also join another tournament, but in this case, this tournament STAYS on my current tournament list.
So, there seems to be no way for me to tell how many member tournaments are actuall active for me at the moment, except for trying to join tournaments and seeing if I'm allowed?
Can any, from the table below, glean how many ACTIVE tournaments I have?
My Current Tournaments