The online status icon should show whether you are a basic or premium member. However, the online status may not always be 100% accurate and up to date because of cacheing. So the online status icon should be relatively accurate most of the time.
Why doesn't it show who is on-line?
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That is strange, I don't ever see the little tower with the radio signals beside my name or the people I am playing turn-based chess against.
When I look at my list of games waiting for moves, it no longer shows who is on-line. Is this now an upgrade feature with a paid account?