The tourneys in online / turn-based chess are most often in days-per-move. You can make them quicker than 1 move every three days, of course. But Live Chess is the better forum for allowing 1 move per minute or faster, I think.
I want to participate in chess tournament but there's some problem.
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When I was trying to participate in chess tournament here I found some problem and that is one move per minimum 3 days. I felt bored and got out of tournament. I think move per minute or second also should be allowed or system should be implemented.