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@tttppp actually if you can "prove" a checkmate in x-moves a game is won. You don't have to play it out, displaying each and every move is enough. (You can't lose by time if you displayed it - given you still have to display it in regular game time).
@Rainbolt you don't do nothing, you make your calculations during those two hours. There's, exactly due to the limited information, a lot of fun non trivial equations about chance one has to solve before playing a card. I always find it annoying that halfway such a calculation a "judge" comes over and tells me I can't do that.
While I do understand the limitation of not being able to utilize a game clock - what I do not understand is why there is such aversion agianst games that take 2+ hours, with matches happening over the course of days/weeks. Even there some "guide" has to be employed for making sure one person doesn't take too much time. Yet we don't see this happening at all, and if I suggest it people just state "this is bad".