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tonyh: I don't think you can claim a game. If you are playing a game of Backgammon on a real board against a real opponent, would you go away with the words: I would win? That's nonsense!
Oh, and by the way, a game of Maharadjah Chess or Horde Chess with that 'claim victory button' would be very quickly then.
But there is a difference; there are Go-players who (when the board is full and doing a move would be useless) play stones in their own areas just for the AP's. I have also a game running where my opponent would lose but he just won't give up for his AP's (I think).
Back to my opinion: Just when you would win, give a 'good game' phrase that you would win, and don't claim anything cause that would reduce the friendly 'atmosphere' here at BK.
PS: I always resign a very lost game of Gammon, Go or anything else because I hate to play further in those (already lost) games.
PS 2: I've also a Go game running where my opponent still rejects my ''dead stone offer'' cause he would lose then. But I am really right. What can I do? (Maybe this is for the Go Board instead)