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I think there is stalemate, but nut sure. Similar to rabbitoids position: White: Ka1, Na7, Nb8, pawn b6 Black: Ka8 After white's turn moving the pawn from b6 to b7. Black has no more moves, because no move is allowed which would explode the own king. At Fics it would be 1-0, because there is check and checkmate, but I think at brainking it is 1/5-1/5, but not sure.
Other example: Black: Kc8 White: Kc6, pawn c7 It's black's turn. At Fics it would be a draw, because of the checkrule there. At brainking is no check, so the black king can still move where he wants, except c7. ;)
rabbitoid: I first played at FICS more than a dozen years ago. They already had Fisher Random and several other "wild" variants, next to suicide and bughouse.
FromHell: At first I thought that here on Brainking there couldn't be any atomic stalemate because of the definition of stalemate: "Stalemate is a situation in chess where the player whose turn it is to move is not in check but has no legal moves.". As the BK atomic implementation lacks checks, I thought that there can't be any stalemate (at least in legal positions). Your first example proves the contrary!
Concerning your second example I dare to contradict ;) My understanding of the rules is that a King can always move next to the other King, and as they can't capture each other it's not check! So Kb7 and Kd7 are allowed regardless of the check rule. Only for Kb8 and Kd8 the check rule would make a difference.
rabbitoid: "Don't ask me how the black bishop got to b8 :)" No, I won't do this, I just want to know how the black rook got to b7? :-D
kleineme: You're right. My second example seems to be wrong. Connecting kings seems to be allowed there. But you can't move to b8 or d8 at FICS, but at brainking it's allowed. I'm sorry for my fault.