What happens when you can't move your king when you have to? E.g. if I play 1. Nf3 as white. Is it treated as a stalemate?
Bongcloud chess
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If you dont move the king, you lose
Yes, there is no other way
Why play king move every two move when you can play it every one move 
My new interesting chess variant, in which you are required to move the king every two moves
Example