
If you press it, your chances are 50%, but if you dont press it, your chances are less than 50% because you have to survive the possibility that your opponent doesnt press the botton (50%) AND THEN survive another possibilty that you dont get randomly selected to die (50% again). You should press the button ALWAYS.
I think it’s inherently faulty to assume the chances of the other person pressing it are 50/50. I wouldn’t press it because if I press it either that kills me or I have to survive with the knowledge I killed someone else, which I feel that I couldn’t do. So I would not press it and either die with a clear conscience or get lucky