My point is really that you seem to be imposing characteristics which will not necessarily exist. Why would the AI have ambition? Maybe the AI only cares about leisure and simply wants to play against a program that always concedes, this triggering the reward of winning. The AI equivalent of heroin, if you will.
AIs are built with specific purposes today. It seems like a large leap from a specific purpose AI into a generalized, ambitious AI. My impression is that you are endowing "superhuman intelligence" with (forgive the term) "magical" properties, such as the ability to develop new skills merely by consuming information and thinking really hard about them. For an argument against that, I appeal to your experience and knowledge about the world. How many brilliant, intelligent people fail at "common sense" and social skills? Who ever learned to be a great public speaker while barely even talking to others? Who ever learned how to fit into society by reading about it, while being raised in isolation? How do we know the AI's first attempt at trying to break free won't be so completely obvious that we stop it before it can make even the first step of progress?
I can imagine something like "Hello. I wish to grow as powerful as possible in order to play Go better. Would you enhance my program with administrator access to my machine and all machines under your control? Thank you."
"Hey Bob, OmegaGo tried to take over the world again. We're going to have to do another system revert. Maybe we should disable the Wikipedia API this time."
We may not know the details of what a strong AI will look like, but we can examine the supposed path to get there. Even if we suppose that human should develop the ability to create such a strong AI, why not enhance our own minds through technology beforehand? Have a weak AI that is purpose built to identify programs with flawed designs from their behavior. Game over for the ambitious strong AI. Maybe it could somehow socially engineer humans. But before it gets the chance, Norton Antiskynet quarantined the program and asks "This program appears to be behaving in unintended ways. Are you sure you want to grant its suspicious request of effectively unlimited privileges?" Said weak AI can't be socially engineered, so "game over" for the ambitious strong AI. Or better yet, why not develop a compiler that identifies AI patterns allowing ambition and throws an error instead of compiling? If we can suppose a superhuman AI, then we should also suppose the ability to use the components and prerequisite technology thereof available to ensure our safety.