Argument for deterministic free will
Wow. Where to start?
First, the robots that beat humans at rock, paper, scissors 100% of the time essentially cheat (that is they don't have any "thinking" algorithm) since their camera sees the human hand start whichever motion their human opponent has chosen, then with superhuman speed, has their mechanical "hand" display the winning hand rapidly to end the motion simultaneously with the human, thus fooling the human into thinking the two "chose" at the same time.
As to robot vs robot, since there is no "data" to enter into the algorithm to truly predict what the other robot will choose, the programmer has used some other way to come up with a choice. If one knows what the algorithm is, one can reproduce it.
As to pondering leading to different choices with the same input, I agree with you that humans commonly use the same analysis based on memories, emotions, objective variables such as price etc, however the priotization of the numerous variables leading to different choices in essentially identical situations is a common human experience. Any lay person has experienced this countless times.
If what you imagine is going on in the Black Box of human decision making was actually true, when faced with a decision between two choices of equal merit, humans would be unable to make a choice, yet we do every day.