Is there anyway I could sum this up in a mathmatical equation?

I was going to sum this down but I think it would be best to post the whole thing, sorry for tl;dr
Imagine you have created nanobots, what core functions were to replicate themselves and to collect the data of every subatomic particles position and all other information about them. Becoming omniscient, they have the fundamental knowledge to predicting every single event from that point onward. When and where earthquakes will happen, what random number I choose etc. I meet up with your omniscient nanobots and ask them a simple question, what hand will I put up? The regulations are you have to tell me before I make my decision and whatever you say I will choose the opposite.
Is there any possible way I could sum up the nanobots a subject to be able to know and influence the other subject a man’s decision and his decision would only be decided on two variables his own variables and the nanobots influences?
This question isn’t about is this scenario viable, it’s all purely hypothetical, I want to know could it be summed up in a mathematical equation to know could one subject know how its influences plus other variables would effect another subject to a 100% accuracy all the time.