Deterministic paradox

Imagine hypothetically you have created nanobots, what core function were to replicate themselves and to collect the data of every subatomic particle such as position, movement, etc. Becoming omniscient, they have the fundamental knowledge to predicting every single event from that point onward, when will earthquakes happen what random number I will choose, etc. 

I meet up with your omniscient nanbots and ask them one simple question "What hand will I put up, the only conditions are you have to tell me before I make my decision and whatever you will say I will choose the opposite hand."  What will the nanobots say?

At first glance this is just a more complex version of the liar paradox "This sentence is a false."  if the sentence is false then it is correct but if we assume it's correct then it is false. If we assume the nanobots can only answer left or right it will be incorrect, even if It could say you will raise the opposite hand to what I will say, I could always change my mind and put up the hand it says. 

It says something really interesting in that you can not know the future to a 100% accuracy, especially when you have influence on that future event. The nanbots will workout how I would react after hearing predictions and take that into account to predict a new future, but every time it may say something different my reactions also may constantly change making it almost impossible to predict anything with 100% accuracy when I have influence on that event. 

As this is hypothetical thought experiment we would have to ignore the imitations of Heisenberg's uncertainty principle, the fact where the nanbots would store this information would be the size of the universe unless they compressed all that information and everything else that makes this infeasible to actually do.