Aquí hay respuestas interesantes a la pregunta: https://www.quora.com/If-a-coin-is-tossed-by-a-robot-with-exact-same-conditions-will-it-produce-same-result-all-the-time
Pego la siguiente que me parece la más acertada (tochopost incoming!!!):
Your question boils down to whether physics is deterministic or not. And whether it is completely predictable or not...
Determinism and predictability are closely related but not the same.
Let's take the classical physics model which was at its peak during the 1700s to 1900s.
Physicists believed (notably Leibniz and Laplace) with enough justification that the laws of physics could be completely specified, and if some super intelligence could know the state of every particle in the universe, it could also calculate the next state in time and so on ad infinitum.
But physicists also knew that that since physical quantities had infinite precision (that's what they believed then), they could never actually calculate a systems exact future. The reason is what is called mathematical chaos.
Mathematical chaos is the notion that for some systems, the evolution of the system over time are very sensitive to the initial conditions.
The classic example is a glass of water, in which you put a small drop of color. As you stir the water, even though each dye molecule was almost exactly at the same location as its neigbour, by some time, each molecule has gone to a completely unique place, completely evenly distributed across the solution.
Suppose you had put only one molecule, could we have predicted where it ends up?
Not unless you could pinpoint the location exactly.
We would say that the act of stirring is a chaotic transformation on the molecules position and some math proves that for such transforms, no matter how small an error you have in measuring initial conditions, your predictions will diverge from the system exponentially with time.
Thus a world with classical physics was deterministic, but still not predictable.
Scientists were quite happy, at least non-chaotic systems could be predicted!
One flaw with this model is that every physical quantity would have infinite precision. This was not a big deal then. But today we know that infinite precision means infinite information contained within and this can be used to violate the laws of thermodynamics - don't ask how, but information entropy and thermodynamic entropy are intertwined. This is the only reason you cannot have a device like Maxwell's demon
Then the quantum theory hullabaloo happened. Suddenly, it was impossible to measure a thing, and things moved completely randomly. Neither could you knw the state of the system, nor could you predict some outcome, other than by probabilities. If you had a 50% probability of a uranium atom decaying, there is no way even in theory of telling whether it did (and weirdly according to QM, it both decays and not decays and only gets fixed to one state when you check it later)
So now that QM is true, you have non-determinism and unpredictability too...
Or so it would seem! But we now know that physical units are all quantized - there are minimum values for Length, Time and Charge. The old classical notion of undivided smooth time and space doesn't hold.
Also, while the results of observation of quantum phenomena are totally unknowable, the wave function is a fixed amount of information that describes the state of the system and that evolves deterministically. The math is deterministic - the results you observe are random.
So it's pretty much accepted that there is a fixed amount of information in the universe - This is known as the Berkenstein bound of the universe (and we know the universe has finite space).
If the universe has fixed number of states, then there exists an algorithm that takes the state of the universe as a long bitstring, and returns the next state bitstring in time. Probably that program is much shorter than te bitstring itself, because the universe is roughly predictable even to our meager brains.
So now to unanswer your question - If we make a robot toss a coin in the same way, will it land on the same side every time?
We don't know yet if it will -
Engineering-wise we cannot replicate the conditions exactly yet, but If we do replicate it, we will be hit by quantum randomness.
But maybe if you could setup the universe in the exact same way again and again (after all it has finite number of bits) then it will fall the exact same way.