  A physical theory is called non-local when observers can produce
instantaneous effects over distant systems. Non-local theories rely on two
fundamental effects: local uncertainty relations and steering of physical
states at a distance. In quantum mechanics, the former one dominates the other
in a well-known class of non-local games known as XOR games. In particular,
optimal quantum strategies for XOR games are completely determined by the
uncertainty principle alone. This breakthrough result has yielded the
fundamental open question whether optimal quantum strategies are always
restricted by local uncertainty principles, with entanglement-based steering
playing no role. In this work, we provide a negative answer to the question,
showing that both steering and uncertainty relations play a fundamental role in
determining optimal quantum strategies for non-local games. Our theoretical
findings are supported by an experimental implementation with entangled
photons.
