  Given entropy's central role in multiple areas of physics and science, one
important task is to develop a systematic and unifying approach to defining
entropy. Games of chance become a natural candidate for characterising the
uncertainty of a physical system, as a system's performance in gambling games
depends solely on the uncertainty of its output. In this work, we construct
families of games which induce pre-orders corresponding to majorization,
conditional majorization, and channel majorization. Finally, we provide
operational interpretations for all pre-orders, show the relevance of these
results to dynamical resource theories, and find the only asymptotically
continuous classical dynamic entropy.
