  We consider cyclic Lotka-Volterra models with three and four strategies where
at every interaction agents play a strategy using a time-dependent probability
distribution. Agents learn from a loss by reducing the probability to play a
losing strategy at the next interaction. For that, an agent is described as an
urn containing $\beta$ balls of three respectively four types where after a
loss one of the balls corresponding to the losing strategy is replaced by a
ball representing the winning strategy. Using both mean-field rate equations
and numerical simulations, we investigate a range of quantities that allow us
to characterize the properties of these cyclic models with time-dependent
probability distributions. For the three-strategy case in a spatial setting we
observe a transition from neutrally stable to stable when changing the level of
discretization of the probability distribution. For large values of $\beta$,
yielding a good approximation to a continuous distribution, spatially
synchronized temporal oscillations dominate the system. For the four-strategy
game the system is always neutrally stable, but different regimes emerge,
depending on the size of the system and the level of discretization.
