  We investigate the large-scale circulation (LSC) in a turbulent
Rayleigh-B\'enard convection flow in a cubic closed convection cell by means of
direct numerical simulations at a Rayleigh number $Ra=10^6$. The numerical
studies are conducted for single flow trajectories up to $10^5$ convective
free-fall times to obtain a sufficient sampling of the four discrete LSC
states, which can be summarized to one macrostate, and the two crossover
configurations which are taken by the flow in between for short periods. We
find that large-scale dynamics depends strongly on the Prandtl number $Pr$ of
the fluid which has values of 0.1, 0.7, and 10. Alternatively, we run an
ensemble of 3600 short-term direct numerical simulations to study the
transition probabilities between the discrete LSC states. This second approach
is also used to probe the Markov property of the dynamics. Our ensemble
analysis gave strong indication of Markovianity of the transition process from
one LSC state to another, even though the data are still accompanied by
considerable noise. It is based on the eigenvalue spectrum of the transition
probability matrix, further on the distribution of persistence times and the
joint distribution of two successive macrostate persistence times.
