The ignition behavior of a non-premixed multiple-burner annular combustion chamber was investigated numerically, focusing on the stochasticity and average speed of the light-round mechanism ensuring flame propagation from burner to burner that have been observed experimentally. During the propagation sequence, the flame expansion process is tracked by a previously developed stochastic low-order ignition model adapted to full combustor ignition. A stochastic model based on the probability that a flame fragment coming from an ignited burner leads to successful ignition of the next un-ignited one is developed in order to explain and quantify the global ignition behavior of the combustor. The stochastic behavior of the rig, highlighted through the experimentally observed variability of the burner-to-burner propagation times during the ignition sequence, was clarified and quantified. The lean light-round ignition limiting conditions and the mean light-round speed measured experimentally are explained and reasonably accurately predicted, demonstrating the validity of the use of the probabilistic model together with the low-order ignition model for the combustor considered. The results presented in this paper can be used to predict the ignition envelope of annular gas turbines combustors at the design stage.