  We introduce a formal notion of masking fault-tolerance between probabilistic
transition systems based on a variant of probabilistic bisimulation (named
masking simulation). We also provide the corresponding probabilistic game
characterization. Even though these games could be infinite, we propose a
symbolic way of representing them, such that it can be decided in polynomial
time if there is a masking simulation between two probabilistic transition
systems. We use this notion of masking to quantify the level of masking
fault-tolerance exhibited by almost-sure failing systems, i.e., those systems
that eventually fail with probability 1. The level of masking fault-tolerance
of almost-sure failing systems can be calculated by solving a collection of
functional equations. We produce this metric in a setting in which the
minimizing player behaves in a strong fair way (mimicking the idea of fair
environments), and limit our study to memoryless strategies due to the infinite
nature of the game. We implemented these ideas in a prototype tool, and
performed an experimental evaluation.
