hold even under fairness assumptions. However, FLP does not state that consensus can never be reached: merely that under the model's assumptions, no algorithm can always reach consensus in bounded time. In practice it is highly unlikely to occur. Some consensus protocols The Paxos consensus algorithm by Leslie Lamport, and variants of it such as Raft, are used pervasively in widely deployed distributed and cloud computing systems. These algorithms are typically synchronous, dependent on an elected leader to make progress, and tolerate only crashes and not Byzantine failures. An example of a polynomial time binary consensus protocol that tolerates Byzantine failures is the Phase King algorithm by Garay and Berman. The algorithm solves consensus in a synchronous message passing model with n processes and up to f failures, provided n > 4f. In the phase king algorithm, there are f + 1 phases, with 2 rounds per phase. Each process keeps track of its preferred output (initially equal to the process's own input value). In the first round of each phase each process broadcasts its own preferred value to all other processes. It then receives the values from all processes and determines which value is the majority value and its count. In the second round of the phase, the process whose id matches the current phase number is designated the king of the phase. The king broadcasts the majority value it observed in the first round and serves as a tie breaker. Each process then updates its preferred value as follows. If the count of the majority value the process observed in the first round is greater than n/2 + f, the process changes its preference to that majority value; otherwise it uses the phase king's value. At the end of f + 1 phases the processes output their preferred values. Google has implemented a distributed lock service library called Chubby. Chubby maintains lock information in small files which are stored in a replicated database to achieve high availability in the face of failures. The database is implemented on top of a fault-tolerant log layer which is based on the Paxos consensus algorithm. In this scheme, Chubby clients communicate with the Paxos master in order to access/update the replicated log; i.e., read/write to the files. Many peer-to-peer online Real-time strategy games use a modified Lockstep protocol as a consensus protocol in order to manage game state between players in a